Mathematics Options

Choosing your options in mathematics is an important part of the Maths/Physics course. Whereas it is possible in the first year to cover the main areas of mathematics, this is difficult in the second and later years - even for students studying maths on its own. Remember that all lecture modules are taught on the basis that you are keeping up with the material and completing the problem sheets. Only the modules which would normally be taken by a significant number of Maths/Physics students are included in the course specifications but you are free to take other modules available in the diet.

The modules can be loosely grouped into four categories below. The natural areas for maths/physics students to concentrate on are Applied Mathematics and Analysis. Within the Applied Mathematics section, good modules to consider are the modules which are about physics or the mathematics directly used in physics. These are listed in the menu Mathematical Physics. Not all modules are taught every year and new modules may be introduced and others discontinued.

In general it is ONLY sensible to take modules on algebra or analysis if you are committing to take significantly more than one module in these areas (as many maths students do). The modules reinforce each other strongly. If you want to continue with analysis beyond the second year, you should take Metric Spaces.

Modules marked with an asterisk are those which are not listed explicitly in the Maths/Physics course regulations. All names should work as links.

Applied Maths

Second Year
Partial Differential Equations (core); Methods of Mathematical Physics (core); Hamiltonian and Fluid Mechanics (core); Modelling Nature's Nonlinearity^*; Theory of ODEs^*; Introduction to Mathematical Biology^*; Asymptotics Methods^*; Complex Methods*; Probability: Structures and Examples^*; Numerical Analysis and ODEs^*

Third Year
Fluid Dynamics (core for MMathPhys students);

Mathematics of Cryptography*; Waves and Metamaterials^*; Electromagnetism; Topics in Mathematical Biology; Matrix Analysis and Algorithms^*; Data Driven Mathematical Modelling^*; Theory of PDEs; Numerical Analysis and PDEs^*; Markov Processes and Percolation Theory*; Control Theory^*; Bifurcations, Catastrophes and Symmetry*; Mathematical Modelling with PDEs; Approximation Theory and Applications^*; Probability in Many Variables^*; Maths of Machine Learning; Problem Solving with Python^*; Mathematics of Digital Signal Processing^*; Optimisation^*;

Fourth Year
Dynamical Systems; Quantum Mechanics^*; Calculus of Variations^*; Continuum Mechanics^*; Structures of Complex Systems^*; Advanced Topics in Fluids; Statistical Mechanics; Mathematics of Cancer^*; Epidemiology by Example^*; Mathematics of Inverse Problems^*; Mathematics of Neuronal Networks^*; Theorem Proving with LEAN^*; Transport Processes in Mathematical Biology^*; Finite-element methods for PDEs^*;

Analysis

Second Year
Mathematical Analysis 3 (1-10, core); Metric Spaces; Multivariable Calculus;

Third Year
Complex Analysis; Measure Theory; Functional Analysis I; Functional Analysis II; Manifolds^*;

Fourth Years
Ergodic Theory^*; Fourier Analysis; Stochastic Analysis^*; Advanced PDEs; Advanced Real Analysis^*; Symmetric Functions and Integrable Probability^*;

Algebra, Combinatorics, Numbers

Second Year
Multilinear Algebra ; Combinatorics^*; Groups and Rings; Introduction to Number Theory^*;

Third Years
Rings and Modules^*; Matrix Analysis and Algorithms^*; Algebraic Number Theory^*; Galois Theory^*; Groups and Representations^*; Algebraic Topology^*; Commutative Algebra^*; Set Theory^*; Combinatorics II^*; Introduction to Group Theory^*; Boolean Functions^*;

Fourth Years
Lie Algebras^*; Presentations of Groups^*; Reflection Groups^*; Lie Groups^*; Geometric Group Theory^*; Modular Forms^*; Commutative Algebra II^*; Analytic Number Theory^*; Theorem Proving with Lean^*; Topics in Set Theory^*

Geometry and Topology

Second Year
Geometry^*

Third Year
Fractal Geometry^*; Geometry of Curves and Surfaces^*; Introduction to Topology^*; Algebraic Topology^*; Knot Theory^*;

Fourth Year
Elliptic Curves^*; Hyperbolic Geometry^*; Algebraic Geometry^*; Differential Geometry^*; Graph Theory^*; Cohomology and Poincare Duality^*; Algebraic Curves^*; Theory of Random Graphs^*;

MATHEMATICAL PHYSICS
Complex Methods (2nd/3rd Yr)
Continuum Mechanics (4th Yr)
Electromagnetism (3rd Yr)
Fluid Mechanics (3rd Yr)
Fluid Mechanics (4th Yr)
Quantum Mechanics (4th Yr)
Statistical Mechanics (4th Yr)
Transport Equations (3rd Yr)
Waves and Metamaterials (3rd Yr)