Advanced Mathematics · University & competition
An extra-deep second-year BSc mathematics core with 15 units, 75 rigorous lessons in analysis, algebra, probability, applied mathematics and numerical methods.
Every topic, lesson by lesson.
Term 1 · Unit 1
Metric structure, rigorous continuity, differentiation and integration.
Term 1 · Unit 2
Multiple integration, vector fields and integral theorems.
Term 1 · Unit 3
Linear maps, canonical forms, inner products and spectral structure.
Term 1 · Unit 4
Abstract algebra through groups, homomorphisms and actions.
Term 1 · Unit 5
Complex functions, analytic structure and contour methods.
Term 2 · Unit 6
Systems, series solutions, transforms and nonlinear behaviour.
Term 2 · Unit 7
Continuous distributions, transforms, limit theorems and conditioning.
Term 2 · Unit 8
Likelihood, estimation, tests and linear models.
Term 2 · Unit 9
Conditioning, iterative linear algebra and approximation algorithms.
Term 2 · Unit 10
Connectivity, matchings, planarity and network optimisation.
Term 3 · Unit 11
Convexity, constrained methods and linear programming.
Term 3 · Unit 12
Lagrangian methods, oscillations and central-force motion.
Term 3 · Unit 13
Classification and foundational methods for heat, wave and potential equations.
Term 3 · Unit 14
Dimensional analysis, nondimensionalisation, validation and uncertainty.
Term 3 · Unit 15
Integrate rigorous pure and applied methods in extended 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.
