Advanced Mathematics · University & competition
An extra-deep final-year BSc mathematics core with 15 units, 75 rigorous lessons spanning modern pure, applied, stochastic and computational mathematics.
Every topic, lesson by lesson.
Term 1 · Unit 1
Sigma-algebras, measurable functions and Lebesgue integration.
Term 1 · Unit 2
Power series, residues and conformal structure.
Term 1 · Unit 3
Open sets, continuity, compactness, connectedness and quotient spaces.
Term 1 · Unit 4
Ideals, quotient rings, polynomial arithmetic and field extensions.
Term 1 · Unit 5
Normed spaces, operators, orthogonality and infinite-dimensional reasoning.
Term 2 · Unit 6
Weak formulations, Fourier methods and qualitative PDE analysis.
Term 2 · Unit 7
Nonlinear flows, stability, bifurcations and chaos.
Term 2 · Unit 8
Markov chains, Poisson processes, martingales and Brownian motion.
Term 2 · Unit 9
Bayesian inference, generalised models and multivariate methods.
Term 2 · Unit 10
Congruences, arithmetic functions and public-key ideas.
Term 3 · Unit 11
Integer optimisation, queues, decisions and stochastic operations.
Term 3 · Unit 12
High-quality computational linear algebra, simulation and reproducibility.
Term 3 · Unit 13
Multiscale structure, inverse problems, uncertainty and model ethics.
Term 3 · Unit 14
Literature, conjecture, proof, computation and mathematical exposition.
Term 3 · Unit 15
Integrate three years of mathematics in research-style unfamiliar problems.
Built from your saved practice attempts in this course, weakest question types first.
Complete a practice set in any lesson to see which question types to practise again.
This course satisfies the following education systems.
