# Mathematics and Physics - 2nd Year

This document provides information for second year students taking either the BSc or MMathPhys Mathematics and Physics courses, which are identical in content for the first 2 years. It should be read in conjunction with the general teaching documents here.

We hope that you will find this document useful, and that it will help you to complete successfully your second year at University. If you consider that there is information which could usefully be added, or if you discover an error, please inform Nicholas d'Ambrumenil.

## Introduction

The core modules in the second year complete your basic training in analysis and the mathematical techniques of theoretical physics and introduce some of the most fundamental ideas in physics. The implications of some of these ideas will be explored in the third and fourth years.

You will have to choose 30% (or more if you take more than the normal load) from lists of options. There is a lot on offer particularly in mathematics and it is unlikely that you could cope with everything even if you wanted to! As a result, you will need to think carefully about your choice of options.

The mathematics options allow you to continue with algebra and geometry and to study some advanced analysis. It is certainly worth starting some of these modules and making up your mind after you have seen what is involved.

The picture with regard to physics options is slightly different. The large part of physics which you leave out, namely laboratory work, is not available. As a result you have room to cover most of the mainstream areas of physics.

This year's course has been designed with the following aims and objectives.

## Aims

- To continue the training in Real Analysis required by future mathematics courses
- To teach mathematical techniques and their applications in applied mathematics and physics including: Vector Calculus, Fourier methods, Separation of Variables, Variational Principles, Complex Variable Theory
- To teach concepts in the three areas of fundamental physics: Electromagnetism, Quantum Mechanics and Statistical Mechanics
- To help students identify their talents and interests and guide each student towards an appropriate combination of modules
- To encourage initiative, self-reliance and the development of transferable skills in communication, problem-solving and computing

## Objectives

At the end of the second year, you should

- Be familiar with some important theorems on integration, convergence of sequences of functions. (These will be assumed in future mathematics modules.)
- Know how to use Fourier methods, separation of variables, results from vector analysis (divergence and Stokes' theorem in particular), complex analysis and variational methods
- Have a good working understanding of the principles of quantum mechanics, statistical mechanics and electromagnetism
- Have studied further topics in mathematics and physics including fluid mechanics
- Be aware of your particular strengths and be ready to choose which modules to study in your third year

## MMathPhys

Please note that continuation to the 3rd and 4th years of the MMathPhys programme is ** not automatic**. To continue on the MMathPhys Mathematics and Physics degree programme you will need to obtain a II.i in the second year examinations. If you drop below this level, you will normally be required to revert to the 3rd year of the BSc degree programme.

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