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 all the key areas of mathematics, this is very difficult in the second and later years - even for students studying maths on its own.

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. 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.

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 almost any other module available to mathematics students as unusual options. Please note that you may not take Mathematical Methods for Physicists nor Mathematical Methods for Physicists III (which cover material you meet in the modules Vector Analysis, Partial Differential Equations and Variational Principles), nor may you take MA117 Programming for Scientists after year 1. 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 (available from the Undergraduate Office - Room 568).

The second year mathematics modules which are core for mathematics students but not for maths/physics students are Algebra I: Advanced Linear Algebra, Algebra II: Groups and Rings, Metric Spaces and Differentiation. The last two of these are available to you as normal options in both the second and third years. Algebra I would probably be the most valuable to you overall, as it deals with some basic ideas used in many parts of mathematics. Metric Spaces contains material needed by many later modules in both analysis and geometry. If you are keen to push ahead with your analysis, this module is recommended although it has the reputation of being 'demanding'.

It is recommended that you 'sample' more options than you are required to take before committing yourself and you may, if you wish, attend a complete module and not register for the examination. You should note that any options you do not take in the third year can normally be taken in the fourth year.

In addition to the options listed, it is possible to take certain other modules, offered by other departments, as so-called `Unusual Options'; If you wish to avail yourself of this possibility 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).

In the lists below, most of the maths modules are listed. 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); Vector Analysis (core); Methods of Mathematical Physics (core); Physics of Fluids (core); Numerical Analysis; Theory of ODEs; Virtual Mathematics^*; Variational Principles (core); Introduction to Systems Biology;

Third and Fourth Years
Fluid Dynamics (core for MMathsPhys students); Topics in Mathematical Biology; Problem Solving^*; Theory of PDEs; Numerical Analysis and PDEs^*; Markov Processes and Percolation Theory^*; Control Theory^*; Equivariant Bifurcation Theory^*; Mathematical Modelling and PDEs^*; Dynamical Systems; Quantum Mechanics: Basic Principles and Probabilistic Methods; Asymptotic Methods; Population Dynamics: Ecology and Epidemiology^*; Brownian Motion^*; Introduction to Theoretical Neuroscience; Calculus of Variations^*; Mathematics and Biophysics of Cell Dynamics; Introduction to Uncertainty Quantification^*; Optimisation and Fixed Point Theory^*; Topics in Interacting Particle Systems^*; Advanced Topics in Fluids; Math Modelling in Biology and Medicine^*; Statistical Mechanics; Large Deviation Theory^*

Analysis

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


Third and Fourth Years
Complex Analysis; Measure Theory; Functional Analysis I: Applied Analysis; Functional Analysis II: Linear Analysis; Manifolds^*; Ergodic Theory^*; Fourier Analysis; Riemann Surfaces^*; Stochastic Analysis^*; Advanced PDEs; Modular Forms^*; Advanced Real Analysis^*;

Algebra

Second Year
Combinatorics^*; Algebra I: Advanced Linear Algebra; Algebra II: Groups and Rings; Number Theory^*; Combinatorial Optimization^*; Probability and Discrete Mathematics^*, Introduction to Number Theory^*

Third and Fourth Years
Rings and Modules^*; Algebraic Number Theory^*; Galois Theory^*; Groups and Representations^*; Further Combinatorics^*; Commutative Algebra^*; Set Theory^*; Tensors, Spinors and Rotations^*;Group Theory^*; Lie Algebras^*; Representation Theory^*; Lie Groups^*; Geometric Group Theory^*; Ring Theory^*;

Geometry and Topology

Second Year
Geometry

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