While the majority of modules at Warwick come with lecture notes, sometimes it’s nice to have some additional reading material to complement the notes. (Or to entirely replace them if the lecturer decides to handwrite them illegibly.) You might also be looking for sources or learning material for essays or research projects, or just for something interesting to get in to.
To this end, we have compiled together a collection of recommendations of various reading materials for you to browse. Note that, despite the title, many of the linked texts may be interesting papers/preprints rather than full textbooks.
This section of the website is under construction! Many of these pages are empty – please contribute!
- Abstract Algebra - Introductory abstract algebra; groups, rings, etc.
- Algebraic Geometry - Algebraic and affine varieties, stacks, sheaves, schemes, moduli spaces, and complex geometry.
- Algebraic Topology - Homotopy theory, (co)homology theory, and homological algebra.
- Calculus - Introductory calculus; differentiation and integration, line and contour integrals, curl and flux, etc.
- Category Theory - Topoi, abelian categories, monoidal categories, monads, and homological algebra.
- Combinatorics - Graph theory, enumeration, extremal combinatorics, combinatorial optimisation, Ramsey theory, information theory, combinatorial game theory, symmetric functions.
- Commutative Algebra - Commutative rings, modules, ideals, homological algebra, connections to algebraic number theory and algebraic geometry.
- Complex Analysis - Holomorphic functions, automorphic group actions and forms, complex geometry.
- Differential Geometry - Complex, Riemannian, and pseudo-Riemannian geometry, differential forms, gauge theory.
- Differential Topology - Manifolds and diffeomorphisms, exterior algebras, homotopy theory.
- Foundations - Logic, set theory, type theory, topos theory, model theory.
- Functional, Harmonic, and Fourier Analysis - Hilbert spaces, Banach spaces, function spaces, convex geometry, integral transforms, spectral analysis, representation theory.
- Linear Algebra - Matrix decompositions, spectral theory, representation theory of algebras and groups, Lie theory, associative algebras, multilinear algebra.
- Modelling and Numerical Analysis - Numerical stability and convergence, optimisation.
- Number Theory - Algebraic and analytic number theory, Galois theory, elliptic curves, diophantine equations, arithmetic geometry.
- Partial Differential Equations - Existence and uniqueness, boundary conditions, linear and non-linear operators, dynamical systems and flows.
- Point-Set Topology - Normed and metric spaces, topological spaces, compactness, connectedness, completeness.
- Probability Theory - Measure theory, stochastic processes, central limit theorems, percolation theory, large deviations, stochastic differential equations, statistical mechanics and information theory, random graphs.
- Real Analysis and ODEs - Measure theory, calculus of variations, approximations, expansions, asymptotics.
- Set Theory - Ordinals, cardinals, axiom systems, ZFC, large cardinals, order theory, lattice theory, model theory, forcing.
- General Maths - Texts that cover a variety of topics, typically at an easier level than a textbook dedicated to one area; general reference books.
- Popular Maths - Maths books intended for a general audience, broader than just maths undergraduates.