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Mathematics Options

Choosing your options in mathematics is an important part of the Maths/Physics degree in the second, third and fourth years. 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. You can 'sample' more options than you are required to take before committing yourself. However, lecture modules are taught on the basis that you are keeping up with the material and completing the problem sheets.

The maths modules can be loosely grouped into the four categories shown below. The natural areas for maths/physics students to concentrate on are Applied Mathematics and Analysis. The categories are rough and ready. 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 dropdown menu Mathematical Physics on the right-hand side. You should note that not all modules are taught every year and that from time to time new modules may be introduced and others discontinued.

Choices in pure mathematics in the second year are particularly important. If you want to continue with analysis beyond the second year, you should take Metric Spaces.

Only the modules which would normally be taken by a significant number of Maths/Physics students are included in the course regulations and these are predominantly from the categories Applied Mathematics and Analysis. However, you are free to take other modules available to mathematics students. Please note that you may not take Mathematical Methods for Physicists. To take an unusual option, you should obtain the necessary permission from the lecturer offering the module. You should then complete an unusual option form.

In addition to the options listed, it is possible to take certain modules, offered by other departments, as unusual options. You must consult your Personal Tutor, in advance, in order to obtain the necessary permission (you will also need to obtain approval from the department offering the module).

The maths modules are listed below by area. However, you should note that the provision does change from year to year. Fourth year (Maths List C) modules are in italics. Modules marked with an asterisk are those which are not listed explicitly in the Maths/Physics course regulations.

APPLIED MATHEMATICS
Second Year
Partial Differential Equations (core); Methods of Mathematical Physics (core); Hamiltonian and Fluid Mechanics (core); Mathematical Methods and Modelling 3; Theory of ODEs*; Introduction to Mathematical Biology*; Asymptotics and Integral Transforms*; Numerical Methods and Computing*;

Third and Fourth Years
Fluid Dynamics (core for MMathPhys students);
Topics in Mathematical Biology; Theory of PDEs; Numerical Analysis and PDEs*; Markov Processes and Percolation Theory*; Control Theory*; Bifurcations, Catastrophes and Symmetry*; Mathematical Modelling with PDEs*; High-dimensional Probability*; Maths of Machine Learning; Problem Solving with Python*; Mathematics of Digital Signal Processing*; Dynamical Systems; Quantum Mechanics: Basic Principles and Probabilistic Methods; Population Dynamics: Ecology and Epidemiology; Applied Dynamical Systems*; Continuum Mechanics*; Structures of Complex Systems; Advanced Topics in Fluids; Large Deviation Theory*; Epidemiology by Example*; Mathematics of Inverse Problems*; Topics in Complexity Science*; Complex Dynamics*; Mathematics of Neuronal Networks*; Theorem Proving with LEAN*; Hyperbolic Dynamics*;

ANALYSIS
Second Year
Mathematical Analysis III (1-10, core); Metric Spaces; Multivariable Analysis;

Third and Fourth Years
Complex Analysis; Measure Theory; Functional Analysis I: Applied Analysis; Functional Analysis II: Linear Analysis; Manifolds*; Ergodic Theory*; Fourier Analysis; Stochastic Analysis*; Advanced PDEs; Brownian Motion*; Modular Forms*; Advanced Real Analysis*; Symmetric Functions and Integrable Probability*;

ALGEBRA, COMBINATORICS and NUMBER THEORY
Second Year
Multilinear Algebra; Combinatorics*; Groups and Rings*; Combinatorial Optimization*; Introduction to Number Theory*;

Third and Fourth Years
Rings and Modules*; Matrix Analysis and Algorithms*; Algebraic Number Theory*; Galois Theory*; Groups and Representations*; Commutative Algebra*; Set Theory*; Combinatorics II*; Introduction to Group Theory*; Boolean Functions*; Topics in Set Theory*; Group Theory*; Lie Algebras*; Reflection Groups*; Lie Groups*; Geometric Group Theory*; Ring Theory*; Commutative Algebra II*; Analytic Number Theory*; Category Theory*; Theorem Proving with Lean*;

GEOMETRY and TOPOLOGY
Second Year
Geometry

Third and Fourth Years
Fractal Geometry*; Geometry of Curves and Surfaces*; Introduction to Topology*; Algebraic Topology*; Elliptic Curves*; Hyperbolic Geometry*; Algebraic Geometry*; Differential Geometry*; Graph Theory*; Cohomology and Poincare Duality*; Algebraic Curves*; Theory of Random Graphs*;