# Self Evaluation

**First Year** and **Second Year** examination questions

First-year questions

First-year answers

Second-year questions

Second-year answers

You should feel comfortable with all questions at this level. There may be small gaps in your knowledge and there may be material which you have forgotten over time or which you learned in a different way. For example you may be unfamiliar with certain notation used in these examples. The questions were clearly written for someone who had followed the module in question. With a small amount of review you should be able to answer these questions. **The essential thing is that you feel comfortable with all of this material.**

**Third Year** examination questions

Algebraic Number Theory

Commutative Algebra

Complex Analysis

Fluid Dynamics

Fractal Geometry

Functional Analysis I

Functional Analysis II

Galois Theory

Geometry of Curves and Surfaces

Groups and Representations

Introduction to Mathematical Biology

Introduction to Topology

Knot Theory

Matrix Analysis and Algorithms

Measure Theory

Modern Control Theory

Probability Theory

Qualitative Theory of ODEs

Rings and Modules

Theory of PDEs

Topics in Mathematical Biology

Here the material is much more varied and it is possible that you will not have studied a number of these subjects before.

Students interested in Interdisciplinary Mathematics who have previously studied in some subject outside of mathematics may find this material to be quite advanced. As a rule, if you come from a discipline outside of mathematics, you should minimally be able to do all the first and second year questions.

Students interested in the Two-year MSc may not have seen most of this material before. As a rule, to undertake the Two-year MSc you should minimally be able to do all the first and second year questions **and** you should be prepared to take third-year modules and at least one masters level module in your first year. However, you should feel that this is material is at a level which you can master if you come to Warwick.

As an MSc or qualifying PhD student you will be taking modules with fourth year Warwick undergraduate mathematics students who have passed several third year examinations in the preceding year. It is possible you will want to do some background reading over the summer.

**Fourth Year and Masters Level** examination questions

Advanced PDEs

Algebraic Topology

Applied Dynamical Systems

Dynamical Systems

Ergodic Theory

Hyperbolic Geometry

Lie Algebras

Lie Groups

Manifolds

Population Dynamics

Riemann Surfaces

Stochastic Analysis

Here too the material is quite varied. It is possible that you have not have studied any of these subjects before. You should focus on those modules you think you would like to follow. (Note that not all modules are available every year.) You should feel that this is material is at a level which you can and want to master if you come to Warwick.

We do not want to discourage prospective students - we want to give you a straightforward method of determining whether you are prepared for serious mathematical study at Warwick.