This page holds fundamental concepts and methods from the arts and sciences. It’s inspired by Professor Richard Feynman's notebook of “Things I Don’t Know About”.

The basic idea is to take a field in its entirety and enquire into each of the concepts and methods that constitute it. This is in order to draw out the essential features of each domain, determine the relationships between concepts, and how they represent the natural or social world.

Scientific Method
Major Thinkers • Aristotle: systematised logic (the syllogism) and empirical natural philosophy • Ibn al-Haytham (Alhazen): an early experimental method, set out in optics • Francis Bacon: the inductive method and empiricism (Novum Organum) • René Descartes: rationalism and methodic doubt • Galileo Galilei: the controlled experiment and the mathematisation of nature • Isaac Newton: the hypothetico-deductive synthesis (“hypotheses non fingo”) • David Hume: the problem of induction • Thomas Bayes: conditional probability and Bayesian inference • John Stuart Mill: systematic methods of inductive inference • Charles Sanders Peirce: abduction and pragmatism • Karl Popper: falsifiability as the criterion of demarcation • Thomas Kuhn: paradigms and scientific revolutions • Imre Lakatos: scientific research programmes • Paul Feyerabend: epistemological anarchism (“against method”) • Carl Hempel: the deductive-nomological model of explanation • Pierre Duhem and W. V. O. Quine: underdetermination and confirmation holism • Ronald Fisher: statistical inference and the design of experiments
Reasoning and Confirmation Science as a body of properly ordered knowledge • Explanatory causes • Methods of reasoning: induction, prediction, analogy • Confirmation/Verification: proceeding from what is observed to more encompassing or general principles; opposite: proceeding from general principles to instances of principles • Inference of explanations from observations (Newton: "I frame no hypotheses") • The scientist is humble before nature; unbeholden to dogma; obeys only his eyes; pursues the truth wherever it may lead. • Hypothetico-deductive: come up with hypotheses from which true empirical consequences can be deduced • Hypothesis Testing • Induction: search for regularities among events which become laws; law of laws • Hypothetico-Deductive Method as logic of confirmation • Bayesian statistical confirmation • falsification
Bayesian Statistics Conditioning and Bayes rule: Conditional probability, Bayes’ theorem, conditional mean and variance, conditional entropy and chain rules, complete data log-likelihood, observed data log-likelihood, learning unobservable states using Bayes theorem • Principles of Bayesian learning: Prior and posterior probabilities and densities over parameters, marginal likelihood, sequential updates, summaries of posterior distributions and credible intervals, Bayesian and frequentist interpretation of probability. • Standard models: Beta-binomial model (for a proportion), normal-normal model (for the mean), inverse-gamma-normal model (for the variance), properties of Bayesian learning. • Bayesian model comparison: Log-marginal likelihood as penalised likelihood, model complexity, Bayes factor, Schwarz approximation and Bayesian Information Criterion (BIC), Bayesian testing using false discovery rate. • Choosing priors and optimality properties: default priors, uninformative priors, empirical Bayes, shrinkage estimation, James-Stein estimator, Frequentist properties of Bayesian estimators, optimality of Bayes inference (e.g. Cox theorem).
Probability Theory Probability space: sample space and counting principles; events and probability • Conditional probability and independence • Discrete and continuous random variables; joint distributions • Expectation; variance of a random variable • Classical distributions: Binomial, Geometric, Poisson, Normal and Exponential distributions • Probability theory: central limit theorem; law of large numbers • Multivariate random variables • Bivariate distributions • Independence (origins in Brownian motion?) • Multivariate random variables; Bivariate Distributions; Independence; Sums of several variables; Conditional distributions; the bivariate transform. • Expectation; Expectation of a univariate random variable; Variance and higher Moments; Expectation of a bivariate random variable and conditional expectation; Probability generating functions; Moment generating functions; Sums of random variables using generating functions • Sampling and convergence; The sample mean; Chebyshev's Inequality; Poisson Limit Theorem and characteristic functions; Introduction to the multivariate normal distribution • Likelihood: Entropy foundations: Shannon and differential entropy, cross-entropy, Kullback-Leibler (KL) divergence, expected Fisher information, minimum KL divergence and maximum likelihood • Likelihood-based estimation: Likelihood function, regular models, score function, maximum likelihood estimators (MLE), invariance principle, relationship to ordinary least-squares estimation (OLS), observed Fisher information • Quadratic approximation and normal asymptotics: Quadratic approximation of log-likelihood function and normal distribution, quantifying the uncertainty of MLEs using Fisher information, (squared) Wald statistic, normal confidence intervals, non-regular models • Likelihood-based inference: Likelihood-based confidence interval, Wilks log-likelihood ratio statistic, likelihood ratio test, generalised likelihood ratio test, optimality properties
Multi-valued Logic Mamdani rule • Fuzzification; defuzzification • Fuzzy sets • Neuro-Fuzzy • Basic fuzzy logic; probability logic

Mathematics
Major Thinkers • Euclid: systematised geometry in the Elements, establishing the axiomatic method • Archimedes: anticipated the integral calculus and made profound advances in geometry and mechanics • Al-Khwarizmi: a founder of algebra, whose name gives us the word “algorithm” • Pierre de Fermat and Blaise Pascal: founders of probability theory and modern number theory • René Descartes: analytic geometry, uniting algebra and geometry through coordinates • Isaac Newton and Gottfried Wilhelm Leibniz: the independent invention of the calculus • Leonhard Euler: prolific founder of much of modern analysis, graph theory and mathematical notation • Carl Friedrich Gauss: deep contributions across number theory, algebra, geometry and statistics • Augustin-Louis Cauchy: placed analysis on a rigorous footing and founded complex analysis • Bernhard Riemann: reshaped analysis, geometry and number theory (Riemannian geometry, the Riemann hypothesis) • Évariste Galois: founded group theory and Galois theory • Georg Cantor: created set theory and the mathematics of infinity • David Hilbert: champion of formalism and foundations, and author of a famous list of open problems • Henri Poincaré: founder of algebraic topology and an originator of chaos theory • Emmy Noether: a founder of modern abstract algebra • Kurt Gödel: the incompleteness theorems • Andrey Kolmogorov: the axiomatic foundations of probability theory • Srinivasa Ramanujan: extraordinary results in number theory and analysis
Foundations, Logic & Set Theory • Mathematical logic: propositional and predicate (first-order) logic; quantifiers; formal proof; soundness and completeness • Set theory: sets, relations and functions; cardinality and countability; Cantor’s theorem; the continuum • Axiomatic foundations: the Zermelo-Fraenkel axioms; the axiom of choice; Russell’s paradox • Methods of proof: direct proof, contradiction, contraposition, induction and strong induction • Gödel’s incompleteness theorems and the limits of formal systems • Computability and decidability • Ordinals, cardinals and the well-ordering principle • The foundational schools: logicism, formalism and intuitionism
Number Theory • Divisibility and the Euclidean algorithm • Prime numbers; the fundamental theorem of arithmetic; the infinitude of primes • Modular arithmetic and congruences; the Chinese remainder theorem • Fermat’s little theorem and Euler’s theorem; the totient function • Diophantine equations • Quadratic reciprocity • The distribution of primes and the prime number theorem • Continued fractions • Introduction to algebraic and analytic number theory • Famous problems: Fermat’s Last Theorem, the Goldbach conjecture and the Riemann hypothesis
Combinatorics • Counting principles: the rules of sum and product; permutations and combinations • The pigeonhole principle • Binomial and multinomial coefficients; Pascal’s triangle • Inclusion-exclusion • Recurrence relations and generating functions • Graph theory: paths, cycles, trees, connectivity, colouring, matchings and planarity • Ramsey theory • Design theory and combinatorial structures • Extremal and enumerative combinatorics
Linear Algebra • Vectors and vector spaces; subspaces, span, linear independence, basis and dimension • Matrices and matrix algebra; rank and nullity • Systems of linear equations; Gaussian elimination • Determinants • Linear transformations and their matrix representations • Eigenvalues, eigenvectors and diagonalisation • Inner product spaces; orthogonality; the Gram-Schmidt process • The spectral theorem • Singular value decomposition • Bilinear and quadratic forms
Abstract Algebra • Groups: subgroups, cosets, Lagrange’s theorem, homomorphisms, normal subgroups and quotient groups; cyclic, symmetric and permutation groups • Group actions and the orbit-stabiliser theorem • Rings, integral domains and fields • Ideals and quotient rings; polynomial rings • Field extensions and finite fields • Galois theory: the link between field extensions and group symmetry; the insolvability of the quintic • Modules • An introduction to category theory
Real Analysis • The real numbers; completeness; supremum and infimum • Sequences and series; convergence; Cauchy sequences • Limits and continuity; the intermediate and extreme value theorems • Differentiation; the mean value theorem; Taylor’s theorem • Riemann integration; the fundamental theorem of calculus • Sequences and series of functions; uniform convergence; power series • Metric spaces; open and closed sets; compactness and connectedness • Introduction to measure theory and the Lebesgue integral • Multivariable calculus: partial derivatives, the gradient, multiple integrals and the theorems of Green, Stokes and Gauss
Complex Analysis • Complex numbers and the complex plane • Analytic (holomorphic) functions; the Cauchy-Riemann equations • Complex integration; Cauchy’s theorem and integral formula • Taylor and Laurent expansions • Singularities, poles and the residue theorem • Conformal mappings • The argument principle; Liouville’s theorem; the fundamental theorem of algebra • Analytic continuation
Topology • Topological spaces; open and closed sets; bases and subspaces • Continuity, homeomorphism and topological invariants • Compactness and connectedness • Separation axioms and Hausdorff spaces • Metric spaces and completeness • The fundamental group and covering spaces • Homotopy and homology (algebraic topology) • Surfaces and manifolds; the classification of surfaces; the Euler characteristic
Geometry • Euclidean geometry and the parallel postulate • Non-Euclidean geometries: hyperbolic and elliptic • Analytic (coordinate) geometry • Projective geometry • Transformations, symmetry and groups (the Erlangen programme) • Differential geometry: curves and surfaces; curvature; geodesics • Riemannian geometry and manifolds • Tensors and the geometry underlying general relativity
Differential Equations • Ordinary differential equations: first-order separable, linear and exact equations • Second- and higher-order linear equations; homogeneous and particular solutions • Systems of differential equations; phase-plane analysis and stability • Series solutions and special functions (Bessel, Legendre) • Laplace and Fourier transforms • Partial differential equations: the heat, wave and Laplace equations • Boundary value problems; separation of variables; Fourier series • Sturm-Liouville theory • Nonlinear dynamics and chaos
Probability & Measure Theory • Probability spaces; sigma-algebras; measures • Random variables and distributions • Expectation as an integral; the Lebesgue integral • Independence and conditional expectation • Modes of convergence; the laws of large numbers; the central limit theorem • Characteristic functions • Markov chains and stochastic processes • Martingales • Brownian motion and an introduction to stochastic calculus
Numerical Analysis • Floating-point arithmetic, error and conditioning • Root-finding: bisection, Newton’s method and fixed-point iteration • Interpolation and approximation; splines; least squares • Numerical differentiation and integration (quadrature) • Numerical linear algebra: LU, QR and singular value decompositions; iterative methods; eigenvalue computation • Numerical solution of ordinary and partial differential equations; finite-difference and finite-element methods • Stability, convergence and the computational cost of algorithms

Physics
Major Thinkers • Galileo Galilei: kinematics, inertia and telescopic astronomy • Isaac Newton: the laws of motion, universal gravitation and the calculus • Michael Faraday: electromagnetic induction and the field concept • James Clerk Maxwell: the electromagnetic theory of light • Ludwig Boltzmann: statistical mechanics and the kinetic theory • Max Planck: the quantum hypothesis • Albert Einstein: special and general relativity and the photoelectric effect • Niels Bohr: the quantum atom and complementarity • Werner Heisenberg: matrix mechanics and the uncertainty principle • Erwin Schrödinger: wave mechanics • Paul Dirac: relativistic quantum mechanics and the prediction of antimatter • Marie Curie: radioactivity • Enrico Fermi: quantum statistics and nuclear physics • Emmy Noether: the link between symmetry and conservation laws • Richard Feynman: quantum electrodynamics and the path-integral formulation
Dynamics • frame of reference and coordinate Systems
• newton's laws • energy, work, power, momentum, force, impulse, angular velocity, angular acceleration, torque
• conservation of energy, momentum, and angular Momentum
• rotation of rigid bodies
• motion in a gravitational field
• motion in 2d and 3d; Position, velocity and acceleration as vectors; simple vector calculus.
• Description of motion using polar coordinates
• Reference frames, relative velocity, change of frame.
• Newton I, II and III; application to circular motion.
• Static and Dynamic Friction (also, motion in a vertical circle).
• Work energy theorem, centre of mass, reduced mass.
• Forms of potential energy and their application
• momentum and its conversation; elastic and inelastic collisions
• ridig body rotation; vector product; moments of inertia; torque (Newton II)
• Rolling without slippage; combination of rotation and translation; angular momentum; vector form
• Gravitation; Newton's law of gravitation; Kepler's laws of planetary motion; gravitational potential energy; spherical mass energy; tidal forces
Quantum Physics and Relativity • galilean relativity
• inertial frame of reference
• concept of the observer
• principles of special relativity; derivation of time dilation and length contraction
• Lorentz transformation formula
• relativistic energy and momentum
• spacetime and four-vectors
• wave-particle duality
• uncertainty principle and the de broglie relation
• quantum wave-function of a particle moving in one dimension; momentum operator; time-independent schrodinger equation; infinite square well
• Bohr formula for energies and wavelengths of atomic hydrogen
• velocity transformations; doppler effect
• properties of atoms and molecules; atomic units; avogadro's number
• wave function and role of probability
• energy spectra and lifetimes
• advanced topics; time-dependent schrodinger equation and time evolution; commutators and compatibility; operators and quauntum states; commutation relations; compatibility of different observables; the harmonic oscillator; stationary states, vibrational states of a diatomic molecule; orbital angular momentum; particle in two dimensions (eigenfunctions and eigenvalues); particle in three dimensions; rotational states of a diatomic molecule
Astrophysics and Cosmology • common astronomical units • physics of detectors, telescopes, geometric optics • astronomical distance measurement • global properties and evolution of stars • structure of galaxies • fundamental constituents of the universe: baryons, dark matter, dark energy and observational evidence • evidence for the big bang; evolution of the universe • derive properties of the universe from the equations of the evolution of the universe • scale and contents of the universe; gravity; pressure; radiation • electromagnetic spectrum; geometrical optics; resolving power; diffraction limit; types of detectors; gravitational waves • parallax measurement; standard candles • blackbody radiation; planck; Stefan-Boltzmann and Wien laws, effective temperature, interstellar reddening); hydrogen spectral lines and Doppler effect); Hertzprung-Russell diagram; Freefall and Kelvin-Helmholtz time; nuclear fusion; basic stellar structure (hydrostatic equilibrium, equation of state); white dwarfs, neutron stars, and black holes • extrasolar planet detection methods • star formation; interstellar medium; stellar populations; galaxy rotation curves; mass and dark matter; galaxy collisions; central engines • Olber's paradox; hubble's law; age of the universe; evolution of the universe; Madau diagram; evidence for the big bang (blackbody radiation, nucleosynthesis); dark energy and its relation to the acceleration of the universe • Part Two: Stars and Stellar Evolution • Physics of stellar structure • observerd properties of stars; measurement of stellar distances; luminosity; temperature; masses and radii; Hertzprung-Russell diagram • Equations of stellar structure: time scales; mass conversation; hydrostatic equilibrium; energy transport; virial theoreom; radiative transport and convection • Equations of State; pressure as function of temperature and density for: photos; ideal gas; degenerate electron gas; mean molecular weight; ionization • Radiative transfer and opacity; rosseland mean opacity; opacity mechanisms; optical depth • nuclear fusion in stars: Energy yields; cross sections: Gamow peak; reaction rates and temperature dependence; reaction chain in stars; neutrinos • stellar modelling; limits to mass; eddington luminosity; mass-radius relations; HR diagram • Asteroseismology; Pressure and gravity waves; helioseismology • Early stellar evolution; Hayashi line; onset of nuclear burns; main sequence evolution; stellar lifetimes • Post-main sequence evolution; Isothermal cores; shell burning; degeneracy: helium flash; RGB and AGB; mass loss; white dwarfs; core collapse; supernovae; neutron stars • Formation of heavy elements • H and He burning in stars •Part Three * Galaxies Views of galaxies: Hubble and de Vaucouleurs classification schemes; the distance ladder and methods of measuring distances to Galaxies; luminosity function of galaxies; surface brightness magnitude; galaxy surveys; • The Milky Way: principal components and their kinematics; stellar mass function; rotation curve; Oort constants; mass budget and evidence for dark matter; satellite streams; galactic centre • Disk galaxies: surface brightness distribution; Tully-Fisher relation: application as a distance measurement; dynamics of disk galaxies; origin of spiral arms; properties of galactic bars • Elliptical galaxies: composition and structure: surface brightness distribution; King models and comparisons with globular clusters; the fundamental plane; black hole mass versus velocity; dispersion relation; dynamics of elliptical galaxies • Groups, clusters and Galaxy formaation: membership of galaxy groups and clusters; the Local group; methods for estimating the mass of groups and clusters; morphology versus density relation for galaxies and for clusters of galaxies; classic and modern views of galaxy formation;
Vibrations & Waves • behaviour of oscillating systems and wave motion • simple harmonic motion; energy in a vibrating system • Damped simple harmonic motion; Q values; power response curves • Forced simple harmonic motion; resonance; transients • Coupled simple harmonic motion; normal modes • 1-d wave equation • Waves at interfaces; wave energy and power; standing waves • Wave equation in 2-d and 3-d; superposition • Phase and group velocity; beats; dispersion • Interference; diffraction • Schrodinger equation; finite wells; potential steps; barriers; tunnelling
Electricity & Magnetism • electric field and potential; related concepts for stationary charges • electrostatic properties • coulomb's law; gauss's law; electric potential • magnetic field of steady currents and moving charges • Biot-Savart and Ampere's Laws • electromagnetic induction • Faraday laws • Lenz's laws • Maxwell's laws • electromagnetism as a force of nature; electric charge and its properties; vectors; fields; flux; circulation • electric fields and stationary charges; coulomb's law and superposition; electric field and potential; capacitance; electric dipoles; energy in electric fields • Magnetic fields and steady currents; Lorentz force; Biot-Savart and Ampère’s laws; magnetic dipoles • Electromotive force; electromagnetic induction; Faraday and Lenz’s laws; inductance; energy in magnetic fields. • Maxwell’s fix of Ampère’s law; Maxwell’s equations in integral form. • Advanced topics: production of electromagnetic radiation by accelerated charges; propagation of waves in dialectrics and conductors; reflection and refraction of waves; scattering of free and bound electrons; interference; diffraction; polarised light Electromagnetism: empirical laws of electromagnetism; electrostatics; magnetostatics; electromagnetic induction in a vacuum. • Dirac delta function • Laplace’s & Poisson’s equations and their uniqueness theorem • Maxwell's equation in vacuum: Continuity equation; Integral forms of Maxwell’s equations; Differential forms of Maxwell’s equations; Potential formulation; Electrostatics and magnetostatics as the time independent limit; Calculation of field configurations; Electric and magnetic dipoles; Connections between electromagnetism and special relativity. electromagnetic effects in material: Conductors: mechanisms for conduction; the method of images and the motion of particles near a conductor. Dielectrics: capacitance, relative permittivity; polarization & electric susceptibility; mechanism for polarization; electrostatics in a dielectric; Interfaces between dielectrics. Magnetism: inductance & permeability; magnetization & magnetic susceptibility; diamagnetism and paramagnetism; magnetostatics. Ferromagnetism: ideal ferromagnets; hysteresis. Electromagnetic waves: Maxwell’s equations in free space; Plane waves; Wave solutions for E & B fields; Poynting vector, irradiance & radiation pressure; Polarization of EM waves; Reflection of EM waves at a perfect conductor; EM waves in the presences of a current; EM waves in a dielectric.
Physics of Everyday Life • method of dimensions • orders of magnitude and dimensions • physical basis of atmospheric phenomena • physics of the human body; hearing and sight • physics in sport • Units, length, energy and time scales in physics; the method of dimensions; estimating; ordering of magnitude. • The Sun; the Earth’s atmosphere as an ideal gas; pressure, temperature and density; Pascal’s Law and Archimedes’ Principle; Coriolis acceleration and weather systems; Rayleigh scattering; the blue sky; the red sunset; refraction and dispersion of light; the rainbow. • The eyes as an optical instrument; vision defects; Rayleigh criterion and resolving power; sound waves and hearing; sound intensity; the decibel scale; ion transportation and cellular excitation. • The sweet spot; dynamics of rotating objects; running, jumping and pole vaulting; motion of a spinning ball; continuity and Bernoulli equations; the Magnus force; turbulence and drag. • Microwave ovens; the Lorentz force; the Global Positioning System; CCDs; lasers; displays
Random Processes • probability - what is probability? permutations and combinations; conditional probability • probability distributions; discrete random variables; expectation value and variance e.g geometric distribution; continuos random variables; probability density function; uniform distribution; normal or gaussian distribution • exponential probability distribution; probability of radiactive decay; probability of gas collisions; mean free path; generalisation - failure rate and survival probability • Poisson probability distribution; probability of occurence of n random events; properties of the Poisson distribution; Gaussian limit of the Poisson distribution • Binomial probability distribution; binomial distribution for n trals; irreversible expansion of a gas; Poisson and Gassuain limits of the binomial distribution; random walks and diffusion • parameter Estimation • maximum likelihood; extended maximum likelihood • least square; chi2; correlations • monte carlo basics • probability and confidence level • hypothesis testing • goodness of fit tests • limit setting • multivariate analysis techniques
Properties of Matter • Properties of gases, liquids, solids, plasma • Laws of thermodynamics • Entropy • Thermal equilibrium
Waves and Fields • wave problems in one diemsion • motion of a string • fourier series; orthogonality and completeness of sines and cosines; complex form of fourier Series • partial differential equations; laplace's equation; heat-flow equation • integral transforms; fourier transform; convolutions; wave packets and dispersion • eigenfunction; series solutions to differential equations; bessel functions; legendre polynomials • wave guide; normal modes of circular and spherical systems; square membrane; heat flow in circular and spherical systems; laplace's equations in cartesian and polar coordinates • dirac notation; vector spaces; ket notation; hilbet spaces; inner products and Bras
Statistical Mechanics • understanding of statistical basis of thermodynamics • connection between microscopic properties of atoms and the macroscopic properties of many-bodied systems formed by them • statistical mechanics and disorder; statistical origin of second law of Thermodynamics • indistinguishability of particles for systems of non-interacting quantum particles • Bose-Einstein condensation; origin; experimental confirmations • Fermi-Dirac distribution (white dwarf stars, blackbody radiation) • statistical theory of thermodynamics: Basic of probability theory; microstates and macrostates; the concept of ensembles; the statistical interpretation of entropy and temperature; isolated systems and the microcanonical ensemble •Statistical physics of non-isolated systems: Derivation of the Boltzmann distribution and the canonical ensemble; the independent-particle approximation; the partition function and its connection with thermodynamics; examples of non-interacting systems (paramagnet set of harmonic oscillators – quantum and classical , ideal gas, classical and quantum rotors). Equipartition theorem; Density of states. Grand-canonical ensemble and chemical potential. • Quantum gases: Fermi-Dirac and Bose-Einstein distributions. The ideal Fermi gas: Fermi energy. Electronic heat capacity. White Dwarf stars. The ideal Bose gas: Photon gas blackbody radiation (Stefan’s Law and the Planck formula). Bose-Einstein condensation.
Atmospheric Physics & Weather • Study of atmosphere and atmospheric processes that cause the weather we experience • Overview: air motion (wind); behaviour of dry and moist air (clouds and rain) • Structure and composition of atmosphere • Stratospheric zone • Ideal gas law; laws of motion; laws of thermodynamics; latent and specific heat; radiation laws • Hydrostatic equation; dry adiabatic lapse rate; Radiosondes • Dynamics: hydrostatic balance; pressure measurement; unequal heating and PGF • Sea breeze, coriolis force, friction, gradient and surface wind • Wind observations; global circulation (3 cell model) • Converge; divergence; jet stream; moist air: evaporation: saturation; condensation; humidity • Measurements of temperature and humidity; convection, satured adiabatic lapse rate • Buoyancy • Cloud classification; homogenous nucleation; aerosols, nucleation • Droplet growth; ice and the growth process; measurement of precipitation; visibility, clouds • air masses; fronts; polar front model of cyclogenesis • UK weather: cyclones and anticyclones • Principles of weather forecasting
Fluid Mechanics • Study of the motion of fluids; liquids and gases • Conservation of mass; Bernoulli's Equation • Fluids as continua; streamlines and pathlines; conservation of mass and the equation of continuity; rate of change following the fluid; conservation of momentum and the stress tensor; the constitutive equations and the Navier-Stokes equations • Conditions for viscous flow; unidirectional flows in two dimensions; Poiseuille and Couette flow; Poiseuille flow in a tube; flow down an inclined plane • Inviscid flows; Bernoulli’s equation; vorticity and its physical meaning; Kelvin’s theorem; potential flow; the stream function; irrotationnal flows in various geometries; flow around aerofoils; lift force • boundary layer theory; Prandtl’s boundary layer theory; Blasius flow; boundary layer separation • Hydrodynamic instabilities and turbulence; kolmogorov spectrum • Angular velocity in fluids • Two-dimensional flows (aircraft wing section) • Assumptions: Differences between fluids and solids; differences between liquids and gases; typical flow speeds and compressibility; fluid particles and the continuum approximation; Lagrangian and Eulerian descriptions of flow; steady flow Vector calculus: Grad, Div and Curl; Divergence Theoreom; Stoke's Theoreom Visualisation of fluid flows: Streamlines; Stagnation points; Streaklines; Particle paths • Rates of change: Material Derivate; acceleration of a fluid particle • Suffix Notation • Modelling of Forces; Pressure; Hydrostatic equilibrium; Conservation of Mass; Equations of Motion; Constitutive Equations; Boundary Conditions; • Energy and Momentum; Bernoulli's equation for steady flow and its applications • Angular velocity; vorticity and irrotational motion; Velocity potential; Laplace's equation; Bernoulli's Equation for irrotational flow • Two-dimensional motion: stream-function and vorticity in cartesian and other coordinate systems; Equipotentials and streamlines; complex potential and the complex velocity; special 2-d flows; method of images; source in a uniform stream; dipole in a uniform stream; the Circle Theoreom and examples of it; Force on a cylinder; Blasius' Theoreom; the lift on a circular cylinder with circulation; lift on an aerofoil. •
Physics of Energy Sources • forms of energy, production, transport, storage • nuclear physics and interactions with matter • sustainable chain reactions in fissile material • design criteria for the control of a nuclear reactor • principles of nuclear fusion; stellar fusion • greenhouse effect; human energy requirements; energy consumption • biological forms of enegy; fossil fuels; energy transformation in power plants; biofuels • nuclear physics; the atom; radioactivity; decay laws; interaction between radiation and matter • nuclear fission; principles of nuclear fission; chain reaction dynamics; reactor types • nuclear fusion; principles of nuclear fusion • thermonuclear fusion; fuels; ignition; Lawson criterion • magnetic and inertial confinement • stellar fusion; proton-proton chain cycle; CNO cycle • solar thermal power; solar photovoltaic power • wind, waves and tides; power from fluids; the nature of wind; wind power; wind turbines; Betz criterion; principles of water waves, energy and power; wave power extraction; origin and properties of tides; tidal stream power; tidal range power • energy transportation; hydro power
Advanced Dynamics • newton's laws of motion; linear and angular momentum; force and torque • two-body system • gravity; force fields and potentials; newtonian gravity; kepler's motion in a central force field; orbits as conic sections and kepler's laws • noninertial frames of reference; motion in rotating frames; centrifugal and coriolis forces • rigid body motion; angular velocity; angular momentum vectors; moment of inertia tensor; principal moments of inertia; Euler's equations; free rotation and stability; gyroscopes • relativistic dynamics; principles of special relativity; covariant formalism; lorentz transformations and relatistivic invariance; relativistic momentum and energy; relativistic kinematics
Physics of the Solar System • coordinates and time-keeping; date and time in the solar system • kepler's laws; energy; orbits; tides; space travel • the sun; plasma; magnetism; nuclear energy; solar neutrinos; helioseismology • planetary atmospheres; origins; pressure and temperature profiles; equilibrium temperatures; atmospheric escape; composition; clouds; climate • planetary surfaces; isotope dating • planetary interiors; Moments of inertia; seismology; volcanoes & plate tectonics; heating & cooling; magnetic fields. • planetary evolution: planetary scale processes; origins of cores, mantles, crusts (modified by volcanism and magmatism, impact cratering, and erosion • Features of the Earth
Lagrangian Dynamics • Lagrangian and Hamiltonian formulations of classical Mechanics • Variety of Dynamical problems involving more than one degree of freedom • Review of Newtonian mechanics: internal forces, external forces, forces of constraint; rotational problems and polar coordinates; conservation laws and conservative systems; partial derivatives • Lagrangian Dynamics: energy method plus other conservation laws; The Lagrangian and Lagrange's equation; small oscillations and normal modes • Calculus of Variations: functional minimization; Euler-Lagrange equations; constrained variation; Hamilton's principle of least action; • The Hamiltonian Formalism: Legendre transformations; Generalized momenta, the Hamiltonian and Hamilton's equations; Phase space; Liouville’s theorem • Symmetries and Conversation Laws: Generators of transformations; Poisson brackets; Symmetries of the Lagrangian produce constants of motion; Noether’s theorem; • Normal Modes from Matrices: mathematics of matrices; eigenvalues and eigenvectors; normal modes from symmetries; Diagonalizing a matrix using its eigenvectors; Small oscillations as eigenvalue problems; • Lagrangian for charged particle moving in electric and magnetic fields; Continuous systems: the Lagrangian Density
Photonics • Photonics as application and use of light in modern technologies • Four broad themes: properties of light; the production of light; detection of light; information encoding using light and different applications of these technologies • Nature of light and how it is manipulated: Wave descriptions (spectrum, superposition, interference effects), photon effects (photoelectric effect, momentum, interaction with matter). Characteristics of light (polarization, coherence, monochomaticity), ways to define these mathematically (Stokes parameters, Jones vectors & matrices) • How light is produced - LASER and LED; Einstein A and B coefficients, rate equations, gain and losses, optical feedback, laser threshold, 3 and 4 level lasers, cavity stability, cavity modes, Gaussian beams; The LED and laser diode, p-n junction, heterojunction and stripe geometries • Detection of light radiation; light detectors: photomutiplier tubes, photodiodes; Generic system issues: sources of noise and signal-to-noise ratio, limitations on temporal response and effective bandwidth; • Transmission and modulation techniques: delivery methods: optical fibre techniques: step index fibre; acceptance angles, single and multimode fibres, dispersion limitations, transmission characteristics. Acousto-optic and electro-optic techniques, LED switching, analogue and digital techniques using lasers, AM, FM, phase modulation techniques; • Applications: Digital communications Display systems (LCD’s, plasmas etc) Range-finding systems and applications (LIDAR etc) More exotic applications (laser trapping, laser tweezering, different forms of measurements)
Nuclear Physics • Basic concepts: Quarks, hadrons and leptons; strong, electromagnetic and weak force; Symmetries and conservation laws; Parity and charge conjugation; Feynman diagrams and exchange forces; Decay rates and scattering cross sections; Quark model for light hadrons; Parity violation in the weak interaction • Nuclei: Nuclear forces; nuclear sizes; semi-empirical mass formula; nuclear stability; alpha decay; Shell model • Particles: three generations; Flavours and flavour mixing; Quark model with three flavours; Heavy-quark hadrons; CP violation; origin of mass; phases of nuclear matter; pions and nucleons; symmetries; pion-exchange force • Nuclear reactions: resonances; compound nucleus; optical potential; direct reactions; reaction cross sections • Part Two • Applied Nuclear Physics: interaction of radiation with matter; theory and features of charged particles - bethe-bloch equation; photon interactions - photoelectric effect, Compton scattering, pair production • Neutron scattering and absorption • Attenuation and shielding • Radiation detection: Gas-filled counters - ionization chambers; proportional and geiger counters; Scintillators - properties of different phosphors; Semiconductor detectors - silicon; germanium • Biological effects of radition: tissue damage and response to radiation types; radiation dosimetry; radiobiological effects - molecular damage and repair; cell survival; human exposure and risk; • Nuclear fission: fission and nuclear structure; energy in fission; fission products, prompt and delayed neutrons - chain reaction and critical mass; thermal neutrons, neutron moderation; thermal fission reactor - neutron economy, criticality; homogenous reactors - infinite and finite reactor • Nuclear fusion; reactions and energetics; controlled fusion - magnetic confinement and inertial confinement • Applications of nuclear methods: nuclear forensics; radiometric dating; radiation diagnosis and therapies •

Chemistry
Major Thinkers • Robert Boyle: the gas laws and a corpuscular view of matter (The Sceptical Chymist) • Antoine Lavoisier: conservation of mass and the oxygen theory of combustion • John Dalton: the modern atomic theory • Amedeo Avogadro: the molecular hypothesis • Dmitri Mendeleev: the periodic table • Friedrich Wöhler: the synthesis of urea, founding organic chemistry • August Kekulé: structural theory and the structure of benzene • Svante Arrhenius: ionic dissociation and reaction-rate theory • J. J. Thomson and Ernest Rutherford: the structure of the atom • Gilbert N. Lewis: the covalent bond and electron-pair theory • Linus Pauling: the nature of the chemical bond and electronegativity • Dorothy Hodgkin: X-ray crystallography of biomolecules
Chemical Principles • Basic properties of matter: atomic theory; the periodic table; bonding; structures of molecules (structure determines molecular properties) • How matter reacts: thermodynamics; chemical equilibrium (quotient Q and constant K); solubility; acid-base; oxidation-reduction reactions; transition metals; kinetics
Energy and Change • molecular orbital approaches to chemical bonding • 1st law of thermodynamics: internal energy; heat; work; enthalpy; heat capacity • 2nd law of thermodynamics: entropy; spontaneous processes; gibbs energy; chemical potential; equilibrium constant; 3rd law of thermodynamics • Reaction kinetics: elementary reactions; rate laws; order of reaction; parallel and consecutive reactions; rate determining step; steady state approximation; Arrhenius equation • Quantum mechanics: wave-particle duality; wavefunctions; probability interpretation of wavefunctions; observables and operators; eigenvalue equations; schrodinger equation; the four exact solutions to the schrodinger equation • Molecular spectroscopy: born-oppenheimer approximation; transitions between energy levels; quantum mechanical selection rules; quantisation of energy levels for nuclear motion; pure rotational spectroscopy; harmonic oscillator; rotational and vibrational absorption spectra of small molecules; • First Law of Thermodynamics and U, q, w, ΔH; The Second Law of Thermodynamics and ΔH, ΔG, ΔS; relationship between ΔS, ΔG and K; Rate laws for 0th, 1st and 2nd order reactions; determination of reaction order, rate constants and activation energy; schrodinger equation and energy levels; particle in a box; particle on a ring; particle on a sphere; simple harmonic oscillator; born-oppenheimer approximation in simplification of molecular wavefunctions into nuclear and electronic terms; spectral parameters such as B and ω; bond lengths; fore constants from spectroscopic data
Coordination Chemistry • chemistry and physical properties of d-block compounds • chemistry of the 3d, 4d and 5d series of transition metals • structure and reactivity of coordination complexes • electronic properties of coordination complexes • features of the d-block elements; metal oxidation state; d^n configuration; translation of a coordination compound into geometric structure; bonding in coordination complexes via CF and MO theories; solution phase reactivity of co-ordination complexes; stable and unstable d^n configurations and geometries for metal ions in diff oxidation states • differences of behaviour of 3d, 4d and 5d metal ions • d^n free-ions; octahedral and tetrahedral geometries; electronic absorption spectra; magnetic measurements of coordination complexes;
Structure and Reactivity • carbonyl group chemistry; saturated carbon; alkenes; arenes • reactions at s2 centres in terms of interaction of orbitals; knowledge of structure and bonding for rationalisation of mechanism of reactions at sp2 centres; organic reactivity; orbital description of reactions; stereoelectronics • kinetics • aromaticity; reactivity of arenes
Practical Chemistry • kinetic sampling with gas burette; synthesis of inorganic complexes; IR spectroscopy; ketone reduction; distillation at atmospheric pressure; synthesis and recrystallization; multistep synthesis; kinetic sampling with titration and conductiometrics; chromatography; hydrogen spectrum emission; colour - the Beer-Lambert Law; separation and extraction of mixtures or organic compounds; acid - base titrations; resolution of racemic mixtures
Biological Chemistry • chemistry of life • comprised of analytical, organic and physical chemistry • intermediary metabolism; growth, reproduction, heredity • organic matter constitution: protein, carbohydrate, lipid • chemical changes; catalysts; enzymes • four major classes of biomolecules: carbohydrates; lipids; nucleic acids; proteins • molecular structure of biomolecules; principles of chemical reactivity • general properties of the major classes of biomolecules with reference to their molecular structure and fundamental principles of chemical reactivity • carbohydrates: monosaccharides; disaccharides; oligosaccharides; polysaccharides - naturally occurring compounds; abundant organic substances; essential constituents of all living things • Relation of properties of biomolecules to their observed functions • "carbohydrate" - watered carbon • lipids (fats, waxes, hormones, components of membranes; energy storage function; chemical messengers between cells, tissues and organs): insoluble in water - hydrophobic - some are amphipathic - diverse group; phospholipids; cholesterol; triglycerides • lipid-derived hormones: testosterone and estrogens • proteins as species and organ specific • protein structure: chains of alpha amino acids; peptide bonds • acids • bases
Physical Chemistry • electrochemistry • photochemistry • electrolysis • electroplating • catalysis • surface chemistry • thermodynamics of solutions • practical application of electrochemistry
Inorganic Chemistry • ligands • organometallic chemistry; organometallic structure • origins of s- and p-block periodic table elements • hard-soft acid base theory • Lewis acids/bases • solution speciation • valency vs. oxidation state • delocalised bonding • Wade’s rules • inorganic aromaticity • non-coordinating anions. • bonding models of d-block organometallic compounds • key electron counting methods
Organic Synthesis • study of occurrence, synthesis and behaviour of organic compounds • retrosynthetic analysis • heterocyclic chemistry • structural relationships of organic compounds • stabilised carbanions in organic synthesis • electronic structure and bonding of carbonyl containing and heteroaromatic compounds • aromatic hydrocarbon compounds • heteroaromatics: aromatic compounds where -C or -CH=CH- is replaced by a heteroatom: oxygen, nitrogen, or sulfur • reactivity of carbonyl compounds based on structure and bonding • spectroscopic methods in prediction of compounds • synthesis of heteroaromatics from carbonyl compounds • reactivity of heteroaromatics • petrochemicals • chemistry of carbonyl group; reactivity • tautomerism • deprotonation and pKa values of carbonyl compounds; structural, stereoelectronic and solvent effects • enolate anions • electrophiles • important heterocyclic compounds: natural products and drugs • electrophilic aromatic substitution; nucleophilic aromatic substitution • pyridine; pyrrole; furan; thiophene • indole; quinoline; isoquinoline; saturated heterocycles • structural relationships: cyclohexane, boat conformations, axial; equatorial bonds • Diastereoisomers, meso compounds, threo and erythro nomenclature • stereogenic centres • allenes; biaryls; restricted rotation and axial chirality • resolution of enantiomers • enantiomeric purity • Prochirality, enantiotopicity and diastereotopicity • Stereoselective reactions
Group Theory • symmetry elements (identity, proper and improper axes of rotation, mirror plane, inversion centre) • shape determines the group of a molecule • point group character tables • symmetries of degrees of freedom in molecules • complete or partial vibrational analysis; determination of molecular structure • high and low symmetry • Walsh correlation diagram • d-transition metals • ordering of ligands in spectrochemical series • symmetry considerations and distortions • projection operator • MO theory to explain chemical trends in p-block of periodic table
Organic Molecules • Study of structure and reactivity of organic molecules • bond rotation and interconversion • synthesis of cyclic molecules • reactivity, stereochemistry and stereoelectronics; examine nature of carbohydrates • synthetic route to oligosaccharides • nature of amino acids • synthesis of oligopeptides • primary and secondary structure of oligopeptides • synthons • reagents in planned synthesis
Spectroscopy • Molecular spectroscopy; chromatography; mass spectrometry; tools for chemical analysis • NMR and IR spectroscopy; mass spectrometry; chromatography • NMR spectroscopy: quantization of angular momentum; chemical shift; scalar coupling; features of NMR spectra • NMR spectra and isotopic abundance, intromolecular and intermolecular dynamics • nuclear magnetism; pulse fourier transform experiments • inversion recovery; spin echo experiments; spin-lattice and spin-spin times • multiple pulse sequences; DEPT; NOE; enhancement of chemical information • multispectral data • vibrational spectroscopy; physicochemical basis of IR spectroscopy; Raman scattering; pure-compound infrared spectra; Raman spectra • chromatography: adsorption; desorption; van Deemter A, B, C terms; sample injection; gas flow; liquid flow; eluate detection • Mass spectrometry: mass spectra - parent ions, major framents, isotopic distributions • Anhydrous and inert techniques
Environmental & Industrial Chemistry • survey of raw material or feedstock: e.g. latex, crude oil, cotton, coal, raw biomass, iron ore, plastic, air, logs, and water • key reactions and processes in chemical industries • petrochemicals; oil • organic raw material: sugars, lignin, CO2, fats, syngas • aldose to ketose conversation; transesterification, fructose dehydration to Hydroxymethylfurfural and Lignin deploymerization • oxidation and reduction in routes from hmf to furandicarboxylic acid • atmospheric processes • methods and instruments of atmospheric composition • enzymatic transformations • microporous materials: zeolites • materials and processes for desalination, wastewater treatment, biofuel production and purification, and carbon dioxide capture;
Core Chemistry Part One • understanding of synthetic and mechanistic organic chemistry • Stereoselective synthesis; ring systems; conformation analysis; Diastereoselectivity in acyclic systems; Prochirality; Reactions at C=O: Prochirality, Felkin-Anh model, Chelation control; Reactions at C=C: Houk model; Reactions of enolates: alkylation and aldol reactions, cyclic transition states; Diastereoselective reactions in synthesis: production of single enantiomers • Asymmetric synthesis; Chiral pool approaches; Chiral auxiliaries (alkylation/aldol reactions); Chiral reagents; resolution • Asymmetric catalysis; Catalysis with transition metals (asymmetric reduction of ketones); Organocatalysis (asymmetric conjugate addition) • Applications of stereoselective reactions in synthesis (fine chemicals, pharmaceuticals); • Reactive intermediates; Neutral reactive intermediates; Carbenes, Nitrenes, Arynes • Radicals: The structure of carbon-centred radicals; The relative stability of different radical species; Historical aspects of radical chemistry; Sources of radical intermediates; Radical reactions in synthesis • Pericyclic Reactions; Covalent bonding; Frontier molecular orbitals (FMOs); • The Diels-Alder [4 + 2] cycloaddition reaction; FMO interactions; Stereoselectivity and regioselectivity; Substituents effects • other cycloaddition reactions; [2 + 2] Processes ('forbidden' and 'allowed' variants); Other (4n + 2) and 4n pairings; Cycloadditions exemplified; selection rules and orbital assymetry • Electrocyclic reaction; Conservation of orbital symmetry in the ring-opening of cyclobutene; Hexatriene–cyclohexadiene • Sigmatropic rearrangements; hydrogen shifts; Sigmatropic shifts; Sigmatropic rearrangements; Cope and Claisen rearrangements
• Part Two • polymer Chemistry • Heterogenous Catalysis • F-block Chemistry • structure of polymers, composition, names, sources; • step growth polymerisation of polyesters, polyamides and high performance polymers; • chain growth polymerisation of monomers by ionic, radical, and ring-opening mechanisms • monomers • analysis of homogeneously catalysed reaction; combination of ligands, metals and conditions; mechanism of catalysed reactions; homogenous vs heterogenous catalysis • history, occurrence, synthesis, periodicity, and physicochemical properties of the f-block elements; • electronic structure, oxidation states, radii, ionisation energies, redox potentials, and chemical bonding of the f-block elements; • f-block vs rest of periodic table elements • relatistivic effect and spin orbit coupling in determination of f-block Elements • organometals vs transition metals • applications of f-block elements in technology, catalysis, nuclear power, radiochemistry industry
• Part Three • statistical Thermodynamics • potential energy surfaces • photochemistry • physical-organic chemistry • Boltzmann distribution; tools of statistical thermodynamics to predict gaseous properties; • basis of chemical reaction dynamics for small molecules in potential energy surfaces • transition-state theory • Eyring equation • intensity of absorption of light; probability of primary photophysical processes • Jablonski diagrams • photochemical processes and reactions as electronic excited states • relations between free energy, equilibrium constant and Reactivity • structure and properties of topical supramolecular materials
• Part Four • Crystallography • Single crystal x-ray diffraction • Powder x-ray diffraction • extended crystalline solids; solid structure determined by bonding and chemical composition within solid; properties as relations to structure, bonding and composition • importance of surface chemistry • bonding types; band theory; electronic conduction • metallic bonding • Defects, non-stoichiometry and ionic conduction • Simultaneous electronic and ionic conduction • Surfaces, Catalysis and Interfaces: structure and properties of solid surfaces (surface structures for elements and compounds, surface coordination numbers, adsorbates, surface reconstructions); • surface reactivity: electronic structure of surfaces, bonding to surfaces, physisorption and chemisorption, mechanisms of surface reactions, thermodynamics at surfaces; • surface kinetics: rates of adsorption and desorption, equilibrium coverage, simple isotherms, competing reactions • liquid surfaces: surface tension, adsorption & surface activity, Gibbs adsorption isotherm & surface pressure, surfactants and micelles • Heterogenous catalysis

Biology
Major Thinkers • Aristotle: the earliest systematic classification of living things • Carl Linnaeus: binomial nomenclature and taxonomy • Charles Darwin and Alfred Russel Wallace: evolution by natural selection • Gregor Mendel: the laws of inheritance • Louis Pasteur: germ theory and microbiology • Robert Hooke and Antonie van Leeuwenhoek: the cell and early microscopy • Matthias Schleiden and Theodor Schwann: cell theory • Thomas Hunt Morgan: the chromosomal theory of heredity • Rosalind Franklin, James Watson, Francis Crick and Maurice Wilkins: the structure of DNA • Ronald Fisher, J. B. S. Haldane and Sewall Wright: the modern synthesis and population genetics • Lynn Margulis: the endosymbiotic theory • E. O. Wilson: sociobiology and biodiversity
History of Biology • Development of biology • Nomenclature • Major scientists • Biological objects; topics of inquiry, key organisms, research tools • Life as an object of inquiry • human body • sex • plants • skeletons and embryos • voyages of discovery • the cell • kymograph • the pigeon, birds and animals (darwin) • the gene • behaviour (pavlov, skinner) • populations • ultracentrifuge and molecular biology • information, DNA and genomics
Biochemistry • chemical properties of molecules which make life possible; relations to macromolecular structure and function • Proteins, carbohydrates, nucleic acids, lipids, biological membranes • Mode of action of enzymes • Macromolecular complexes as protein machines • Functions of: mitochondria and chloroplasts in oxidative phosphorylation and photosynethesis • energy release in catabolism; energy storage in anabolism • chemistry of life: geometry of covalent bonds; key functional groups, linking bonds in biomolecules; non-covalent interactions; properties of water; pH and buffering • Protein structure: amino acids, primary, secondary, tertiary and quaternary structure of proteins • carbohydrates and nucleic acids: carbohydrate taxonomy; stereochemistry; ring formation; polysaccharides and glycoproteins; nucleosides, nucleotides, RNA and DNA; structure of DNA • biological membranes: types and structure of lipids; structure and properties of biological membranes; three classes of membrane proteins; membrane transport • Enzymes: thermodynamics of catalysis, types and mechanisms of enzymes, substrate binding, active site, specificity and rate of reaction, effect of temperature, pH, concentration, Michaelis-Menten, Lineweaver-Burk; enzyme inhibition: reversible, non-reversible; allosteric regulation • biochemical and biophysical method: cell disruption and separation of cell components; protein purification and detection methods, chromatography, electrophoresis, mass spectrometry, use of antibodies; introduction to protein folding, the Levinthal paradox, diseases in protein folding • metabolism and bioenergetics: metabolic pathways, catabolism, anabolism and free energy changes; concept of high energy carriers, ATP, acetyl CoA, and co-factors NAD+, NADP+, and FAD; glycolysis, the citric acid cycle, glycogen breakdown, gluconeogenesis, fatty acid metabolism, amino acid metabolism
Cell Biology • Cell types • Intracellular compartments of Eukaryotes: structure and function of membrane-bounded organelles; protein targeting; endoplasmic reticulum; secretory pathway and vesicular transport; cell membrane and endocytic pathway; molecular basis of disease resulting from defects in these processes • The cytoskeleton and cell movement: microtubules, actin filaments and intermediate filaments; Molecular motors; • Interactions between cells in multicellular systems: extracellular matrix and connective tissue; epithelia and cell junctions • Cell response to the environment: cell communication and signalling • Cycles of division and growth in cell populations: cell division; cell cycle; control of cell proliferation and differentiation; cancer; cell death
Molecular Biology • Structure, function and replication of DNA: DNA as the heritable material; structure of DNA • DNA replication: semi-conservative replication, DNA polymerases, events at the replication form, replication of the lagging strand, telomeres, consequences of defects in telomerase • Replication of genomes: origins of replication, control of DNA replication • Structure of chromosomes: DNA packaging, features of metaphase chromosomes • Gene expression: From DNA to RNA: the structure and function of the gene, promoters and terminators; Transcriptional initiation, elongation and termination; RNA polymerases • Structure, function and Biochemical properties of RNA; • From RNA to Protein: the genetic code, codons & anticodons, the ribosome & translation • Gene expression in Prokaryotes: the Lac operon; • Gene expression in Eukaryotes: regulation of transcription, promoters, enhancer elements; RNA spl; • Molecular basis of mutation: Consequences of mutation: genotype versus phenotype, molecular basis of dominant and recessive alleles, somatic versus germline mutations • Gene mutations: missense versus nonsense mutations, insertions, deletions and frameshifts; Genetic reversion and suppression • Chromosomal mutations: changes in chromosome number or structure; Consequences for fertility • Occurrence of mutations: spontaneous mutations and effects of environmental factors • Recombinant DNA Technology: Principles of Genetic Engineering: gene cloning and genomics
Animal Behaviour & Biodiversity • Animal behaviour - adaptive value of animal behaviour and its analysis • behavioural ecology • comparative evolution • biodiversity • classification of species based on behaviour • diurnal variation • social behaviour of birds and large mammals • concepts of neurobiology (e.g. learning, neuronal control of behaviour, sensory systems and communication), animal behaviour (e.g. foraging, predator prey interactions, sexual selection) and evolutionary theory (e.g. kin selection and cooperation, conflicts of interest, evolutionary strategies) • Biodiversity • Range of life on Earth; microorganisms to diversity of animal species • autotrophs; species which capture resources and energy from their environment • origins of life • first photosynthetic organisms; algae; bacteria • heterotrophs; all animals and fungi • development of body plans; • changes in the environment and evolution • key characteristics of major groups of Prokaryotes and Eukaryotes • how Eukaryotes developed from Prokaryotes • multicellular organisms from unicells • key evolutionary concepts which have led to the diversity of life; natural selection, mutation and genetic drift
Genes, Evolution & Development • Natural selection • principles of inheritance • principles of developmental biology • mechanisms of evolution: descent with modification; mutations; natural selection; genetic drift; migration; non-random mating; evidence for evolution; major transitions in the evolution of life; speciation and its mechanisms; levels of selection; sexual selection; social evolution; population genetics and genetic variation; Hardy-Weinberg equilibrium; processes which change genotype and allele frequencies; molecular and genomic evolution; human evolution • phylogenetics and phylogeography; phylogenetic trees; taxa; geographic patterns of biodiversity; • speciation and macroevolution; mechanisms of speciation; rates of speciation; extinction over time; adaptive raditions; • Co-evolution and evolution of sex; host-parasite evolution, evolution of virulence, the cost of sexual reproduction, hypotheses for the advantages of sex, why is there a 1:1 sex ratio? • comparative anatomy; homology and modification of form • Human evolution; origin of modern humans; relationship with neanderthals; global migration patterns. • Patterns and principles of inheritance: mendelian inheritance and probability; relation between Mendelism and behaviour of chromosomes during meiosis; gene interactions; sex determination and sex-linked inheritance; genetic linkage and gene mapping; maternal inheritance and organelles; genetic of complex characters and human genetics • Developmental biology: principles of animal development; egg to embryo to full body; cell fate and differentiation; mechanisms of developmental commitment and maintenance of cell differentiation; stem cells and human medicine; experimental developmental biology: model organisms and how development is studied; development and evolution; evo-devo concept • Genomic alterations: large scale chromosomal arrangements; ploidy; dosage balance; duplication events; hybrid organisms • Model systems used in genetics - yeast, plants, worms, flies etc • Different types of mutant alleles • link between genotype and phenotype variations • genetic manipulations in dissecting gene function • genetifc analysis; loss of function and gain of function • complex traits; non-mendelian phenotypes; mouse models of human disease • Alleles and genetic interactions • Fitness, Epistasis and Plasticity: genetic interactions, copy number variations, and genotype-environment interaction • Human genetics
Human Evolution • Major trends in human evolution • Evolution of bipedalism • Exploitation of terrestrial habitat • Increase of brain size and complexity • Manipulation of natural objects; motor skills for tool making • Increasing acquisition of meat protein • Humans and the animal kingdom • Vertebrate evolution • Mammalian traits and subclasses • Primate traits • Foraging societies • Evolution of monkeys and transition to apes • Early hominins • Trends; body size; limb proportions; jaws and teeth; skull, brain size, structure, and the face • early hominins and tools? • hominin divergence; pliocene hominins • pleistocene hominins • morphological evolution • transition to archaic homo sapiens; neanderthals; culture • appearance of homo sapiens; upper paleolithic • Human primate • Social carnivore • Diet, dwellings, group organisation, tool inventory, major features • aesthetic expression; cave art, sculpture, engraving • Questions and gaps in our understanding • Human status?
Body Systems • Physiology and major tissue types which form structures of the body • Homeostasis and control system; endocrine and neural control systems; autonomic nervous system and dual control • Tissue diversity: lining and covering tissues; muscle tissues; supporting tissues; haemopoietic tissues; physiology of the blood • Cardiovascular system; structure and physiology of blood vessels; anatomy of circulations; anatomy of the heart and initiation of the heart beat; energetics of circulation and cardiac cycle; control of cardiac output and blood pressure; local control of circulation; physiology of coronary and pulmonary circulations; disease • Respiratory system; anatomy of respiratory tract and lungs; anatomy and physiology of ventilation; gaseous exchange in the lungs; transport of oxygen and carbon dioxide in the blood; control of breathing; disease of the lung • Sensory Systems: comparative sensory systems; neuronal cell and circuit level analysis; integration of senses at cognitive level; chemoreception; vision; comparative aspects of colour vision • Motor Systems: muscle contractions; motor units; spinal interneurons and spinal reflexes; motor neuron diseases; proprioception and motor control; rhythmic movements; voluntary control and descending pathways; primary motor cortex; neural coding; superior colliculus; cerebellum and diseases; basal ganglia and disease; vestibular and oculomotor systems; • Excitable Cells: cells which respond to stimuli by production of electric current; organisation of the nervous system; history of neuroscience; cellular organisation of nervous system; cytosol, extracellular fluids, membranes; proteins, ion channels, pumps and transporters; diffusion, permeability and electricity; resting membrane potential; action potential; transmission and saltatory conduction; electrical synapses; chemical transmission; research techniques such as fluorescent probes and optogenetics; cellular structure of muscles; excitation-contraction coupling in muscle cells; disorders of the nervous system; neurodiversity; invertebrate learning; vertebrate learning, memory, language and the brain

Earth and Planetary Sciences
Major Thinkers • James Hutton: deep time, and the idea that the slow processes seen today shaped the deep past (uniformitarianism) • William Smith: the first geological map, ordering rock layers by their fossils • Charles Lyell: established geology as a rigorous science of gradual change • Alfred Wegener: continental drift, the forerunner of plate tectonics • Harry Hess: seafloor spreading, which showed how the plates move • Inge Lehmann: discovered the Earth’s solid inner core from earthquake waves • Milutin Milankovitch: how slow cycles in the Earth’s orbit pace the ice ages (Milankovitch cycles) • Charles Keeling: the precise record of rising atmospheric carbon dioxide (the Keeling curve)
The Earth System and Deep Time • The Earth as a set of interacting systems: the rocky interior, the surface, the oceans, the atmosphere and life (the Earth system) • The immense span of geological time, far beyond human intuition (deep time) • Reading the age of rocks and events from radioactive decay (radiometric dating; geochronology) • The flows of matter between reservoirs, such as carbon and water (biogeochemical cycles)
The Solid Earth and Plate Tectonics • The layered interior of crust, mantle and core, mapped using earthquake waves (seismology) • The unifying theory of the solid Earth: rigid plates drifting on a slowly flowing mantle (plate tectonics) • What drives them: heat from the interior stirring the mantle (mantle convection) • Where plates meet: spreading ridges, subduction zones and faults (plate boundaries) • The making and recycling of crust (seafloor spreading and subduction) • How mountains rise and rock slowly deforms (tectonic deformation)
Minerals and Rocks • Minerals: the naturally occurring crystalline building blocks of rock • The three great rock families: igneous (cooled from melt), sedimentary (laid down in layers) and metamorphic (transformed by heat and pressure) • The endless conversion among them (the rock cycle) • How rocks record the conditions under which they formed (petrology)
Surface Processes • How wind, water and ice wear down and sculpt the land (geomorphology; weathering and erosion) • The transport and laying-down of sediment that builds new rock (sedimentation) • Rivers, glaciers, coasts and deserts as shaping agents • Soil as the living interface between rock, water, air and life
The Atmosphere, Weather and Climate • The composition and layered structure of the atmosphere • Why air moves: uneven heating, pressure differences and the spinning Earth (atmospheric circulation; the Coriolis effect) • The day-to-day state (weather) versus the long-term average (climate) • How the atmosphere traps heat and keeps the planet warm (the greenhouse effect) • Natural cycles that pace the climate, from orbital wobbles to ocean patterns (Milankovitch cycles; El Niño)
The Oceans • The oceans as the planet’s great reservoir of heat, water and carbon • How currents circulate and redistribute heat around the globe (ocean circulation; the global conveyor) • Waves, tides and the mixing of the seas • The chemistry of seawater and its exchange with the atmosphere
The History of Earth and Life • Ordering the rock record into a single timeline (stratigraphy; the geological time scale) • Using fossils to date rocks and trace the history of life (palaeontology) • Great turning points: the rise of oxygen, mass extinctions and the spread of life • Reconstructing past climates from ice, sediment and rock (proxies)
Planetary Science • How the Sun and planets formed from a collapsing cloud of gas and dust (the solar nebula) • Comparing the worlds of the solar system: rocky planets, gas giants, moons, asteroids and comets • What other planets teach us about our own (comparative planetology) • The search for planets around other stars and for conditions that could support life (exoplanets; habitability)
Natural Hazards and Resources • Earthquakes, volcanoes, tsunamis, floods and landslides, and how they are forecast and mitigated • The Earth’s resources: water, soil, minerals, and fossil and renewable energy • Humanity as a geological force reshaping the planet (the Anthropocene)

Ecology and Environmental Science
Major Thinkers • Alexander von Humboldt: the interconnected view of nature and the founding of biogeography • Ernst Haeckel: who coined the word “ecology” • Arthur Tansley: the concept of the ecosystem • Charles Elton: food chains, food webs and the ecological niche • Eugene Odum: ecosystem ecology and the study of energy flow • Robert MacArthur and E. O. Wilson: the theory of island biogeography • Rachel Carson: the founder of the modern environmental movement (Silent Spring)
Foundations of Ecology • Ecology as the study of how organisms interact with one another and their environment • The nested levels of study, from the individual through populations and communities to whole ecosystems and the biosphere • The living and non-living parts of an environment (biotic and abiotic factors) • The conditions and resources that determine where a species can live (its niche; tolerance limits) • The carrying capacity of an environment: how many individuals it can sustain
Population Ecology • How the numbers of a species rise and fall over time • Unchecked growth versus growth that levels off against limits (exponential and logistic growth) • What regulates populations: birth, death, food, predators and disease • Boom-and-bust cycles, as between predators and their prey (predator-prey dynamics) • Life-history strategies: many cheap offspring versus few well-tended ones
Community Ecology • How species living together interact (competition, predation, parasitism and cooperation) • How rivals divide up resources in order to coexist (the competitive exclusion principle; niche partitioning) • Mutual benefit between species (mutualism and symbiosis) • How communities rebuild after disturbance (ecological succession) • Keystone species: those whose presence holds a whole community together
Ecosystem Ecology • How energy flows one way through an ecosystem, from sunlight through plants to animals, dwindling at each step (food chains and webs; trophic levels) • How matter, by contrast, cycles round and round (the carbon, nitrogen and water cycles) • Primary production: the capture of energy by plants that feeds everything else • Ecosystems as providers of clean air and water, pollination and fertile soil (ecosystem services)
Biodiversity and Biogeography • The variety of life, from genes through species to ecosystems (biodiversity) • Why some places teem with species and others are sparse (species richness; the latitudinal gradient) • How geography and history shape where species are found (biogeography) • How the size and isolation of a habitat set how many species it holds (island biogeography)
Evolutionary and Behavioural Ecology • How environmental pressures drive adaptation over generations (natural selection) • Why organisms behave as they do, from foraging to mating, weighed as costs and benefits • Cooperation and conflict, and why animals sometimes help their relatives (kin selection) • Species locked in shared evolution, such as flowers and their pollinators (coevolution)
Environmental Science and Human Impact • Environmental science: the interdisciplinary study of natural systems and how humans affect them • Pollution of air, water and soil, and how contaminants spread and build up in living things (bioaccumulation) • Habitat loss, fragmentation and the overuse of resources • Human population and consumption, measured as an ecological footprint • Humanity as a planet-shaping force, and the safe limits of that force (the Anthropocene; planetary boundaries)
Climate Change • How greenhouse gases trap heat and warm the planet (the greenhouse effect) • The evidence from instruments, ice cores and other records • Consequences: shifting weather, rising seas, ocean acidification and stressed ecosystems • Feedbacks and tipping points that can accelerate change • Reducing emissions and adapting to the changes already under way (mitigation and adaptation)
Conservation and Sustainability • Why species go extinct, and the current accelerated loss (the biodiversity crisis) • Protecting species and habitats (conservation biology; protected areas) • Using resources without exhausting them for the future (sustainability) • Repairing damaged ecosystems (restoration ecology) • Balancing human needs against the health of the living world

Medicine
Major Thinkers • Hippocrates: the founder of medicine as a rational discipline, separated from superstition (the Hippocratic Oath) • Galen: the anatomy and physiology that dominated for over a thousand years • Andreas Vesalius: modern anatomy from direct dissection • William Harvey: the circulation of the blood • Edward Jenner: vaccination, beginning with smallpox • Louis Pasteur and Robert Koch: the germ theory of disease • Joseph Lister: antiseptic surgery • Florence Nightingale: modern nursing and medical statistics • Alexander Fleming: penicillin and the antibiotic era
What Medicine Is • Medicine: the science and practice of preventing, diagnosing and treating disease, and of preserving health • Health and disease: the difference between normal function and its disturbance, both hard to define precisely • The clinical encounter: the meeting of doctor and patient, built on history, examination and trust • Evidence-based medicine: grounding practice in rigorous studies rather than authority (the randomised controlled trial) • Art and science: hard biology joined to judgement, communication and care for the whole person
Anatomy and Physiology • Anatomy: the structure of the body, from organs to tissues and cells • Physiology: how the body works, the function behind the structure • Homeostasis: the body’s constant self-regulation to hold its internal state steady • The body systems: cardiovascular, respiratory, nervous, digestive, endocrine, immune and musculoskeletal • Levels of organisation: molecules, cells, tissues, organs and systems
The Molecular Body • Cells: the basic unit of life and of the body, each a tiny chemical factory • Biochemistry and metabolism: the reactions that power and build the body • Genetics in medicine: how inherited DNA shapes health, disease and drug response • Molecular medicine: understanding and treating disease at the level of genes and proteins
Pathology and Disease • Pathology: the study of disease and the changes it makes in the body • Aetiology and pathogenesis: what causes a disease, and how it develops • Categories of disease: infectious, genetic, degenerative, autoimmune, metabolic and cancerous • Cancer: cells escaping the controls on growth and spreading (malignancy; metastasis) • Signs and symptoms: what the doctor observes versus what the patient feels
Microbiology and Immunology • Pathogens: the bacteria, viruses, fungi and parasites that cause infection • The germ theory: the insight that microorganisms cause many diseases • The immune system: the body’s layered defences, from barriers to antibodies and immune cells • Vaccination: training the immune system in advance to recognise a threat • Antibiotics and resistance: drugs that check bacteria, and microbes that evade them (antimicrobial resistance)
Pharmacology • Pharmacology: how drugs act on the body and the body on drugs • Pharmacodynamics: what the drug does to the body, binding to targets such as receptors • Pharmacokinetics: what the body does to the drug, its absorption, distribution, metabolism and excretion • Dose and response: the balance between too little to work and enough to harm (the therapeutic window) • Side effects and interactions: the unwanted actions of drugs, and their effects on one another
Diagnosis and Clinical Reasoning • Diagnosis: working out what is wrong, the central intellectual task of medicine • History and examination: the patient’s story and the physical exam, still the foundation • Investigations: blood tests and imaging (X-ray, ultrasound, scans) that extend the senses • Differential diagnosis: weighing the possible causes and narrowing them down • Reasoning under uncertainty: judging probabilities, since findings rarely prove a case (the sensitivity and specificity of tests)
Treatment and Surgery • Therapeutics: the means of treatment, from drugs and lifestyle to surgery and radiation • Surgery: the physical repair, removal or replacement of parts of the body • Anaesthesia: the control of pain and consciousness that made modern surgery possible • Prevention: stopping disease before it starts, often more powerful than any cure • Rehabilitation and palliative care: restoring function, and easing suffering when cure is impossible
Public Health and Epidemiology • Public health: protecting the health of whole populations, not just individuals • Epidemiology: how disease is distributed and spread, and what causes it (risk factors) • The great gains: clean water, sanitation, vaccination and nutrition, which saved more lives than any drug • Outbreaks and pandemics: how disease spreads through a population, and how it is contained • Social determinants of health: how wealth, environment and behaviour shape who gets ill
Medicine and Society • Medical ethics: the guiding principles of doing good, doing no harm, respecting autonomy and acting justly • Consent and the doctor-patient relationship • The limits and costs of medicine, and how care is rationed and delivered • The frontier: genomics, personalised medicine, and artificial intelligence in diagnosis

Psychology
Major Thinkers • Wilhelm Wundt: founder of experimental psychology and the first psychology laboratory • William James: functionalism and the study of consciousness (The Principles of Psychology) • Sigmund Freud: psychoanalysis and the theory of the unconscious • Ivan Pavlov: classical conditioning • John B. Watson: the founding of behaviourism • B. F. Skinner: operant conditioning and reinforcement • Jean Piaget: the stages of cognitive development in children • Lev Vygotsky: the social and cultural basis of learning • Carl Rogers and Abraham Maslow: humanistic psychology and the hierarchy of needs • Carl Jung: analytical psychology and the collective unconscious • Kurt Lewin: a founder of modern social psychology • Solomon Asch: conformity • Stanley Milgram: obedience to authority • Albert Bandura: social learning and self-efficacy • Ulric Neisser: a founder of cognitive psychology • Daniel Kahneman and Amos Tversky: heuristics and biases in judgement • Elizabeth Loftus: the reconstructive nature of memory • Aaron Beck: cognitive therapy
Approaches & History of Psychology • Psychology as the scientific study of mind and behaviour • Structuralism: analysing the mind into its basic elements through introspection • Functionalism: studying the purpose of mental processes • Psychoanalysis: the influence of unconscious drives and early experience • Behaviourism: the study of observable behaviour and learning • Humanistic psychology: free will, growth and self-actualisation • The cognitive revolution: the mind as an information processor • Biological psychology: behaviour explained through the brain and nervous system • Evolutionary psychology: behaviour shaped by natural selection • The sociocultural approach: the role of culture and social context • Levels of explanation and the nature-nurture debate
Biological Psychology & Neuroscience • The neuron: structure, the action potential and synaptic transmission • Neurotransmitters and their effects • The central and peripheral nervous systems • The structure of the brain: brainstem, cerebellum, limbic system and cerebral cortex • Localisation of function and brain plasticity • Methods: lesions, EEG and brain imaging (fMRI, PET) • The endocrine system and hormones • The autonomic nervous system and the stress response • Genetics and behaviour; heritability • Biological rhythms and sleep
Sensation & Perception • The distinction between sensation and perception • Psychophysics: absolute and difference thresholds; signal detection theory • Vision: the eye, the retina and visual processing • Hearing: the ear and auditory processing • The other senses: touch, taste, smell and the body senses • Bottom-up and top-down processing • Perceptual organisation: the Gestalt principles • Depth, motion and perceptual constancy • Perceptual set and the role of expectation • Visual illusions
Cognitive Psychology • Attention: selective, divided and the limits of processing • Memory: sensory, short-term (working) and long-term memory • Encoding, storage, retrieval and forgetting • The reconstructive nature of memory and false memory • Knowledge representation: concepts, categories and schemas • Language: structure, comprehension and production • Thinking and reasoning • Problem-solving and expertise • Judgement and decision-making; heuristics and biases • The information-processing approach and cognitive models
Learning & Behaviour • Classical conditioning: the association of stimuli (Pavlov) • Acquisition, extinction, spontaneous recovery, generalisation and discrimination • Operant conditioning: behaviour shaped by its consequences (Thorndike, Skinner) • Reinforcement and punishment, positive and negative • Schedules of reinforcement • Shaping and chaining • Observational and social learning (Bandura) • Cognitive aspects of learning and latent learning • Biological constraints on learning
Developmental Psychology • Development across the lifespan • Nature and nurture in development • Prenatal development and infancy • Piaget’s stages of cognitive development • Vygotsky and the zone of proximal development • Attachment theory (Bowlby, Ainsworth) and the strange situation • Language acquisition • Moral development (Kohlberg) • Social and emotional development • Adolescence and identity (Erikson); adulthood and ageing
Social Psychology • The influence of others on thought, feeling and behaviour • Attitudes, persuasion and cognitive dissonance • Conformity (Asch) and obedience (Milgram) • Group processes: social facilitation, social loafing, groupthink and polarisation • Attribution theory and attributional biases • Prejudice, stereotyping and discrimination • Prosocial behaviour and the bystander effect • Aggression • Interpersonal attraction and relationships • The self and social identity
Personality & Individual Differences • Defining and measuring personality • Psychodynamic theories (Freud, Jung) • Humanistic theories (Rogers, Maslow) • Trait theories: Eysenck and the “Big Five” (openness, conscientiousness, extraversion, agreeableness, neuroticism) • The social-cognitive approach • Intelligence: definitions and theories (general intelligence, multiple intelligences) • Psychometrics: reliability, validity and standardisation • IQ testing and its controversies • The person-situation debate
Emotion & Motivation • Theories of emotion: James-Lange, Cannon-Bard and the Schachter-Singer two-factor theory • The physiology and expression of emotion • The amygdala and cognitive appraisal • Theories of motivation: drives, incentives and arousal • Maslow’s hierarchy of needs • Intrinsic and extrinsic motivation • Hunger, thirst and sexual motivation • Stress, coping and well-being • Positive psychology
Abnormal Psychology & Clinical Approaches • Defining abnormality and the concept of mental disorder • Classification and diagnosis (DSM and ICD) • Models of psychopathology: biological, psychological and the biopsychosocial model • Anxiety disorders • Mood disorders: depression and bipolar disorder • Schizophrenia and psychosis • Obsessive-compulsive and trauma-related disorders • Eating disorders • Personality disorders • Neurodevelopmental and neurocognitive disorders • Treatments: psychodynamic, behavioural, cognitive-behavioural, humanistic and biological (drug) therapies
Research Methods & Statistics • The experimental method: independent and dependent variables and control • Non-experimental methods: observation, surveys, correlation and case studies • Sampling and generalisation • Reliability and validity • Operationalisation and measurement • Ethics in research: informed consent and debriefing • Descriptive statistics: measures of central tendency and dispersion • Inferential statistics: hypothesis testing, significance and p-values • Correlation and regression • The replication crisis and open science

Sociology
Major Thinkers • Auguste Comte: who coined “sociology” and championed a science of society (positivism) • Karl Marx: class, capital and social conflict • Émile Durkheim: social facts, solidarity and the founding of sociological method • Max Weber: social action, authority, bureaucracy and the Protestant ethic • Georg Simmel: the forms of social interaction • W. E. B. Du Bois: race and “double consciousness” • Erving Goffman: the dramaturgy of everyday life • Pierre Bourdieu: habitus, cultural capital and social fields
What Sociology Is • Sociology: the systematic study of society, of human social life, groups and institutions • The sociological imagination: seeing how personal lives are shaped by larger social forces and history • The core insight: that much of what feels natural or individual is in fact socially produced • Structure and agency: the tension between society shaping us and us shaping society • The levels: from face-to-face interaction (micro) to whole societies (macro)
Foundational Theories • Functionalism: society as a system of interlocking parts, each serving the whole (Durkheim) • Conflict theory: society as an arena of struggle over power and resources (Marx) • Symbolic interactionism: society built from the meanings people create in everyday interaction • Social facts: patterns and forces that exist beyond any individual and constrain them (Durkheim) • Verstehen: understanding social action by grasping the meaning actors give it (Weber)
Social Structure • Social structure: the durable patterns that organise social life • Status and role: the positions people hold and the behaviour expected of them • Norms and values: the shared rules and ideals that guide conduct • Institutions: the established ways of meeting social needs (family, religion, education, the economy, the state) • Networks: the webs of relationships connecting people and groups
Culture and Socialisation • Culture: the shared beliefs, values, symbols, language and practices of a group • Socialisation: how people learn the culture and become members of society • Norms, taboos and rituals: the rules and ceremonies that bind a group • Subcultures and cultural change: variation within a society, and how culture shifts • Cultural capital: the tastes, knowledge and manners that confer social advantage (Bourdieu)
Inequality and Stratification • Social stratification: the layered ranking of people by wealth, power and prestige • Class: position in the economic order, and its grip on life chances • Race and ethnicity: socially constructed divisions with real, unequal consequences (Du Bois) • Gender: the social roles and inequalities built on sex • Mobility: whether and how people move between social positions
Order, Deviance and the Self • Bureaucracy: the large, rule-bound organisations that run modern life (Weber) • Social order: how societies hold together and secure cooperation • Deviance: behaviour that breaks norms, and how norms are made and enforced • Labelling: how being named deviant can shape identity and behaviour • The self as social: identity formed through interaction and the dramaturgy of everyday life (the looking-glass self; Goffman)
Social Change • Modernity: the transformation from traditional to industrial, urban society • Globalisation: the deepening connection of the world’s societies and economies • Social movements: how collective action drives, or resists, change • Technology and society: how new tools reshape social life
Methods in Sociology • Studying society with evidence: surveys, interviews, observation and statistics • Quantitative and qualitative: measuring patterns versus understanding meanings • The challenge of objectivity, when the researcher is part of what is studied • Correlation and cause in the social world (the difficulty of causal inference)

Economics
Major Thinkers • Adam Smith: founder of modern economics; the division of labour and the “invisible hand” of markets (The Wealth of Nations) • David Ricardo: comparative advantage and the theory of rent • Thomas Malthus: population growth and its limits • Karl Marx: the labour theory of value and a critique of capitalism • Alfred Marshall: supply and demand, marginal analysis and partial equilibrium • Léon Walras: general equilibrium theory • Vilfredo Pareto: efficiency and welfare (Pareto optimality) • John Maynard Keynes: aggregate demand and the case for active macroeconomic policy • Friedrich Hayek: the price system as a carrier of information and a critique of central planning • Milton Friedman: monetarism and the role of the money supply • Paul Samuelson: the mathematical formalisation of economics • John Nash: equilibrium in non-cooperative games • Kenneth Arrow: social choice and the impossibility theorem • Gary Becker: the economics of human behaviour • Ronald Coase: transaction costs and the theory of the firm • Daniel Kahneman: behavioural economics and judgement under uncertainty • Amartya Sen: welfare economics and the capabilities approach • Elinor Ostrom: the governance of common-pool resources
Foundations & Economic Methodology • Economics as the study of how societies allocate scarce resources among competing uses • Scarcity, choice and opportunity cost • Marginal analysis: weighing additional benefit against additional cost • Incentives and rational choice • Positive versus normative economics: what is versus what ought to be • Microeconomics versus macroeconomics • Models, assumptions and the ceteris paribus condition • Equilibrium and comparative statics • Efficiency and equity • Markets, prices and the role of information
Microeconomics • Demand, supply and market equilibrium • Elasticity: price, income and cross-price • Consumer theory: utility, indifference curves, budget constraints and utility maximisation • Producer theory: production functions, costs and profit maximisation • Market structures: perfect competition, monopoly, monopolistic competition and oligopoly • Marginal revenue and marginal cost • Factor markets: labour, capital and land; wages, interest and rent • Welfare economics: consumer and producer surplus; deadweight loss • Market failure: externalities, public goods, asymmetric information and market power • General equilibrium and the welfare theorems
Macroeconomics • National income accounting: gross domestic product (GDP), nominal and real • Aggregate demand and aggregate supply • Economic growth: capital accumulation, productivity and the Solow model • The business cycle: booms and recessions • Unemployment: frictional, structural and cyclical • Inflation: causes, costs and the quantity theory of money • The Phillips curve • Money, interest rates and the IS-LM framework • Fiscal policy: government spending, taxation and the multiplier • Monetary policy and central banking • Consumption, saving and investment • Open-economy macroeconomics: exchange rates and the balance of payments
Game Theory & Strategic Interaction • Strategic interaction among rational agents • Players, strategies and payoffs • Dominant and dominated strategies • Nash equilibrium • The prisoner’s dilemma and the tragedy of the commons • Pure and mixed strategies • Sequential games, backward induction and subgame-perfect equilibrium • Repeated games and cooperation • Bargaining • Complete, incomplete and asymmetric information • Auctions and mechanism design • Signalling and screening
Behavioural & Experimental Economics • The limits of the rational-agent model; bounded rationality • Heuristics and cognitive biases • Prospect theory: the asymmetric valuation of gains and losses • Loss aversion and the endowment effect • Framing and anchoring • Time inconsistency and present bias (hyperbolic discounting) • Fairness, reciprocity and social preferences • Nudges and choice architecture • Experimental methods in economics
Public Economics & Welfare • The role of government in the economy • Public goods: non-rivalry, non-excludability and the free-rider problem • Externalities: Pigouvian taxes and the Coase theorem • Taxation: efficiency, equity, incidence and deadweight loss • Optimal taxation • Social insurance and redistribution • Cost-benefit analysis • Social choice and collective decision-making; Arrow’s impossibility theorem • Public choice theory
International Trade & Finance • The gains from trade; absolute and comparative advantage • The Heckscher-Ohlin model and factor endowments • Tariffs, quotas and trade policy • Trade agreements and globalisation • Exchange rates: fixed and floating • The balance of payments • International capital flows • Currency crises and the international monetary system
Money, Banking & Financial Economics • The functions of money and the measures of the money supply • Banks and the creation of credit; fractional-reserve banking • Central banks and the instruments of monetary policy • Interest rates and the term structure • Financial markets and institutions • Asset pricing; risk and return; the efficient-market hypothesis • Portfolio theory and diversification • The capital asset pricing model • Bubbles, crashes and financial crises
Econometrics & Quantitative Methods • The application of statistical methods to economic data • Regression analysis and ordinary least squares • The classical linear regression assumptions • Hypothesis testing and confidence intervals • Multiple regression and omitted-variable bias • Endogeneity and instrumental variables • Time-series analysis: stationarity, autocorrelation and forecasting • Panel-data methods • Causal inference: randomised experiments, difference-in-differences and regression discontinuity • The distinction between correlation and causation
Development & Growth • Measuring development: income, poverty, inequality and the Human Development Index • Theories of economic growth and convergence • Capital, technology and human capital • Institutions and the rule of law • Poverty traps • Health, education and development • Foreign aid and microfinance • The capabilities approach • Structural transformation and industrialisation
Schools of Economic Thought • Classical economics: markets, free trade and the invisible hand • Marxian economics: class, labour and capital • The marginal (neoclassical) revolution: marginal utility and equilibrium • Keynesian economics: demand management and the role of the state • Monetarism: the primacy of the money supply • The Austrian school: subjectivism, the price system and the business cycle • New classical and rational-expectations economics • New Keynesian economics: sticky prices and wages • Institutional and behavioural economics • Ecological and feminist economics

Political Science
Major Thinkers • Plato and Aristotle: the first systematic study of justice, the state and the forms of government • Niccolò Machiavelli: politics as the realistic pursuit and keeping of power • Thomas Hobbes: the social contract and the case for a strong sovereign (Leviathan) • John Locke: government by consent, natural rights and limited power • Montesquieu: the separation of powers • Jean-Jacques Rousseau: popular sovereignty and the general will • Karl Marx: politics as the expression of class and economic conflict • Max Weber: the state as the holder of legitimate force, and the study of authority and bureaucracy
Core Concepts and Political Theory • What political science studies: power, and how people are governed (politics as who gets what, when and how) • Power, authority and legitimacy: the difference between mere force and the recognised right to rule • The state: a body claiming the sole legitimate use of force within a territory (sovereignty) • The enduring questions of justice, liberty, equality and rights (political philosophy) • Why people accept being governed at all (the social contract; consent) • The major ideologies, such as liberalism, conservatism and socialism, as rival visions of the good society
Comparative Politics • Comparing political systems across countries to explain how they work and why they differ • Forms of government: democracy versus authoritarianism, and the varieties of each • How democracies are arranged: presidential versus parliamentary systems • Why states democratise, endure or break down (democratisation; state failure) • Institutions as the rules of the game that shape political behaviour (institutionalism)
Political Institutions • Constitutions: the basic rules that define and limit government • The separation of powers among the law-making, governing and judicial branches (the legislature, executive and judiciary) • How votes are turned into seats and power (electoral systems; proportional versus majoritarian) • Parties, legislatures and the machinery of representation • Federalism: dividing power between central and regional government
International Relations • How states and other actors interact in a world with no overarching ruler (anarchy in the international system) • The pursuit of power and security among states (realism) • Cooperation through trade, law and shared institutions (liberalism) • How shared ideas and identities shape what states do (constructivism) • War and peace, diplomacy, alliances and the balance of power • Problems that cross borders: trade, climate, human rights and security
Political Economy • How politics and economics shape each other • The role of the state in markets, and the politics of who gets what (distribution) • Why shared interests are hard to organise (collective action; the free-rider problem) • How institutions and policy drive prosperity or stagnation • The welfare state, regulation and development
Political Behaviour • Why and how people vote, and what shapes their choices • How public opinion forms and is measured • Parties, campaigns and the role of the media • Participation, protest and social movements • Identity, partisanship and growing polarisation
Public Policy and Administration • How governments decide what to do, and then do it (the policy cycle) • Turning decisions into action through the bureaucracy (public administration) • Weighing the costs and benefits of policies, and judging whether they work (policy evaluation) • Why well-meant policies often fail or backfire (unintended consequences)
Methods in Political Science • Studying politics systematically with evidence rather than assertion • Comparing cases, running statistical analyses, and increasingly using experiments • The challenge of establishing cause, not just correlation, in the social world (causal inference) • The trade-offs between qualitative depth and quantitative breadth

History
Major Thinkers • Herodotus: the first to gather and weigh accounts of the past as inquiry (the “father of history”) • Thucydides: rigorous, evidence-based political and military history • Sima Qian: the great historian of early China (Records of the Grand Historian) • Ibn Khaldun: the first to treat history sociologically, with cycles of cohesion and decline (the Muqaddimah; asabiyyah) • Edward Gibbon: the sweeping narrative history (The Decline and Fall of the Roman Empire) • Leopold von Ranke: the founder of modern source-based history (“how it actually was”) • Karl Marx: the view that economic forces and class conflict drive history (historical materialism) • Marc Bloch, Lucien Febvre and Fernand Braudel: deep social and economic structures over the long term (the Annales school; the longue durée) • E. H. Carr and Hayden White: that history-writing is shaped by the historian and built as narrative (What Is History?)
The Nature of History • History as the disciplined study and interpretation of the human past • The crucial gap between the past itself, all that happened, and history, the always-partial accounts we build of it • The twin concerns of change and continuity over time • That history is interpretation, not mere chronicle: the same events support different accounts (the problem of objectivity) • The error of judging the past by the standards of the present (anachronism; presentism) • Understanding people of the past on their own terms (historical empathy)
Sources and Evidence • The raw materials of history: anything that survives from the past (sources) • First-hand traces from the time studied versus later accounts about it (primary versus secondary sources) • Not only written records, but objects, images, buildings, landscapes and spoken testimony (material and oral sources) • Weighing a source’s reliability, bias, purpose and authenticity (source criticism) • Where the records are kept and how they are found (archives) • The silences in the record: whose voices were never written down (bias and gaps in the archive)
Historical Method • How historians work: from a question, through evidence, to a reasoned argument • Framing historical questions and forming interpretations to be tested against the evidence • Cross-checking independent sources against one another (corroboration) • Building an argument and citing the evidence behind every claim • Writing history as a craft that combines narrative with analysis
Historiography • Historiography: the study of how history itself has been written, and how its interpretations shift over time • The founding of modern, source-based scientific history (Leopold von Ranke) • History driven by economic forces and class conflict (historical materialism; Marx) • The move from kings and battles to deep structures unfolding over centuries (the Annales school; the longue durée) • Recovering the lives of ordinary and marginalised people (social history, or history from below) • The recognition that every history bears the mark of its author’s own time, language and narrative choices
Causation and Explanation • The central question of why things happened, not merely what happened • Separating deep underlying causes from immediate triggers (long-term and short-term causes) • The tension between vast impersonal forces and the choices of individuals (structure versus agency) • The role of accident and the might-have-been (contingency; counterfactuals) • Resisting the trap of treating what happened as having been inevitable (hindsight bias; the teleological fallacy) • Many causes interacting, rather than any single one
Periodisation and Chronology • Chronology: placing events accurately in time, the backbone of all history • Dividing the continuous past into named eras to make it comprehensible (periodisation, such as ancient, medieval and modern) • That every such division is a useful invention rather than a natural fact, and is always debated • Dating systems and calendars across different cultures • Working at different scales of time, from a single event to the very long run
Fields of History • Political history: states, power, rulers, war and diplomacy, long the traditional core • Social history: everyday life, class, family, work and community • Economic history: trade, money, production and material life • Cultural and intellectual history: ideas, beliefs, art and ways of thinking (mentalities) • Histories of those long left out: women’s, gender, ethnic and subaltern history • Global and world history: connections and comparisons across whole regions and the planet • Environmental history: the changing relationship between people and the natural world
The Broad Sweep of Human History • Prehistory: human origins, the peopling of the world, and the farming revolution that produced settled life • The first civilisations: cities, writing and states in Mesopotamia, Egypt, the Indus, China and the Americas • The classical world and the great empires, and the founding of enduring religions and philosophies • The post-classical world: a connected Eurasia, the spread of world religions, and long-distance trade • The early modern age: global voyages and exchange, gunpowder empires, and the Scientific Revolution • The modern transformation: industrialisation, revolutions, nationalism, imperialism and the modern state • The contemporary era: the world wars, decolonisation, the Cold War, globalisation and the digital age
Memory, Heritage and the Uses of the Past • How groups remember and commemorate a shared past (collective memory) • The difference between living memory and written history • Preserving and presenting the past to the public (heritage; museums; public history) • How the past is used, and abused, to serve identity, nation and politics (myth-making and propaganda) • Contested histories: monuments, reckonings and painful pasts • Why each generation rewrites history for itself

History of Ideas
Major Thinkers • Jacob Burckhardt: a founder of cultural history (The Civilization of the Renaissance in Italy) • Arthur Lovejoy: the founder of the formal history of ideas, tracing persistent “unit-ideas” (The Great Chain of Being) • Isaiah Berlin: the history of ideas and the defence of value pluralism (The Hedgehog and the Fox) • Quentin Skinner and J. G. A. Pocock: the Cambridge School, recovering ideas in their own context and as acts of argument (contextualism) • Reinhart Koselleck: how key concepts change their meaning over time (conceptual history; Begriffsgeschichte) • Michel Foucault: the hidden systems of thought and power that set what can be known in an era (discourse; the episteme; genealogy) • Hans-Georg Gadamer: the theory of how we interpret texts from a distant world (hermeneutics) • Karl Mannheim: how thought is shaped by social position (the sociology of knowledge)
What the History of Ideas Is • The study of how ideas, concepts and systems of thought arise, change, spread and shape the world (intellectual history) • Its concern with the inner life of the past: what people believed, valued and took for granted, not only what they did • Tracing a single idea as it persists and mutates across centuries and disciplines (Arthur Lovejoy’s unit-ideas) • How it differs from philosophy, which argues for ideas, and from general history, which centres on events: this field asks where ideas came from and what they did • How the unspoken assumptions of an age frame everything thought within it (the climate of opinion; the spirit of the age)
Methods and Approaches • Reading great texts closely for their enduring arguments (the history of ideas as a canon of “great books”) • Recovering what an author was actually doing in their own context and language, rather than what later readers wish they had meant (contextualism; the Cambridge School) • Treating a text as a move in an argument of its time (ideas as speech acts) • Tracking how a single key concept, such as “revolution” or “the state”, shifts meaning across eras (conceptual history) • Uncovering the deep, often invisible frameworks that decide what can even be thought in a period (Foucault’s discourse and episteme) • The theory of interpretation itself: how we understand a text written in a vanished world (hermeneutics; the hermeneutic circle)
Central Problems • Influence: how to show that one thinker truly shaped another, and how easily links are imagined that were never there • The trap of reading present meanings back into the past (anachronism; the “mythology of doctrines”) • Reception: how an idea is transformed by those who take it up, often far from its author’s intent • Continuity versus rupture: whether thought evolves gradually or breaks sharply between eras • How far ideas drive history, and how far they merely reflect deeper social and economic forces
The Transmission of Ideas • How ideas travel: through texts, teachers, translation, correspondence and institutions • The role of translation in carrying ideas between languages and cultures • Universities, academies, salons, the printing press and, now, networks as the carriers of thought • The movement of ideas between civilisations, such as Greek thought passing through the Islamic world back to Europe • How ideas are preserved, lost and rediscovered
Recurring Great Ideas • Reason and its limits: the trust in, and the revolt against, rational thought • Progress: the modern faith that history improves, and the doubts cast upon it • Liberty, rights and the individual: the slow rise of the autonomous self • Nature: changing ideas of the natural world and the human place within it • God, the sacred and secularisation: the long argument over religion and its decline • Equality, the nation and the social order: ideas that remade the political world
Periods of Thought • The axial age: the roughly simultaneous birth of lasting religious and philosophical traditions across Eurasia • Classical philosophy: the Greek and Roman foundations of Western thought • Medieval thought: the synthesis of faith and reason (scholasticism) • Renaissance humanism: the recovery of antiquity and a new focus on the human • The Scientific Revolution: a new method and a mechanical picture of the world • The Enlightenment: reason, progress, rights and the criticism of authority • Romanticism: the reaction that prized feeling, nature, history and the particular • Modern and contemporary thought: ideology, evolution, the unconscious, and the critiques of reason itself
Allied Fields • Its close ties to philosophy, history, the history of science, literature and theology • The collective attitudes and feelings of ordinary people (the history of mentalities) • How thought is shaped by social position (the sociology of knowledge) • Cultural history and the broader study of how meaning is made

Linguistics
Major Thinkers • Pāṇini: the ancient grammarian whose formal rules for Sanskrit prefigured modern linguistics • Ferdinand de Saussure: the founder of structural linguistics; the sign, and language as a system of differences • Roman Jakobson: phonology and the functions of language • Noam Chomsky: an innate grammatical capacity and the theory of generative grammar (universal grammar) • Joseph Greenberg: language universals and typology • Edward Sapir and Benjamin Lee Whorf: the idea that language shapes thought (linguistic relativity) • William Labov: the founder of modern sociolinguistics, who studied language as it varies
The Nature of Language • Linguistics as the scientific study of language: describing how it works, not prescribing how it should be used (descriptive versus prescriptive) • The features that set human language apart, above all using finite means to make endlessly many sentences (productivity) • The link between a word and its meaning is mostly convention, not resemblance (the arbitrariness of the sign) • The levels of structure, from sound to meaning, that every language is built from • A speaker’s underlying knowledge versus their actual, error-prone speech (competence versus performance)
Phonetics and Phonology • Phonetics: the physical sounds of speech, how they are made, carried and heard (articulation and acoustics) • Phonology: how each language organises sound into a meaningful system (the phoneme, a sound that can change a word’s meaning) • How sounds shift in context and combine into syllables • Stress, tone and the melody of speech (prosody and intonation)
Morphology • How words are built from smaller meaningful pieces (the morpheme) • Roots, prefixes and suffixes, and the difference between making new words and marking grammar (derivation versus inflection) • How languages differ in how much meaning they pack into a single word (morphological typology)
Syntax • How words combine into phrases and sentences according to rules (grammar) • The idea that a sentence has a nested, hierarchical structure, not just a left-to-right string (constituent structure; the parse tree) • The capacity to embed structures within structures without limit (recursion) • The search for rules and principles shared by all languages (generative grammar; universal grammar)
Semantics and Pragmatics • Semantics: the literal meaning carried by words and sentences • How the meaning of a whole is built from the meanings of its parts (compositionality) • Pragmatics: how meaning depends on context and on what the speaker intends (implicature, what is meant beyond what is said) • Reference and sense, and the many ways language points at the world
Historical and Comparative Linguistics • How languages change over time in sound, grammar and meaning • Reconstructing ancestral languages by comparing their descendants (the comparative method; proto-languages) • Grouping languages into families with a shared ancestor (language families, such as Indo-European) • The regular ways sounds shift over centuries (sound change)
Sociolinguistics • How language varies with region, class, age and situation (variation) • Dialects, accents and the social meaning carried by how we speak • What happens when languages meet: borrowing, bilingualism, pidgins and creoles • Language, identity, power and policy, and why languages thrive or die (language endangerment)
Psycholinguistics and Language Acquisition • How the brain produces and understands language in real time • How children acquire language so fast and with so little instruction (language acquisition) • How much of language is innate versus learned (the critical period; nature versus nurture) • Where language lives in the brain, and what its disorders reveal (aphasia)
Computational Linguistics • Getting computers to process human language (natural language processing) • Modelling the patterns of language statistically from large bodies of text (corpora; language models) • Machine translation, speech recognition and text understanding • What artificial systems reveal, and conceal, about how human language works

Computer Science
Major Thinkers • Charles Babbage and Ada Lovelace: the analytical engine and the first algorithm • George Boole: Boolean algebra • Alan Turing: the Turing machine, computability and the Turing test • Alonzo Church: the lambda calculus and the Church-Turing thesis • Kurt Gödel: the incompleteness theorems • John von Neumann: the stored-program architecture • Claude Shannon: information theory • Grace Hopper: the compiler and high-level languages • John McCarthy: artificial intelligence and Lisp • Edsger Dijkstra: algorithms and structured programming • Donald Knuth: the analysis of algorithms • Tony Hoare: Quicksort and Hoare logic • Stephen Cook and Richard Karp: NP-completeness • Barbara Liskov: data abstraction • Vint Cerf, Bob Kahn and Tim Berners-Lee: the internet protocols and the World Wide Web
Theory of Computation • Models of computation; the Church-Turing thesis • Finite automata: deterministic (DFA) and non-deterministic (NFA); equivalence of DFA and NFA; epsilon-transitions • Regular languages and regular expressions; closure properties; the pumping lemma for regular languages; Myhill-Nerode theorem and the minimal automaton • Context-free grammars and context-free languages; derivations and parse trees; ambiguity; Chomsky normal form; pushdown automata; the pumping lemma for context-free languages • The Chomsky hierarchy • Turing machines: deterministic, non-deterministic, multi-tape; equivalence of variants; the universal Turing machine • Computability and decidability; recursive (decidable) versus recursively enumerable languages • The halting problem and its undecidability; diagonalisation • Reductions (mapping reductions) and proving undecidability; Rice's theorem • The lambda calculus and the equivalence of computational models
Computational Complexity • Asymptotic notation: big-O, big-Omega, big-Theta; worst-, average- and best-case analysis • Time and space complexity; the model of computation and its effect on cost • Complexity classes: P, NP, co-NP, PSPACE, EXPTIME, L and NL • Verifiers and certificates as a definition of NP • Polynomial-time (Karp) reductions • NP-completeness; the Cook-Levin theorem (SAT is NP-complete) • Canonical NP-complete problems: 3-SAT, vertex cover, clique, independent set, Hamiltonian cycle, travelling salesman, subset-sum, knapsack, graph colouring • The P versus NP question • The polynomial hierarchy • Randomised complexity classes: BPP, RP, ZPP • Counting problems and #P • Approximation algorithms; approximation ratios; hardness of approximation; the PCP theorem (overview) • Space complexity; Savitch's theorem; PSPACE-completeness
Algorithms • Algorithm correctness: loop invariants, proof by induction, pre- and post-conditions • Algorithm analysis and the master theorem for recurrences • Divide and conquer: merge sort, quicksort and its expected analysis, binary search, Strassen's matrix multiplication, the fast Fourier transform • Greedy algorithms: activity selection, Huffman coding, minimum spanning trees (Kruskal, Prim), Dijkstra's shortest-path algorithm; the exchange argument • Dynamic programming: optimal substructure and overlapping subproblems; longest common subsequence, edit distance, matrix-chain multiplication, 0/1 knapsack, Bellman-Ford, Floyd-Warshall • Graph algorithms: breadth-first and depth-first search, topological sort, strongly connected components, maximum flow and the max-flow/min-cut theorem (Ford-Fulkerson, Edmonds-Karp), bipartite matching • Amortised analysis: aggregate, accounting and potential methods • String algorithms: Knuth-Morris-Pratt, Rabin-Karp, suffix structures • Randomised algorithms; Monte Carlo and Las Vegas algorithms • Lower bounds; the Omega(n log n) bound for comparison sorting; decision trees
Data Structures • Abstract data types versus implementations • Arrays, dynamic arrays, linked lists, stacks and queues • Hash tables; hash functions; collision resolution by chaining and open addressing; load factor and rehashing; universal and perfect hashing • Trees: binary search trees; self-balancing trees (AVL, red-black); B-trees and B+ trees for external storage • Heaps and priority queues; binary heaps; binomial and Fibonacci heaps • Tries and prefix structures • Disjoint-set (union-find) with union by rank and path compression; the inverse-Ackermann bound • Augmented structures: segment trees, Fenwick (binary indexed) trees, interval trees • Skip lists and probabilistic balancing • Graph representations: adjacency lists and matrices • The relationship between the choice of data structure and the asymptotic cost of operations
Discrete Mathematics & Logic • Sets, relations and functions; equivalence relations; partial and total orders; cardinality and countability • Propositional logic; truth tables; logical equivalence; normal forms (CNF, DNF) • Predicate (first-order) logic; quantifiers; interpretations and models • Methods of proof: direct, contrapositive, contradiction, construction, mathematical induction and strong induction, structural induction • Combinatorics: the rules of sum and product, permutations and combinations, the pigeonhole principle, inclusion-exclusion, binomial coefficients, generating functions, solving recurrence relations • Graph theory: paths, cycles, connectivity, trees and spanning trees, Eulerian and Hamiltonian graphs, planarity and Euler's formula, graph colouring, matchings • Number theory: divisibility, modular arithmetic, the Euclidean algorithm, Fermat's little theorem, Euler's theorem and totient function, the Chinese remainder theorem • Boolean algebra • Formal proof systems; soundness and completeness; the notion of a decision procedure
Computer Architecture & Organisation • Digital logic: logic gates, Boolean algebra, combinational circuits (adders, multiplexers, decoders), sequential circuits, latches and flip-flops, finite state machines • Number representation: unsigned and two's-complement integers, fixed point, IEEE-754 floating point, rounding and overflow • The von Neumann model; the fetch-decode-execute cycle • Instruction set architecture; RISC versus CISC; addressing modes; assembly language • Datapath and control; single-cycle and multi-cycle implementations • Pipelining; structural, data and control hazards; forwarding, stalling and branch prediction • Instruction-level parallelism; superscalar and out-of-order execution; speculation • Memory hierarchy and the principle of locality; cache organisation (direct-mapped, set-associative, fully associative), replacement policies, write-through and write-back • Virtual memory; paging, page tables, the translation lookaside buffer • Input/output, interrupts, buses and DMA • Performance: CPI, throughput, Amdahl's law • Multicore processors and the basics of parallel architecture
Operating Systems • The role of the operating system; the kernel/user-mode boundary; system calls • Processes and threads; the process control block; context switching • CPU scheduling: first-come-first-served, shortest-job-first, round-robin, priority and multilevel feedback queues • Concurrency and synchronisation: race conditions, critical sections, atomicity; mutexes, semaphores, monitors and condition variables; the producer-consumer, readers-writers and dining-philosophers problems • Deadlock: the four necessary conditions; prevention, avoidance (banker's algorithm), detection and recovery • Memory management: contiguous allocation, paging and segmentation; page replacement (FIFO, LRU, optimal, clock); demand paging, thrashing and the working-set model • File systems: files, directories, inodes, allocation methods, journaling and consistency • I/O management and device drivers • Virtualisation and hypervisors • Protection, isolation and the basics of OS security
Programming Languages • Programming paradigms: imperative, procedural, object-oriented, functional, logic and declarative • Syntax versus semantics; concrete and abstract syntax • Semantics: operational, denotational and axiomatic; Hoare logic and program correctness • The lambda calculus (untyped and typed) as a foundation for programming languages • Type systems: static versus dynamic typing; strong versus weak typing; type checking and type inference (Hindley-Milner); polymorphism (parametric, ad hoc/overloading, subtype) • Binding, scope (lexical versus dynamic), environments and closures • Evaluation strategies: call-by-value, call-by-reference, call-by-name, lazy evaluation • Data abstraction, encapsulation, inheritance and polymorphism • Memory management and garbage collection (reference counting, mark-and-sweep, generational) • Concurrency models: shared memory, message passing, actors, communicating sequential processes • The Curry-Howard correspondence between proofs and programs
Compilers • The phases of compilation; the front-end and back-end division • Lexical analysis: tokens, regular expressions, finite automata, scanner generation • Syntax analysis (parsing): context-free grammars, derivations, parse trees and abstract syntax trees; top-down parsing (recursive descent, LL(k)); bottom-up parsing (LR, SLR, LALR); shift-reduce parsing and conflict resolution • Semantic analysis: symbol tables, scope resolution, type checking, attribute grammars • Intermediate representations: three-address code, control-flow graphs, static single assignment • Code generation: instruction selection, register allocation by graph colouring, instruction scheduling • Optimisation: constant folding and propagation, common-subexpression elimination, dead-code elimination, loop-invariant code motion, data-flow analysis • Runtime environments: activation records, the stack and heap, calling conventions • Bootstrapping and the relationship between interpreters and compilers
Computer Networks • Layered network architectures: the OSI reference model and the TCP/IP model; encapsulation • Physical layer: signals, bandwidth, encoding, modulation • Data-link layer: framing, error detection (parity, checksums, cyclic redundancy checks) and correction, flow control, sliding-window protocols; medium access control (CSMA/CD, Ethernet, ALOHA); switching and bridging • Network layer: IP addressing and subnetting, IPv4 and IPv6, the network as packet-switched; routing algorithms (distance-vector, link-state, Dijkstra and Bellman-Ford), interior and exterior routing (OSPF, BGP) • Transport layer: TCP (connection setup, reliable delivery, flow control, congestion control with slow start and additive-increase/multiplicative-decrease) and UDP • Application layer: HTTP, DNS, SMTP, the client-server and peer-to-peer models • Network performance: latency, bandwidth, throughput, the bandwidth-delay product • Network security; TLS; firewalls
Databases • The relational model: relations, tuples, attributes, keys (candidate, primary, foreign) • Relational algebra and relational calculus as query languages • SQL: data definition, queries, joins, aggregation, grouping, subqueries, views • Database design: entity-relationship modelling; functional dependencies; normalisation through first, second, third and Boyce-Codd normal forms; denormalisation trade-offs • Physical storage and indexing: heap and sorted files, B+ tree and hash indexes, clustered versus secondary indexes • Query processing and optimisation; cost estimation; join algorithms (nested-loop, sort-merge, hash join) • Transactions and the ACID properties (atomicity, consistency, isolation, durability) • Concurrency control: serialisability, two-phase locking, timestamp ordering, multiversion concurrency control, isolation levels • Crash recovery; write-ahead logging; the ARIES protocol (overview) • Distributed databases; the CAP theorem; replication and partitioning; NoSQL data models (key-value, document, column-family, graph)
Artificial Intelligence • Rational agents and the agent-environment framework • Problem solving as state-space search; uninformed search (breadth-first, depth-first, uniform-cost, iterative deepening) • Informed/heuristic search: greedy best-first, A*; admissible and consistent heuristics; optimality • Local search: hill climbing, simulated annealing, genetic algorithms • Adversarial search and games: minimax, alpha-beta pruning, evaluation functions, expectiminimax • Constraint satisfaction problems: backtracking, constraint propagation, arc consistency, heuristics • Knowledge representation and reasoning: propositional and first-order logic, inference, resolution, forward and backward chaining • Planning: STRIPS representation, state-space and plan-space planning, planning graphs • Reasoning under uncertainty: probability, Bayes' rule, Bayesian networks and inference, the Markov assumption, hidden Markov models • Sequential decision making: Markov decision processes, value and policy iteration; reinforcement learning • The frame problem and the symbol-grounding problem
Machine Learning • The learning problem: supervised, unsupervised and reinforcement learning • Generalisation, the bias-variance trade-off, overfitting and underfitting; training, validation and test sets; cross-validation; regularisation • Supervised learning: linear regression and least squares, logistic regression, the perceptron, support vector machines and kernels, k-nearest neighbours, naive Bayes, decision trees • Ensemble methods: bagging, random forests, boosting (AdaBoost, gradient boosting) • Unsupervised learning: clustering (k-means, hierarchical, Gaussian mixture models and the EM algorithm), dimensionality reduction (principal component analysis) • Optimisation for learning: gradient descent, stochastic gradient descent, momentum and adaptive methods; the loss landscape • Neural networks: the multilayer perceptron, activation functions, backpropagation; convolutional networks, recurrent networks (LSTM/GRU), attention and transformers; deep representation learning • Probabilistic and statistical foundations: maximum likelihood, maximum a posteriori estimation • Learning theory: empirical risk minimisation, VC dimension, PAC learning • Evaluation: accuracy, precision, recall, F1, ROC and AUC; confusion matrices
Cryptography & Security • Goals of security: confidentiality, integrity, availability, authentication, non-repudiation; threat models and adversaries • Classical ciphers (substitution, transposition) and why they fail; frequency analysis • Symmetric-key cryptography: stream and block ciphers, the data and advanced encryption standards (DES, AES), modes of operation (ECB, CBC, CTR, GCM); the one-time pad and perfect secrecy • Public-key cryptography: the idea of trapdoor functions; RSA and integer factorisation; Diffie-Hellman key exchange and the discrete-logarithm problem; elliptic-curve cryptography • Cryptographic hash functions: pre-image, second pre-image and collision resistance; the SHA family; the random-oracle model • Message authentication codes and digital signatures; certificates and public-key infrastructure • Key management and cryptographic protocols (TLS, key agreement) • Notions of security: computational versus information-theoretic security; provable security and reductions • Common vulnerabilities: buffer overflows, injection, side-channel attacks; defence in depth
Concurrency & Distributed Systems • Models of concurrency: shared memory versus message passing • Mutual exclusion and synchronisation primitives; atomic operations; the memory model and reordering • Logical time: the happens-before relation, Lamport clocks, vector clocks; global state and consistent snapshots (Chandy-Lamport) • Consistency models: strict, sequential, linearisability, causal and eventual consistency • The CAP theorem and the consistency-availability-partition trade-off • Consensus: the problem statement, Paxos, Raft; the FLP impossibility result • Fault tolerance: crash and Byzantine failures; Byzantine fault tolerance; the two generals problem • Replication, quorums and state-machine replication • Distributed transactions; two-phase and three-phase commit • Failure detectors; leader election; the role of timing assumptions (synchronous, asynchronous, partially synchronous)
Software Engineering • The software development lifecycle; process models (waterfall, iterative, spiral, agile and scrum) • Requirements engineering: elicitation, specification, validation; functional and non-functional requirements • Design principles: abstraction, modularity, information hiding, separation of concerns, coupling and cohesion • Object-oriented design and the SOLID principles; design patterns (creational, structural, behavioural) • Software architecture; architectural styles (layered, client-server, microservices, event-driven) • Version control and collaborative development (Git, branching and merging) • Testing: unit, integration, system and acceptance testing; test-driven development; coverage; black-box and white-box testing; mocking • Debugging, profiling and refactoring; code review; technical debt • Build systems, continuous integration and continuous delivery • Software metrics, maintainability and documentation • Formal methods and verification (overview)
Information & Coding Theory • Information as a measurable quantity; the bit; self-information and surprise • Shannon entropy; joint, conditional and relative entropy; mutual information; the chain rule • The source coding theorem; lossless data compression; Huffman coding, arithmetic coding, Lempel-Ziv • Channel models and channel capacity; the noisy-channel coding theorem • Error-detecting and error-correcting codes: parity, Hamming codes, the Hamming bound, Reed-Solomon and convolutional codes; minimum distance • Redundancy and the trade-off between rate and reliability • Kolmogorov complexity and the notion of algorithmic information • The relationship between entropy, probability and optimal code length
Computer Graphics & Vision • Raster and vector graphics; the frame buffer; colour models (RGB, CMYK, HSV) • The graphics pipeline; modelling, viewing and projection transformations • Homogeneous coordinates; affine and projective transformations; orthographic and perspective projection • Geometric primitives, meshes and parametric curves and surfaces (Bezier, B-splines) • Rasterisation: line and polygon drawing, clipping, scan conversion; hidden-surface removal and the z-buffer • Illumination and shading: the Phong reflection model, Gouraud and Phong shading, texture mapping • Ray tracing, radiosity and global illumination; physically based rendering (overview) • Image processing: sampling and aliasing, filtering and convolution, edge detection, the Fourier transform of images • Computer vision: feature detection, segmentation, stereo and depth, object recognition; the link to machine learning

Aerospace Engineering
Major Thinkers • Daniel Bernoulli: fluid dynamics and Bernoulli’s principle • Sir George Cayley: the founder of aerodynamics; the four forces of flight • Otto Lilienthal: systematic gliding experiments • Nikolai Zhukovsky: aerofoil theory and the Kutta–Joukowski theorem • Wilbur and Orville Wright: the first powered, controlled flight and three-axis control • Ludwig Prandtl: boundary-layer theory and lifting-line theory • Theodore von Kármán: supersonic aerodynamics and the vortex street • Konstantin Tsiolkovsky: the rocket equation and the theory of astronautics • Robert Goddard: the liquid-fuelled rocket • Hermann Oberth: the theory of spaceflight • Frank Whittle: the turbojet engine • Wernher von Braun: large launch-vehicle engineering
Foundational Research Questions • Turbulence (the closure problem): predicting turbulent flow from the governing equations, without empirical models, remains the outstanding unsolved problem of classical physics and caps the accuracy of aerodynamic and combustion prediction • Laminar-turbulent transition: when smooth flow trips into turbulence, and whether it can be delayed to keep wings laminar and cut drag, is still not reliably predicted (laminar-flow control) • Hypersonic flight: sustained control at many times the speed of sound couples extreme heating, chemically reacting air, uncertain transition and combustion in milliseconds (scramjet propulsion; aerothermodynamics) • Sustainable aviation: decarbonising flight despite jet fuel’s unmatched energy density, through hydrogen, sustainable fuels and hybrid-electric propulsion • The rocket equation’s tyranny: because a rocket must accelerate its own unburnt propellant, range and speed cost fuel exponentially, so affordable deep-space travel awaits far higher specific impulse (advanced propulsion) • Reusable access to space: making launch routine and cheap through full, rapid reusability, still limited by reliability, materials and economics • Trustworthy autonomy: certifying autonomous and learning-based flight systems as safe, when adaptive systems resist verification designed for predictable software • Nonlinear aeroelasticity: predicting and exploiting very flexible, morphing structures whose coupling with the airflow turns nonlinear, with flutter a constant threat • Closed-loop life support: keeping humans alive for years in deep space by fully recycling air and water and shielding against radiation, a prerequisite for Mars-class missions • Verification and validation: how far simulation can replace physical testing, and how to rigorously quantify the uncertainty in a prediction
Aerodynamics • Lift: the upward force on a wing, from deflecting air downward and lower pressure over its curved upper surface • Drag: the force resisting motion; lift divided by drag is the lift-to-drag ratio, the measure of aerodynamic efficiency • The aerofoil: the wing cross-section, its camber and angle of attack setting lift and drag • Centre of pressure and aerodynamic centre: the points at which the aerodynamic forces effectively act • Pressure and skin friction: pressure differences give most of the lift, surface friction much of the drag • The boundary layer: the thin film of slowed air at the surface; its separation causes stall • Stall: lift collapse and drag rise when the angle of attack grows too large and the flow separates • The Reynolds number: the ratio of inertial to viscous forces, predicting laminar or turbulent flow • Circulation: the swirl around an aerofoil that produces lift in ideal-flow theory (the Kutta-Joukowski theorem) • Induced drag: the drag from wingtip vortices, reduced by long, slender (high-aspect-ratio) wings • Wind-tunnel testing: measuring forces and visualising flow on scale models
Fluid Mechanics • The continuum assumption: treating a fluid as continuous matter, not discrete molecules • Fluid properties: density, pressure, viscosity (resistance to flow) and compressibility • Hydrostatics: pressure rising with depth, and buoyancy • The Navier-Stokes equations: the governing equations from conservation of mass, momentum and energy • Bernoulli’s principle: in a smooth flow, faster flow means lower pressure • Viscosity: internal fluid friction, the source of drag • Laminar and turbulent flow: orderly layered flow versus chaotic mixing flow, and the transition between • Pipe flow: friction losses and pump or turbine energy (the Moody chart) • Dimensional analysis: dimensionless groups letting a scale model stand for the full-size vehicle (similarity)
Aircraft Performance • The four forces: lift, weight, thrust and drag, whose balance sets the flight condition • The drag polar: the lift-versus-drag curve summarising aerodynamic efficiency • Thrust and power, required versus available: the margin that sets performance • The flight envelope: the speeds and altitudes within which flight is possible • Climb and ceiling: rate and angle of climb, and maximum altitude, set by spare power • Range and endurance: distance and time on a given fuel load (the Breguet range equation) • Take-off and landing: the distances and speeds to get airborne and stop • Load factor: the multiple of weight (the “g” loading) carried in a turn or manoeuvre • The V-n diagram: the chart of design speeds against structural load limits • Operating effects: how weight, altitude and configuration shift performance
Flight Dynamics • Flight dynamics: how an aircraft moves and responds to controls and disturbances • Body axes: the frame fixed to the aircraft, defining pitch, roll and yaw • Equations of motion: Newton’s laws for the aircraft as a rigid body • Static stability: the tendency to return to the original attitude after a disturbance • Trim: the control setting holding steady flight with no pilot effort • Dynamic stability: whether post-disturbance oscillations decay or grow • Longitudinal modes: the slow phugoid and the fast short-period pitch oscillation • Lateral-directional modes: the dutch roll, the spiral mode and the roll response • Stability derivatives: how forces and moments vary with motion and control inputs
High-Speed Aerodynamics and Atmospheric Re-entry • Compressibility: density changes in the air that matter at high speed • The Mach number: flight speed as a fraction of the speed of sound • Flow regimes: subsonic, transonic, supersonic and hypersonic • Shock waves: thin fronts of abrupt pressure, temperature and density rise in supersonic flow • Expansion fans: supersonic flow accelerating and its pressure falling (the Prandtl-Meyer expansion) • Wave drag: the drag rise near the speed of sound, eased by slender, swept and area-ruled shapes • Aerodynamic heating: intense surface heating as high-speed air is compressed and slowed • Atmospheric entry: shedding orbital energy as heat through a narrow entry corridor • Thermal protection: heat shields and ablative materials against entry heating
Propulsion Systems • Thrust: the reaction force from accelerating air or exhaust rearwards • Propulsive efficiency: how well fuel energy becomes thrust, trading speed against economy • The gas turbine (jet engine): compress air, burn fuel, expand through turbine and nozzle (the Brayton cycle) • Turbojet, turbofan and turboprop: engine variants trading speed for fuel economy • Propellers: rotating blades acting as wings (blade-element and momentum theory) • Ramjets and scramjets: compressor-less engines using the vehicle’s own speed to compress air • The rocket: carries its own oxidiser to work in vacuum (the rocket equation) • Specific impulse: thrust per unit of propellant, a rocket’s fuel economy • Chemical rockets: solid, liquid and hybrid motors • Electric propulsion: ion and Hall-effect thrusters, gentle but highly efficient • Advanced propulsion: nuclear-thermal, electric and hydrogen concepts
Thermodynamics and Heat Transfer • Thermodynamics: how heat, work and energy interconvert • The first and second laws: energy is conserved but disperses (entropy) • Thermodynamic cycles: the Carnot, Brayton, Rankine, Otto and Diesel cycles • Thermal efficiency: the limit on turning heat into work (the Carnot efficiency) • Heat transfer: conduction, convection and radiation • Thermal management: keeping engines, electronics and structure within temperature limits • Spacecraft thermal balance: in vacuum, heat is shed only by radiation
Aerospace Structures and Stress Analysis • The structural problem: carrying all loads at minimum weight • Stress and strain: internal force per area and the resulting deformation (Hooke’s law) • Load paths: the routes forces take through the airframe • Semi-monocoque construction: stressed skins stiffened by spars, ribs and stringers • Bending, shear and torsion: the basic structural loadings • Buckling: sudden collapse of slender members in compression (Euler buckling) • Fatigue: crack growth under repeated loading, limiting service life • Damage tolerance: fail-safe design so a crack is detectable, not catastrophic • Fracture: when a crack runs away (the Griffith criterion; the stress-intensity factor) • Composites: fibres in a matrix, analysed as layered laminates
Materials • Materials as the limit: performance is bounded by what materials withstand • Processing-structure-properties: how a material is made sets its properties • Strength versus toughness: resistance to deformation versus resistance to cracking • Elasticity and plasticity: recoverable versus permanent deformation (stiffness is Young’s modulus) • The material families: metals, ceramics, polymers and composites • Metals and alloys: strengthened by alloying and heat treatment • Fatigue and creep: failure under repeated load, and slow deformation under sustained heat and load • Fracture and defects: flaws concentrate stress and trigger failure • Polymers: long-chain materials with a glass transition and viscoelastic behaviour • Composites: strong fibres in a matrix, light but direction-dependent
Vibrations and Aeroelasticity • Vibration: oscillation that can fatigue or destroy a structure • Natural frequencies and mode shapes: a structure’s preferred rates and patterns of vibration (an eigenvalue problem) • Resonance: the dangerous build-up when forcing matches a natural frequency • Damping: the dissipation that makes oscillation decay • Modelling: lumped mass-spring systems or continuous bodies (Newton’s or Lagrange’s methods) • Aeroelasticity: the coupling of aerodynamic forces with structural flexing • Divergence: a static twisting runaway that breaks a wing • Flutter: a dynamic instability where bending and twisting couple into growing oscillation • Self-excited vibration: such as wheel shimmy and vortex-induced shaking
Control Engineering • Control engineering: making a system behave as desired despite disturbances • Open-loop versus closed-loop: a fixed plan versus measuring and correcting • Feedback: driving the system on course from the error between target and actual output • System response: transient and steady-state behaviour (the Laplace transform; transfer functions) • The proportional-integral-derivative controller: acting on present error, its history and its trend • Stability: ensuring corrections settle rather than diverge • Analysis tools: the root-locus, and Bode and Nyquist plots • Applications: autopilots, engine governing and attitude control
Electrical and Electronic Systems • Circuit quantities: charge, current, voltage and power • Components: the resistor, capacitor and inductor • Circuit laws: Ohm’s law and Kirchhoff’s laws • Direct and alternating current: steady versus oscillating supplies • Electric machines: motors and generators • Sensors: converting a physical quantity into an electrical signal • Signal conditioning: cleaning, amplifying and digitising signals • The operational amplifier: the building block for amplifying signals • Analogue and digital signals: continuous voltages versus discrete numbers
Avionics, Guidance, Navigation and Control • Flight instruments: airspeed, altitude and attitude from the pitot-static system, gyroscopes and accelerometers • The glass cockpit: electronic displays replacing dials • Inertial navigation: position from the aircraft’s own motion, accurate but drifting • Radio and satellite navigation: beacons and satellite positioning that fix location • Sensor fusion: blending sensors into one best estimate (the Kalman filter) • The flight management system: the computer that stores and flies the route • Communications: voice radio and digital data links • Surveillance and warning: traffic and terrain collision warning • Automatic flight: autopilot and autothrottle, up to automatic landing • Fly-by-wire: electronic controls with built-in envelope protection • Redundancy and certification: duplicated systems and strict safety standards
Astrodynamics and Orbital Mechanics • Orbit: continuous free-fall fast enough to keep missing the body below • The two-body problem and Kepler’s laws: elliptical orbits swept at a steady rate • Orbital elements: the numbers fixing an orbit’s size, shape and orientation • Orbit types: low Earth, geostationary, polar and Sun-synchronous • The vis-viva equation: the link between orbit size and speed • Orbital manoeuvres: the Hohmann transfer, costed in delta-v (velocity change) • Rendezvous and docking: bringing two craft together in orbit • Perturbations: small forces (the Earth’s bulge, drag, the Sun and Moon) that shift an orbit • Interplanetary trajectories: transfer paths and gravity assists • Lagrange points: balance points in a two-body gravity field • Station-keeping and disposal: holding a slot, then de-orbiting
Spacecraft Subsystems and Systems Engineering • Bus and payload: mission instruments carried by supporting subsystems • Structure and mechanisms: the frame and deployable parts • Thermal control: coatings, heaters and radiators • Electrical power: solar generation, batteries and distribution • Attitude determination and control: pointing via reaction wheels, thrusters or magnetic torquers • Communications: ground links sized by the link budget • On-board data handling: the spacecraft’s computers • The space environment: vacuum, radiation, temperature extremes and debris • Systems engineering: balancing subsystems against mission requirements
Computational Methods and Simulation • Why simulate: cheaper and faster than building and breaking hardware • Discretisation: replacing continuous equations with solvable pieces • Computational fluid dynamics: solving flow over a mesh for lift, drag and heating • Turbulence modelling: approximating turbulence too fine to compute fully • The finite element method: dividing a structure into elements for stress and vibration • Meshing: the grid of cells or elements, whose quality affects the result • Verification and validation: solving the equations right, and the right equations • Design optimisation: searching design variations for the best balance • The limits of models: only as good as their assumptions, to be checked against experiment
Aircraft and Spacecraft Design • Design as integration: balancing all disciplines into one vehicle • Design stages: conceptual, preliminary and detailed • Requirements: the mission goals that drive every choice • The design spiral: iterative refinement as choices ripple through • Sizing and weight estimation: weight drives everything • Trade studies: weighing cost, performance, weight and risk • Systems engineering: managing requirements, interfaces and verification • Reliability and safety: redundancy and failure analysis (failure modes and effects analysis) • Certification and airworthiness: the evidence required before flight • Cost, manufacturability and sustainability: buildable, affordable and responsible
Manufacturing Engineering • Casting: pouring molten metal into a mould • Forming: shaping metal by bending, pressing or rolling • Machining: cutting material to a precise shape • Joining: welding, adhesive bonding and fasteners • Polymer moulding: shaping plastics (injection moulding) • Additive manufacturing (3D printing): building parts up layer by layer • Tolerances: the precision required for parts to fit • Process selection: matching method to material, shape and quantity
Aeroacoustics and Noise • Aeroacoustics: the noise from airflow over and through a vehicle • The acoustic analogy: turbulent flow treated as a source of sound • Noise sources: jet exhaust, engine fan, airframe and rotor blades • Noise regulation: community limits near airports • Noise reduction: quieter engines, acoustic liners and modified procedures • The sonic boom: the ground shock from supersonic flight
Uncrewed and Autonomous Aerial Systems • Uncrewed aircraft: pilotless vehicles, from small drones to large types • Configurations: fixed-wing for range, multirotor for hovering, and hybrids • Low-Reynolds-number flight: stickier air at small scale, needing different wings and propellers • Power and endurance: battery, fuel, hybrid and solar trade-offs • Autopilots: stabilising and path-following without constant input • Levels of autonomy: from remote piloting to self-deciding • Sensing and perception: cameras and sensors that locate and map • Autonomous navigation: route planning and obstacle avoidance • Beyond-line-of-sight: the challenge of flying past the operator’s view • Detect-and-avoid: sensing other aircraft to share airspace safely • Swarms: many aircraft coordinating without central control • Regulation and ethics: airspace integration, privacy and safety
Human Spaceflight and Life-Support Systems • The challenge: surviving an airless vacuum of extreme temperature and radiation • Microgravity effects: bone and muscle loss and fluid shifts • Radiation: cosmic and solar radiation beyond the Earth’s magnetic field • Life-support systems: air, water, temperature and waste, ideally closed-loop • Habitats and human factors: liveable, workable crew spaces • Spacesuits: portable life-support for spacewalks (extravehicular activity) • Launch and re-entry loads: the heavy accelerations the body endures • Long-duration missions: months or years far from rescue
Engineering Mathematics • Linear algebra: vectors and matrices for systems of equations and transformations • Calculus: rates of change and accumulation • Differential equations: the language of systems evolving in time or space • Probability and statistics: handling uncertainty and data • Numerical methods: computer approximation where no formula exists

Mechanical Engineering
Major Thinkers • James Watt: the improved steam engine that drove the Industrial Revolution • Sadi Carnot: the founder of thermodynamics and the ideal heat-engine cycle (the Carnot cycle) • Rudolf Clausius and Lord Kelvin: the laws of thermodynamics and the idea of entropy • Osborne Reynolds: the transition from smooth to turbulent flow (the Reynolds number) • Stephen Timoshenko: the foundations of modern engineering mechanics and elasticity • Nikolaus Otto and Rudolf Diesel: the petrol and diesel internal-combustion engines • Frederick Taylor and Henry Ford: scientific management and the moving assembly line
Statics and Mechanics of Materials • Statics: working out the forces on a body that is not accelerating, so that everything balances (equilibrium) • Free-body diagrams: isolating a part and drawing every force acting on it, the basic tool of analysis • Stress and strain: the internal force a material carries per unit area, and how far it stretches in response, the two linked while elastic by Hooke’s law • The ways a part is loaded: stretching, compression, bending, twisting (torsion) and shear • Bending of beams: how loads create internal bending moments and shear forces along a beam (Euler-Bernoulli beam theory) • Finding the worst stress at a point when several loads combine (Mohr’s circle) • Buckling: the sudden sideways collapse of a slender column under compression (Euler buckling) • Predicting failure and designing with a margin (the factor of safety; yielding and the von Mises criterion)
Dynamics and Vibrations • Kinematics: describing motion (position, velocity and acceleration) without yet asking what causes it • Kinetics: linking forces to motion through Newton’s laws • Energy and momentum methods: shortcuts that analyse motion without tracking every force (conservation of energy and momentum) • Rotation: how the spread of mass resists changes in spin (the moment of inertia) • Vibration: how a disturbed system oscillates, its natural frequencies, and the danger when forcing matches them (resonance) • Damping and forced vibration: how oscillations are bled away and how systems respond when driven repeatedly
Thermodynamics • What it studies: how heat, work and energy turn into one another, with energy always conserved (the first law) • The catch: heat cannot be fully turned into work and disorder tends to grow (the second law; entropy) • The best efficiency any heat engine can reach (the Carnot cycle) • The cycles real machines use: petrol engines (the Otto cycle), diesels (the Diesel cycle), steam plants (the Rankine cycle) and gas turbines (the Brayton cycle) • Refrigerators and heat pumps: running a cycle in reverse to move heat from cold to hot • Describing the working fluid: how pressure, temperature and volume relate (the ideal gas law; steam tables)
Fluid Mechanics • Fluids at rest: how pressure rises with depth, and buoyancy (Archimedes’ principle) • Fluids in motion: the balance of mass, momentum and energy (the continuity and Navier-Stokes equations) • In a smooth flow, where the fluid speeds up its pressure drops (Bernoulli’s equation) • Viscosity and the thin layer of slowed fluid next to a surface (the boundary layer) • Smooth versus chaotic flow, decided by a single ratio (laminar and turbulent flow; the Reynolds number) • Flow in pipes: friction losses and the energy added by pumps and fans (the Moody chart)
Heat Transfer • Conduction: heat seeping through a solid from hot to cold (Fourier’s law) • Convection: heat swept away by a moving fluid, as in a radiator or cooling fins (Newton’s law of cooling) • Radiation: heat given off as infrared, even across a vacuum (the Stefan-Boltzmann law) • Heat exchangers: passing heat between two fluids without letting them mix • Treating a heat path like an electrical circuit to find temperatures (thermal resistance)
Machine Design and Mechanisms • Mechanisms: linkages, cams and gears that convert one motion into another (the four-bar linkage; gear ratios) • Machine elements: the standard parts such as shafts, bearings, gears, belts, springs and bolts • Designing against failure: sizing parts for strength, stiffness and fatigue (cracks grown by repeated loading) • Tolerances and fits: how precisely parts must be made to assemble and work together • Friction, wear and lubrication between moving surfaces (tribology)
Manufacturing • Machining: cutting material away to a precise shape (turning, milling and drilling) • Forming and casting: shaping metal by deforming it, or pouring it molten into a mould • Joining: welding, brazing, adhesives and mechanical fasteners • Building a part up layer by layer (additive manufacturing, or 3D printing) • Designing for manufacture: choosing processes and tolerances that make parts cheap and reliable
Control and Mechatronics • Feedback control: measuring what a system is doing and automatically correcting it (closed-loop control) • The everyday controller that acts on the error, its build-up and its trend (the proportional-integral-derivative controller) • Stability: making sure corrections settle the system rather than set it oscillating • Mechatronics: the marriage of mechanical parts with sensors, electronics and software • Sensors, actuators and robotics: measuring the world, moving things, and programmable machines that do physical work

Electrical and Electronic Engineering
Major Thinkers • Alessandro Volta: the first battery, giving a steady electric current • Georg Ohm: the law linking voltage, current and resistance (Ohm’s law) • Michael Faraday: electromagnetic induction, the basis of motors and generators • James Clerk Maxwell: the unified theory of electricity, magnetism and light (Maxwell’s equations) • Nikola Tesla and Thomas Edison: the alternating- and direct-current power systems • Heinrich Hertz and Guglielmo Marconi: the discovery and first use of radio waves • Claude Shannon: the mathematical theory of information (information theory) • Bardeen, Brattain and Shockley: the transistor, the foundation of modern electronics
Circuit Theory • The basic quantities: charge, current, voltage and power • The three fundamental components: resistors, capacitors and inductors • The laws that let any circuit be solved (Ohm’s law; Kirchhoff’s current and voltage laws) • Simplifying a complicated network into an equivalent source and resistance (Thevenin and Norton equivalents) • How a circuit settles after a switch is thrown (transient response; the time constant) • Handling oscillating signals through the idea of impedance and phasors (alternating-current analysis) • Circuits that respond strongly at particular frequencies, used to select or reject signals (resonance and filters)
Electromagnetism and Fields • The force between electric charges and the field around them (Coulomb’s law; Gauss’s law) • Magnetic fields made by currents, and the force on a current in a field • A changing magnetic field creates a voltage, the principle of generators and transformers (Faraday’s law of induction) • The four equations that unite electricity, magnetism and light (Maxwell’s equations) • Electromagnetic waves: energy travelling as radio, microwaves and light
Electronics and Semiconductor Devices • Semiconductors: materials between conductor and insulator whose conduction can be tuned (silicon; doping) • The diode: a one-way valve for current (the p-n junction) • The transistor: a tiny switch and amplifier, the building block of every chip • Amplifying weak signals with a versatile building block (the operational amplifier) • Integrated circuits: millions or billions of transistors made together on one chip • Continuous signals versus two-state signals (analogue and digital electronics)
Digital Systems • Representing information with just ones and zeros (binary; the bit) • Logic gates: simple circuits carrying out the operations of Boolean algebra • Combining gates into useful blocks: adders, memory and counters • Circuits whose output depends on history, advanced by a timing signal (the clock; sequential logic) • Programmable chips that run instructions (microprocessors and microcontrollers)
Signals and Systems • A signal carries information over time; a system transforms one signal into another • Splitting a signal into the frequencies it contains (the Fourier transform; the frequency domain) • Filtering: keeping or removing parts of a signal by their frequency • Turning a continuous signal into digital samples (the sampling theorem) • Manipulating signals as numbers in a computer (digital signal processing)
Communications • Carrying information by impressing it on a carrier wave (modulation) • The ceiling on how fast information can be sent reliably through a noisy channel (channel capacity; Shannon’s theorem) • Surviving noise and errors by adding cleverly structured redundancy (error-correcting codes) • Why digital communication has largely replaced analogue • Networks: routing and sharing signals among many users
Power Systems and Machines • Generating, transmitting and distributing electricity at scale (the power grid) • Why power is sent as high-voltage alternating current, and the role of the transformer • Electric machines: motors that turn electricity into motion and generators that do the reverse • Three-phase power: the efficient way large amounts of power are delivered • Switching electronics that convert and control power (power electronics; rectifiers and inverters)
Control Systems • Making a system behave by feeding its output back to correct its input (feedback; closed-loop control) • The all-purpose controller acting on the error, its accumulation and its rate of change (the proportional-integral-derivative controller) • Stability: ensuring the system settles rather than oscillating or diverging • Predicting and tuning behaviour with mathematical tools (transfer functions; the Laplace transform; Bode plots)

Robotics Engineering
Major Thinkers • Karel Čapek: the play that gave the world the word “robot” (R.U.R.) • Isaac Asimov: who coined the word “robotics” and posed the Three Laws as an early framing of machine ethics • Norbert Wiener: the founder of cybernetics, who showed that goal-seeking behaviour can be built from a simple feedback loop, blurring the line between machine and living thing • George Devol and Joseph Engelberger: the first industrial robot, Unimate, and the birth of the industry • Hans Moravec: robotics and artificial intelligence, and the paradox that what is hard for people is easy for machines, and vice versa • Rodney Brooks: behaviour-based robotics, and the radical claim that a robot needs no inner model because “the world is its own best model” (the subsumption architecture) • Marc Raibert: dynamic balance and legged locomotion • Sebastian Thrun: probabilistic robotics and autonomous driving
Foundational Research Questions • General-purpose manipulation: robots still cannot reliably pick up and handle the endless variety of everyday objects the way a human hand can, which makes dexterous manipulation in cluttered, unstructured settings perhaps the field’s hardest open problem • Robustness and generalisation: today’s robots are brittle, working beautifully in the lab yet failing on small changes they were not built for, so getting them to cope with the open, ever-changing real world is a central unsolved goal (the open-world problem) • Learning from little: a child or animal can pick up a new skill in a handful of tries, while robots often need millions, so making learning far more sample-efficient, and closer to how living things learn, is a major frontier • Sim-to-real transfer: skills perfected in fast, cheap simulation routinely break on real hardware, because no simulation captures every detail, and closing that gap reliably is still open (the reality gap) • Task-and-motion planning: joining high-level reasoning about what to do with the low-level control of how to move, so a robot can carry out long, multi-step tasks, means bridging two very different kinds of thinking that do not yet fit together cleanly • World models and common sense: robots lack the intuitive grasp of everyday physics that lets people foresee what will happen if they tip, push or drop something, and building that predictive understanding is a deep open question • Tactile sensing: robots can see far better than they can feel, yet much of manipulation depends on a rich sense of touch, which remains underdeveloped and poorly understood • Trustworthy autonomy: when a robot learns and adapts, its behaviour becomes hard to predict, so guaranteeing and formally certifying that it will stay safe while acting among people is largely unsolved (verification of autonomy) • Embodied intelligence: how much of the work of being clever can be handed to the body itself, its shape, springiness and materials, rather than to the controller, is an open and surprising question (morphological computation; soft robotics) • Generalist robots: whether a single robot and a single learned model could handle many different tasks, as one large model came to handle much of language, rather than each robot being built for one job, is the field’s current grand ambition (robot foundation models)
What Robotics Is • Robotics is the engineering of machines that sense the world, decide what to do, and then act on it, over and over (the sense-think-act loop) • What makes it different from ordinary computing: most software lives in a tidy world of numbers, but a robot has to work in the real, physical world, which is messy, uncertain, and never waits • It pulls many fields together at once: the mechanical engineering of moving parts, the electronics of sensors and motors, the mathematics of control, and the software and artificial intelligence that tie them together (mechatronics) • A robot is really three things acting as one: a body that can move, senses that tell it about the world, and a “brain” of software that decides what to do • The whole loop usually runs many times a second, because the world keeps changing while the robot is still working out its answer
Why Robotics Is Hard • The great surprise of the field is that the things we find effortless are the things robots find hardest: a one-year-old can walk across a room, pick up a toy and recognise a face, yet these are far harder to build than playing chess or doing arithmetic, because evolution spent hundreds of millions of years perfecting movement and perception and almost none on algebra (Moravec’s paradox) • Seeing is really guessing: a robot never receives the world directly, only a flood of noisy, ambiguous signals, and it must work backwards to the most likely reality, so perception is a constant, unconscious act of inference • A robot never knows exactly where it is or what is around it, so modern robotics gave up on certainty and instead reasons in probabilities, keeping track of how sure it is and revising that with every new clue (probabilistic robotics) • A famous puzzle: when a robot does one thing, how does it know everything else that did and did not change as a result? Listing all the things that stayed the same is hopeless, yet that knowledge is somehow needed to act sensibly (the frame problem) • There are always more ways to move than the task needs: countless different arm motions all reach the same cup, so a robot, like the brain, must choose one good solution out of infinitely many (the degrees-of-freedom problem) • Touch is where the physics turns nasty: the instant two solid objects meet, friction, squashing and slipping make the behaviour sharp and unpredictable, which is why robots still cannot reliably do what a toddler’s hands do • A model is never the world: a robot tuned to perfection in simulation often fails in reality, because no model captures every quirk of friction, flex and delay (the reality gap), so much of the craft is building robots that cope with their own ignorance • A deep idea from cybernetics underlies all of this: behaviour that looks purposeful, as if the machine wanted something and were striving toward it, can come from a mechanism that wants nothing at all. The trick is feedback. Give the system a target, let it measure how things actually are, and have it act to shrink the difference between the two. A thermostat is the classic case: it holds a target temperature, checks the real temperature, and switches the heater on or off to drive the room toward that target. Nothing in it desires warmth, yet from the outside it looks as though it is trying to keep you comfortable. The lesson is that goal-seeking needs no mind and no wanting: purpose can be built from a plain loop, and that same loop drives almost everything a robot does (feedback as mechanised purpose)
Mechanisms and Kinematics • A robot’s body is a chain of stiff parts (links) joined by joints that either swivel or slide • Degrees of freedom simply means the number of separate ways it can move; to put a hand anywhere in space and point it any way takes six, three to choose the spot and three to choose the direction it faces • To keep track of everything, each part is given its own little set of axes (a frame), and the robot’s shape is described by how each frame sits relative to the next • Working out where the hand ends up from the joint angles is the easy direction (forward kinematics); going the other way, from where you want the hand to be back to the angles that put it there, is much harder and may have many answers or none (inverse kinematics) • Describing which way something points in three dimensions is surprisingly awkward, and the tidy method (quaternions) is preferred because the obvious one can jam, suddenly losing a direction of movement (gimbal lock) • One especially powerful idea links joint motion to hand motion: a small table of numbers (the Jacobian) that says how a slight turn of each joint nudges the hand, and, read the other way, how a push on the hand is felt as load at each joint • At certain awkward poses the arm briefly loses the ability to move in some direction however it tries (a singularity), while spare joints give it extra room to dodge such traps (redundancy)
Dynamics and Actuation • Force can be pictured as an arrow: it points the way it pushes, and the longer the arrow the stronger the push (a vector) • The turning effort at a joint (torque) is the force times how far out it acts, so a gentle push at the end of a long arm can twist a joint as hard as a big push close in, which is why a robot strains most when stretched out • Just holding an arm still takes effort, because every motor must fight the weight of all the parts beyond it, and an outstretched arm slowly droops the moment the motors ease off • Predicting how a robot really moves is hard because, on top of gravity, the parts being already in motion throw up extra forces purely from their own swinging and turning, so the full picture combines the arm’s reluctance to speed up, these motion-born forces, and gravity (the equations of motion) • Control usually runs this backwards: given the motion you want, work out exactly how hard each motor must push to produce it (inverse dynamics) • The motors are the muscles: electric ones push harder the more current they are fed, while some robots use fluid pressure for brute strength • Gears trade speed for strength, so a strong joint is often a slow one, and they bring their own snags, such as a tiny looseness that smears precision (backlash) • Building in a little give, like a spring, lets a robot absorb a knock or touch something gently instead of fighting it rigidly (compliance)
Sensing and Perception • Sensors are how a robot learns anything at all, some watching its own body, such as the angle of each joint, and some watching the outside world, such as cameras, lasers and sound • Cameras are cheap and rich but hard to use, because turning a flat picture back into a real three-dimensional scene is genuinely difficult • Depth from two eyes: a robot, like us, judges distance by comparing the slightly different views from two cameras, since nearer things shift more between them • Depth from light: a laser scanner (lidar) fires pulses and times their echoes, and because light travels at a known speed, the delay gives the distance, building a three-dimensional dot-picture of the surroundings • Every sensor lies a little, so a robot never trusts a single reading; it keeps a running best guess and nudges it with each new measurement, leaning harder on the readings it trusts more (sensor fusion; the Kalman filter) • Some things matter but cannot be measured directly, such as speed, and must be worked out from things that can (state estimation) • Sensing over time tends to drift: devices that track motion by adding up tiny movements slowly lose their place as small errors pile up
Control • Control is how a robot makes itself actually do what was asked, by constantly comparing where it is with where it should be and correcting the difference (feedback; closed-loop control) • The everyday workhorse fixes its mistake in three ways at once: it reacts to the error now, to how long the error has been building up, and to how fast the error is changing (the proportional-integral-derivative controller) • Getting the balance right is an art: react too weakly and the robot is sluggish, too strongly and it shakes itself to pieces (tuning and stability) • Smooth movement has to be planned, easing into and out of motion rather than lurching, by shaping not just the speed but how sharply the speed itself changes (trajectory planning; limiting jerk) • Sometimes a robot should not insist on an exact position but give way when it meets resistance, behaving like a soft spring, so it can press, polish or shake a hand without crushing anything (force and impedance control) • All of this must finish in time, because the world moves on whether or not the robot has found its answer, so the loop has to run fast and on schedule (real-time control)
Localisation, Mapping and Navigation • A robot that moves must answer two questions: where am I, and what does the world around me look like? • It rarely knows its position for certain, so it holds a spread of possibilities and tightens it as familiar landmarks come into view (localisation; the particle filter) • A nasty twist: to know where you are you need a map, but to draw a map you need to know where you are, and a robot exploring somewhere new has neither, so it must build the map and locate itself at the same time (simultaneous localisation and mapping, or SLAM) • To plan a route, the robot thinks not about the room but about the space of every position it could be in, where it shrinks to a single point and walls become no-go zones (the configuration space) • Finding a path is then a search for the cheapest way across that space, sped up by always heading roughly toward the goal (the A* algorithm), or by flinging out random feelers when the space is too huge to search properly (rapidly-exploring random trees) • Because the world keeps changing, the plan is constantly adjusted as new obstacles appear
Planning and Artificial Intelligence • Planning is the robot working out a sequence of actions to get from where it is to where it wants to be, whether that is a path across a room or the steps to assemble a part • Because the robot is never certain, good planning weighs the odds, choosing the actions that pay off best on average across everything that might go wrong (decision-making under uncertainty) • Increasingly, robots learn rather than being told: they improve from experience, and can even teach themselves a skill by trying, failing, and being rewarded for getting closer (machine learning; reinforcement learning) • A long-running debate shapes the field: should a robot carefully think before it acts, or mostly run on reflexes, and most real robots blend the two, with fast instincts underneath and slower deliberation on top (deliberative versus reactive architectures)
Manipulation and Locomotion • Manipulation, using arms and hands to grasp and move things, is one of the great unsolved challenges, because the world is full of objects of every shape, weight and slipperiness • A good grip must hold firm no matter which way the object is pushed or twisted, balancing the squeeze of the fingers against friction (a stable, or force-closure, grasp) • Locomotion is how a robot moves itself, by wheels, tracks, legs, fins or wings, each suited to different ground • Walking on legs is really controlled falling: a legged robot, like a person, tips forward and catches itself step after step, staying upright by keeping its push against the ground inside the patch covered by its feet (dynamic balance; the zero-moment point) • A newer idea drops stiffness altogether, building robots from soft, bendy materials that deform like living tissue, trading precision for gentleness and resilience (soft robotics)
Software and Programming • Software is the robot’s mind: every sense, decision and movement comes down to lines of code, and a modern robot may be running millions of them at once • The hard part is that it must all happen live, while the robot is moving, so the code has to be fast and reliably on time, never pausing to think while the robot tips over (real-time programming) • Many things must happen in the same instant, reading sensors, running control loops, planning ahead and watching for danger, all at once without tripping over each other (concurrency) • A robot is built from many small programs that cooperate by passing messages, often on top of shared frameworks that handle the plumbing so engineers can focus on behaviour (robot operating systems and middleware) • A surprising amount of the code is glue and guardrails: cleaning up raw, imperfect sensor data, and catching the countless ways things can go wrong before they cause harm • Simulation comes first: a robot is usually tested thousands of times in a virtual world before it ever touches real hardware, which is cheaper and safer, though never a perfect substitute (the reality gap again)
Mathematics of Robotics • Robotics leans on a particular toolkit of mathematics, less about crunching numbers and more about space, motion, change and uncertainty • Vectors and matrices are the language of position and movement: a vector pins down a point or a force, and a matrix can rotate, move or reshape a whole set of them at once (linear algebra) • Turning and orientation have their own special mathematics, because rotations in three dimensions behave in non-obvious ways (rotation matrices and quaternions) • Calculus handles how things change from moment to moment, the link between position, speed and acceleration that underlies all motion • How a robot’s many parts move together, and how that motion unfolds over time, is captured by equations that relate rates of change (differential equations) • Because nothing is known for sure, probability runs through everything, letting a robot judge how likely things are and update its beliefs as evidence arrives (probability and statistics; Bayes’ rule) • Picking the best action or path out of countless options is its own branch of mathematics (optimisation), and searching cleverly through vast numbers of possibilities is where the study of algorithms comes in
Autonomy, Interaction and Safety • Levels of autonomy: how much the robot does for itself, from being driven by remote control, through sharing the work with a person, to acting entirely on its own • Human-robot interaction: how people and robots come to understand each other, cooperate, and safely share the same space • Collaborative robots: machines gentle and aware enough to work right beside people, sensing contact and easing off rather than barging through (cobots) • Safety: making sure a strong, fast machine cannot hurt the people around it, the overriding concern whenever a robot shares human space • Ethics and society: the harder questions of who is responsible when a robot errs, the jobs robots replace, autonomous weapons, and what part we want machines to play in our lives
Types and Applications • Industrial robots: the tireless arms that do much of modern manufacturing • Mobile robots: machines that roam, from warehouse carts to planetary rovers • Humanoid and legged robots: machines shaped to move and work in spaces built for people • Service and medical robots: from surgical assistants to vacuum cleaners • Swarm robotics: many simple robots that together achieve what no one of them could • Autonomous vehicles: self-driving cars, drones and ships

Civil Engineering
Major Thinkers • The Roman engineers: enduring roads and aqueducts, and the arch built in concrete • John Smeaton: the first to call himself a civil engineer, and modern lighthouse and harbour design • Thomas Telford and Isambard Kingdom Brunel: pioneering bridges, canals, railways and tunnels • Gustave Eiffel: pioneering wrought-iron and steel structures • Karl Terzaghi: the founder of soil mechanics (geotechnical engineering) • Fazlur Rahman Khan: the structural systems that made the modern skyscraper possible
Structural Engineering • What it does: making sure buildings, bridges and other structures carry their loads safely, without collapsing or sagging too much • The loads to resist: the structure’s own weight (dead load), its contents and traffic (live load), and wind, snow and earthquakes • How structures carry load: members in tension, compression, bending and shear, and the path the load takes down to the ground • The repertoire of forms: beams, columns, trusses, arches, frames, cables and shells • Working out the internal forces, by hand and increasingly by computer (the finite element method) • Designing in the main materials: reinforced concrete, structural steel, timber and masonry • Designing for earthquakes and other dynamic loads (seismic design) • Guarding against buckling, fatigue and progressive collapse
Geotechnical Engineering • The engineering behaviour of the soil and rock that everything is built on and in (soil mechanics) • Classifying soils and understanding how they behave when loaded, drained or compacted • How water pressure within the soil affects its strength (effective stress; pore-water pressure) • How much the ground sinks under load and how much it can bear (settlement and bearing capacity) • Foundations: spreading load through shallow footings or carrying it deep on piles • Holding back soil and keeping slopes stable (retaining walls; slope stability) • Earthworks, embankment dams and tunnelling
Construction Materials • Concrete: a mouldable mix of cement, aggregate and water, strong in compression but weak in tension • Adding steel to carry the tension that concrete cannot (reinforced and prestressed concrete) • Steel: strong in both tension and compression, the other great structural material • Timber, masonry and modern fibre composites • How materials change over time: strength gain, shrinkage, creep, corrosion and durability
Hydraulics and Water Resources • Water at rest and in motion (hydraulics) • Flow in pipes under pressure and in open channels such as rivers and canals • Dams, spillways, pumps and other hydraulic structures • How rainfall becomes river flow, and the prediction of floods and droughts (hydrology) • Supplying water, draining it, and irrigating land
Transportation Engineering • Planning, designing and running the networks that move people and goods • Roads and pavements: their geometry, materials and layered construction • How traffic flows and how it is managed and signalled (traffic engineering) • Railways, ports and airports • Forecasting travel demand and shaping networks (transport planning)
Surveying and Geomatics • Measuring and mapping the land precisely, the starting point of any project • Measuring positions, distances, heights and angles • Satellite positioning and computer-based mapping (geographic information systems) • Setting out: transferring a design accurately onto the ground for building
Environmental and Public-Health Engineering • Supplying clean water and carrying away and treating waste (sanitation), one of history’s great gains for public health • Treating drinking water and sewage to make them safe • Managing solid waste and controlling pollution of air, water and land • Building sustainable and resilient infrastructure
Construction Management • Turning a design into a finished structure, on time and on budget • Planning and scheduling the work, and finding the sequence that controls the timetable (the critical path method) • Estimating cost, procurement and contracts • Site safety, quality control and overall project management

Chemical Engineering
Major Thinkers • George E. Davis: widely regarded as the founder of chemical engineering • Arthur D. Little: who framed the idea of the “unit operation” • Fritz Haber and Carl Bosch: the industrial synthesis of ammonia for fertiliser (the Haber-Bosch process) • Josiah Willard Gibbs: the thermodynamics of chemical and phase equilibrium (free energy; the phase rule) • The founders of transport phenomena: the unified treatment of momentum, heat and mass transfer
Material and Energy Balances • The accounting at the heart of the field: tracking everything that enters and leaves a process (conservation of mass and energy) • Building any process from a few standard, reusable steps (the unit-operation idea) • Processes running in balance versus starting up or changing (steady and unsteady operation) • Scale-up: bridging from a laboratory flask to a full industrial plant
Thermodynamics • Energy, heat and work in chemical processes (the first law) • Which way a process will go, and how far (the second law; entropy and free energy) • When liquid and vapour coexist, which governs most separations (vapour-liquid equilibrium) • How far a reaction proceeds before it stops (chemical equilibrium; the equilibrium constant) • Describing real mixtures and solutions (activity and fugacity)
Transport Phenomena • The insight that momentum, heat and matter all move in mathematically parallel ways • Moving fluids through pipes and equipment (fluid flow; viscosity; the Reynolds number) • Moving heat by conduction, convection and radiation, and the heat exchanger • Moving a substance from one phase or place to another (mass transfer; diffusion; Fick’s law)
Separation Processes • Splitting mixtures into purer products, often the most expensive part of a plant • Separating liquids by their boiling points, the industry’s workhorse (distillation) • Moving a substance between a gas and a liquid (absorption and stripping) • Pulling a substance out using a solvent (extraction) • Other methods: filtration, crystallisation, drying, adsorption and membranes
Reaction Engineering • Designing the vessel where the chemistry actually happens (the reactor) • How fast a reaction goes and what controls its rate (reaction kinetics) • The two ideal reactor models: a well-mixed tank and a tube of flowing fluid (the stirred-tank and plug-flow reactors) • Substances that speed reactions without being used up, central to most industrial chemistry (catalysis) • Combining the reaction with the heat and mass transfer around it
Process Control and Plant Design • Keeping a continuous plant running safely and steadily despite upsets (feedback control; the proportional-integral-derivative controller) • Measuring temperature, pressure, flow and level throughout the plant (instrumentation) • Laying out and linking a whole process (process flow diagrams; process integration) • Preventing runaway reactions, leaks and explosions (process safety; hazard and operability studies) • Making processes economical, efficient and sustainable
Applications and Products • Refining crude oil and making petrochemicals • Polymers, plastics and advanced materials • Pharmaceuticals and fine chemicals • Food, energy and the use of living cells to make products (biochemical engineering) • Cleaning up and preventing pollution (environmental process engineering)

Materials Science
Major Thinkers • Josiah Willard Gibbs: the thermodynamics governing phases and microstructure (the phase rule) • Henry Clifton Sorby: the founder of metallography, studying metal structure under the microscope • Thomas Young: the measure of a material’s stiffness (Young’s modulus) • William Lawrence Bragg: reading crystal structures from X-rays (Bragg’s law) • A. A. Griffith: why real materials are far weaker than theory, because of tiny cracks (fracture mechanics) • Linus Pauling: the nature of the chemical bond • Stephanie Kwolek: the invention of strong, lightweight aramid fibres (such as Kevlar)
The Central Idea • how a material is processed sets its internal structure, which sets its properties, which set its performance (the processing-structure-properties chain) • Working across scales, from single atoms and bonds, through the microscopic structure, up to the bulk material in use
Atomic Structure and Bonding • How atoms are held together, which fixes a material’s basic character (the chemical bond) • The main kinds of bond: metallic, covalent, ionic and weak (van der Waals) forces • Why bonding explains gross behaviour, such as why metals conduct and bend while ceramics are hard and brittle
Crystals and Defects • Crystals: solids whose atoms sit in a regular, repeating pattern (the crystal lattice) • How atoms pack in the common metal structures • Glasses: solids frozen with no long-range order (amorphous materials) • Imperfections that, far more than perfection, control real behaviour (point defects; dislocations) • The line defect whose movement lets metals deform and explains their real strength (the dislocation)
Microstructure and Phase Diagrams • The grains, phases and boundaries seen under a microscope, which govern properties (microstructure) • A map of which phases exist at each temperature and composition (the phase diagram) • How a melt freezes and the structure it leaves behind (solidification) • Rearranging the microstructure by heating and cooling, as in hardening steel (heat treatment; phase transformations)
Mechanical Behaviour • Stiffness: resistance to elastic stretching (Young’s modulus) • Strength: the stress a material bears before it yields or breaks • Bending and stretching versus snapping (ductility versus brittleness) • Resistance to cracks spreading (toughness; fracture mechanics; the Griffith criterion) • Making materials stronger by blocking the movement of dislocations (alloying, grain refinement and work hardening) • Failure that takes time: cracking under repeated load (fatigue) and slow stretching under heat and load (creep)
The Classes of Materials • Metals: strong, stiff, ductile and conductive, the backbone of engineering • Ceramics: hard, stiff and heat-resistant, but brittle • Polymers: light, flexible, easily shaped long-chain molecules (plastics) • Composites: pairing two materials to beat the limits of either (such as fibre-reinforced plastic) • Semiconductors: the carefully controlled materials behind all electronics
Functional Properties • Why some materials conduct, some insulate and some do both on command (the band theory of solids) • Magnetic materials and what they are used for • How materials absorb, reflect and transmit light (optical properties) • Heat capacity, expansion and conduction (thermal properties)
Degradation, Characterisation and Processing • How materials fail in service: corrosion, wear, fatigue and radiation damage • Looking inside materials to find their structure (microscopy; X-ray diffraction and Bragg’s law) • Shaping materials: casting, forming, sintering and building them up layer by layer (additive manufacturing) • Choosing the right material for a job, and designing entirely new ones (materials selection and design)

Architecture
History of Architecture Architecture as the product of culture, religion, politics, economics, climate and available technology • Prehistoric building: post-and-lintel construction, megaliths (Stonehenge) and the first settlements (Çatalhöyük) • The Ancient Near East and Egypt: Mesopotamian ziggurats; Egyptian mastabas, pyramids and temples; monumentality and the afterlife • Classical antiquity: Greek temples and the orders; the Parthenon and optical refinements; Roman engineering: the arch, vault, dome and concrete; the Pantheon, basilica, aqueduct and forum • Late Antique and Byzantine: the basilica plan; the pendentive dome; Hagia Sophia • Islamic architecture: the mosque and courtyard; the arch, dome, geometric ornament and muqarnas; the Alhambra • Medieval Europe: Romanesque massing and the round arch; Gothic structural innovation: the pointed arch, rib vault, flying buttress and stained glass • Non-Western traditions: Indian temple and stupa architecture; Chinese timber framing codified in the Yingzao Fashi; Japanese temples and houses; Mesoamerican pyramids; sub-Saharan African building • The Renaissance: the revival of classicism, linear perspective, proportion and the centralised plan; Brunelleschi's dome; Bramante; Palladio's villas • Baroque and Rococo: dynamic space, curvature, light and theatricality; Bernini and Borromini • Neoclassicism and the Enlightenment: archaeology, reason and a return to origins; Boullée and Ledoux • The nineteenth century: industrialisation, iron and glass (the Crystal Palace), the railway station; historicism and the revival styles; the Gothic Revival; Beaux-Arts; Arts and Crafts • Modernism: the rejection of ornament; steel, reinforced concrete and plate glass; function and abstraction; the Bauhaus, the International Style, Le Corbusier, Mies van der Rohe and Frank Lloyd Wright • Postmodernism and after: the return of history, symbolism and complexity; critical regionalism; deconstructivism; high-tech; parametric and digital architecture; sustainability and the contemporary city
Major Thinkers & Theory Architecture as a tradition of written theory: the treatise, the manifesto and the polemic • Vitruvius: De Architectura, the only surviving ancient treatise; the triad of firmitas, utilitas and venustas (firmness, commodity and delight) and the proportions of the orders derived from the human body • Leon Battista Alberti: De re aedificatoria, the first Renaissance treatise; beauty as concinnitas, the harmony of parts • Andrea Palladio: I Quattro Libri dell'Architettura; codification of the orders and the villa; the enduring influence of Palladianism • Sebastiano Serlio and Filarete: illustrated treatises and the ideal city • Abbot Suger: the spiritual programme of Gothic light at Saint-Denis • Marc-Antoine Laugier: the “primitive hut” and the rational origins of architecture • Johann Winckelmann: the rediscovery of antiquity and the birth of art history • A. W. N. Pugin and John Ruskin: moral and “honest” use of materials; the Gothic Revival (The Seven Lamps of Architecture) • Eugène Viollet-le-Duc: structural rationalism and restoration • Louis Sullivan: “form (ever) follows function” • Adolf Loos: “ornament and crime” • Le Corbusier: Vers une architecture; “a house is a machine for living in”; the Five Points; the Modulor proportioning system • Walter Gropius: the Bauhaus and the union of art and industry • Ludwig Mies van der Rohe: “less is more” and structural clarity • Frank Lloyd Wright: organic architecture • Robert Venturi: Complexity and Contradiction in Architecture; “less is a bore” • Aldo Rossi: urban typology and the architecture of the city • Christopher Alexander: A Pattern Language • Kenneth Frampton: critical regionalism • Manfredo Tafuri: architecture and ideology • Rem Koolhaas: the metropolis and programmatic invention • Li Jie: the Yingzao Fashi, codifying Chinese building practice
Architectural Drawing & Representation Drawing as the architect's primary medium of thought and communication • Orthographic projection: the multiview set drawn perpendicular to the picture plane, true to scale and without distortion • The plan: a horizontal cut, conventionally taken about 1.2 m above the floor • The section: a vertical cut revealing interior space and structure • The elevation: a vertical view of an external or internal face • First-angle and third-angle projection conventions • Paraline (parallel-line) drawing: three dimensions shown in a single view with parallel lines remaining parallel • Axonometric and isometric projection (isometric, dimetric, trimetric), constructed with the 30/60/90 and 45/45/90 set squares and the architect's scale • Oblique projection: plan oblique and elevation oblique; bird's-eye and worm's-eye views; the cut-away axonometric • Linear perspective: the picture plane, station point, horizon line and vanishing points; one-, two- and three-point perspective; foreshortening • Descriptive geometry: Gaspard Monge's method of projecting three dimensions onto two; the Renaissance development of perspective by Brunelleschi, Alberti, Piero della Francesca and Dürer • Drawing conventions and craft: line weights and hierarchy, line types, lettering, scale and graphic scale bars, north arrows, symbols and poché • Rendering: tone, texture, shade and shadow, material indication, entourage (people, trees, vehicles) and the creation of depth through layering • Freehand sketching, the diagram and the parti as tools of design thinking • The physical and study model • Digital representation: CAD, 3D modelling (SketchUp, Rhino), Building Information Modelling (BIM, e.g. Revit), parametric tools (Grasshopper) and photorealistic rendering
Elements, Orders & Principles of Design The classical orders: Doric, Ionic, Corinthian, Tuscan and Composite; the column, capital and entablature • Proportion and the module; symmetry; the golden section; anthropometric proportion (the Vitruvian figure, the Modulor) • Ordering principles: axis, hierarchy, datum, rhythm, repetition and balance • Space, form and order: solid and void, mass and surface, figure and ground • Scale and human scale; circulation and the path; threshold and procession • Light, material and tectonics; structure as expression • Programme, function and building type • Genius loci: the relationship of building to site and context
Building Technology & Structures Structural action: compression, tension, bending, shear and torsion; load paths • Structural systems: post-and-lintel, the arch, the vault and the dome; the truss; the frame; load-bearing walls; the cantilever; shells and membranes; the tall building and the curtain wall • Materials: stone, brick and masonry; timber; iron and steel; reinforced and pre-stressed concrete; glass; composites • Construction and assembly: foundations, the building envelope, detailing, tolerances and joints • Environmental systems and services: heating, ventilation, lighting and acoustics • Building physics: thermal performance, moisture and daylighting • Fire, safety and building regulation
Urbanism & the City The city as the largest work of architecture; figure-ground relationships and urban morphology • Street, square, block and the public realm • Models of the ideal and planned city: the grid, the Renaissance ideal city, the Baroque axis, the Garden City, the Modernist superblock and New Urbanism • Zoning, density and infrastructure • Public space, the monument and civic identity • Landscape and the designed environment
Environment & Sustainability Climate-responsive and vernacular design; orientation, shading and natural ventilation • Passive heating and cooling; thermal mass • Energy, embodied carbon and life-cycle assessment • Daylighting and environmental comfort • Sustainable materials and the adaptive reuse of existing buildings • Resilience and the relationship between architecture and the natural environment

Industrial and Product Design
Major Thinkers • Christopher Dresser: among the first independent industrial designers; designing for mass production • Peter Behrens: a pioneer of corporate and industrial design who shaped a whole company’s products and identity • Raymond Loewy: the great populariser of the profession; streamlining and the idea of the “most advanced yet acceptable” form • Henry Dreyfuss: who put the human body at the centre of design (Designing for People; ergonomics) • Charles and Ray Eames: the marriage of new materials, clean form and mass production • Dieter Rams: ten principles of good design, summed up as “less, but better” • Victor Papanek: design as a social and ecological responsibility (Design for the Real World) • Donald Norman: user-centred design and the psychology of everyday things (affordances; usability)
What Industrial Design Is • The design of objects to be made in quantity by industry, balancing usefulness, usability, manufacture and beauty • The central problem of reconciling how a thing works with how it looks (the relationship of form and function) • Designing the object together with how it is made and sold, not as decoration added afterwards • How an object’s shape and details communicate its purpose, quality and how to use it (product semantics) • How it differs from craft (one-off and handmade) and from engineering (which solves the technical core): design integrates both around the user
The Design Process • Design as a structured journey from a problem to a finished product, looping back and revising along the way (the iterative design process) • Understanding the user and the context before solving anything (design research; user needs) • Defining the problem and writing the brief before reaching for solutions • Generating many possibilities, then narrowing down (ideation; divergent and convergent thinking) • Making ideas tangible early so they can be tested (prototyping) • Refining through repeated cycles of testing and revision (iteration) • The wider mindset of creative, user-centred problem-solving (design thinking)
Human Factors and Ergonomics • Designing objects to fit the human body and its abilities (ergonomics; human factors) • Using data on the range of human sizes and shapes (anthropometrics) • Comfort, reach, posture and the avoidance of strain and error • Designing for the widest possible range of people, including the elderly and disabled (inclusive and universal design) • Safety and guarding against misuse
User-Centred and Interaction Design • Putting the user’s real needs and behaviour at the centre of every decision (user-centred design) • How an object’s form signals what can be done with it (affordances and signifiers) • Making a thing easy and intuitive to use (usability) • The whole experience of using a product, physical or digital (user experience; interaction design) • Matching a design to how people already expect things to work (mental models)
Aesthetics, Form and Visual Language • The visual qualities of an object: form, proportion, line, colour, texture and finish • Composition and balance worked out in three dimensions • A coherent style that ties a family of products together (a design language) • The principle of restraint and clarity (Dieter Rams’s “less, but better”) • How taste and the meaning of objects are shaped by culture and era
Materials and Manufacturing • Choosing materials for their properties, cost, feel and environmental impact (materials selection) • The major processes: moulding plastics (injection moulding), and forming, casting and machining metal • Designing a part so that it can actually be made affordably and reliably (design for manufacture and assembly) • Building parts up layer by layer for prototypes and short runs (additive manufacturing; 3D printing) • Tolerances, surface finishes and how parts are joined
Prototyping and Representation • Sketching as the fast, fluent language of design thinking • Drawing objects convincingly in three dimensions (perspective and rendering) • Building digital three-dimensional models (computer-aided design) • Physical models, from rough study models to lifelike appearance models (mock-ups and prototypes) • Testing a prototype with real users before committing to production
Sustainability and Responsible Design • The environmental cost of a product across its whole life, from raw material to disposal (life-cycle assessment) • Designing to cut waste and keep materials in use (the circular economy; design for disassembly and recycling) • Durability and repairability, against deliberately short-lived goods (planned obsolescence) • The designer’s social and ethical responsibility to real human needs • Designing fairly and accessibly for everyone
Design Strategy and the Market • How design creates value for a business and shapes its brand • Reading the market, the competition and the user to position a product • Branding and the consistent identity carried across a range of products • Innovation: designing genuinely new products rather than restyling old ones • Balancing what people want, what can be built, and what works as a business (the desirable, the feasible and the viable)
History and Movements of Design • The Arts and Crafts movement: a revolt against shoddy mass production, prizing handcraft (William Morris) • The Bauhaus: uniting art, craft and industry, and the birth of modern design education • Streamlining and American consumer design between the wars (Raymond Loewy) • Mid-century modern: new materials married to clean, organic form (the Eames era) • Functionalism and the ideal of good design (Braun and Dieter Rams) • The postmodern reaction: playful, expressive design against strict function (the Memphis group) • The digital age: the rise of interaction, experience and service design

Fine Art
Major Thinkers • Giotto: reawakened naturalism and a sense of depth in Western painting • Leonardo da Vinci: the union of art and science, and soft, smoky transitions of tone (sfumato) • Michelangelo: the human figure raised to its height in sculpture and painting • Caravaggio: dramatic, theatrical contrasts of light and dark (tenebrism) • J. M. W. Turner: light and atmosphere dissolving solid form, anticipating abstraction • Paul Cézanne: reducing nature to its underlying forms, the bridge to modern art • Pablo Picasso and Georges Braque: the shattering of the single viewpoint (Cubism) • Marcel Duchamp: the readymade, which redefined what could count as art • Wassily Kandinsky: among the first to paint pure abstraction • Jackson Pollock: gesture and process themselves made the subject (Abstract Expressionism) • Giorgio Vasari: the first art historian, whose Lives of the Artists shaped the canon • Clement Greenberg: the leading theorist of modernist painting and its “flatness” • E. H. Gombrich and John Berger: how images work, and the politics of how we look (The Story of Art; Ways of Seeing)
The Elements and Principles of Art • The basic visual vocabulary every work is built from: line, shape, form, tone, colour, texture and space (the elements of art) • How those elements are arranged for effect: balance, contrast, emphasis, rhythm, proportion, movement and unity (the principles of design) • The subject and the shaped emptiness around it (positive and negative space) • Tone (value): the range from light to dark that gives an image solidity • The difference between a flat shape and the illusion of solid form
Drawing • Drawing as the foundation of visual art: thinking, seeing and recording with line and tone • Observational drawing: training the eye to see proportion, angle and relationship truthfully • Mark-making: contour, gesture, and building tone by hatching and cross-hatching • Modelling a form with graded tone, from light to shadow (shading; chiaroscuro) • The human figure as the classic discipline of seeing (life drawing) • Media: pencil, charcoal, ink, pastel and chalk
Colour • How colours relate, set out on a wheel of primary, secondary and complementary hues (the colour wheel) • The three dimensions of any colour: its hue, its lightness (value) and its intensity (saturation) • Warm and cool colours, and how colours seem to advance or recede • Mixing pigments (subtractive) versus mixing light (additive) • How opposite colours intensify one another (complementary contrast; colour theory) • Colour as a carrier of mood and symbolism
Composition and Perspective • Composition: arranging the elements within the frame to lead the eye and balance the whole • Common devices for placing a focal point (the rule of thirds; the golden ratio) • The surface and edges that define the image (the picture plane and the frame) • Creating the illusion of depth on a flat surface (linear perspective; vanishing points; foreshortening) • Distant things made paler and bluer to suggest space (atmospheric perspective) • Figure and ground, and the path along which the eye is led
Painting • The major media, each with its own character: oil, acrylic, watercolour, tempera, gouache and fresco • The surface and its preparation (supports and grounds, such as primed canvas or panel) • Handling paint: thin, luminous layers versus thick, textured strokes (glazing; impasto) • The long evolution of technique, from egg tempera to oil to modern acrylics • The traditional genres: portrait, landscape, still life, history painting and abstraction
Sculpture and Three-Dimensional Form • Working in three dimensions, to be seen in the round and in real space • The two great approaches: carving away from a block (subtractive) and building up (additive, by modelling and casting) • Materials: stone, wood, clay, bronze, plaster and, later, almost anything • The poised weight-shift that gives a standing figure life (contrapposto) • Relief versus free-standing sculpture • Modern expansions: assemblage, installation and work made for a particular place (site-specific art)
Printmaking • Making multiple original images from a worked surface (the matrix) • Cutting away what is not to print (relief printing: woodcut and linocut) • Incising lines that hold the ink (intaglio: engraving and etching) • Printing from a flat, chemically treated surface (lithography) • Pushing ink through a stencil (screen printing) • The limited, numbered run of identical impressions (the edition)
The History of Art and its Movements • Prehistoric and ancient art: cave painting and the art of Egypt, Greece and Rome • Medieval and Byzantine art: the sacred image and the icon • The Renaissance: the rediscovery of nature, perspective and the human figure • Baroque drama, Rococo lightness and Neoclassical order • Romanticism and Realism, then the revolution of painting light and the passing moment (Impressionism) • The modern break: Post-Impressionism, Cubism, Expressionism, Surrealism and abstraction • The post-war shift: Abstract Expressionism, Pop Art, Minimalism and Conceptual Art • Non-Western traditions and the global story of art • How patronage, religion, politics and technology shape what art is made
Aesthetics and Art Theory • The branch of philosophy asking what art is and what beauty is (aesthetics) • Art as the imitation of nature, the oldest theory of all (mimesis; representation) • Art as the expression of feeling, and art as significant form • The overwhelming and the awe-inspiring in art (the sublime) • Reading the symbols and subjects within an image (iconography and iconology) • When almost anything can be art, what makes something art at all (the readymade; the “artworld”) • How images carry power and ideology, and the act of looking itself (the gaze; visual culture)
Contemporary and Expanded Practice • How art broke out of painting and sculpture into new forms across the twentieth century • The idea that the concept matters more than the crafted object (conceptual art) • Photography and the moving image as fine-art media (video art) • Art that happens as a live event (performance art) • Whole environments the viewer steps into (installation) • Digital, generative and new-media art • Art that engages society and politics directly (socially engaged art)
The Art World • How art reaches its audience: the studio, the gallery, the museum and the biennial • Curation: selecting and arranging works so they make meaning • The market: collectors, dealers and auctions, and the puzzle of how art is priced • Criticism and scholarship, through which reputations and the canon are made • Conservation: the care, restoration and ageing of artworks • Institutions, access and the question of who decides what counts as art