# Mathematics and Physics - Year 1

This document provides information for first year students taking either the BSc or MMathPhys Mathematics and Physics degree courses, which are identical in content for the first 2 years.

We hope that you will find this document useful, and that it will help you to complete successfully your first year at University. If you consider that there is information which could usefully be added, or if you discover an error, please inform either the Director of Education, who is in overall charge of the teaching, or the Senior Tutor.

#### Introduction

All the first year mathematics modules spend a large fraction of the time setting up the right language and notation to address the questions one would like to ask. You will find that language in mathematics is an integral part of the subject. Identifying the right language and syntax for making statements and constructing logical arguments is important for understanding any result or theorem in mathematics.

Most of the first year physics modules can be seen as natural extensions of A-level physics. They deal with the same important concepts such as energy, mass, electricity and heat. The two possible exceptions are the modules on Relativity and Quantum Phenomena which deal with the breakdown of 'traditional' Newtonian physics at velocities close to the speed of light and at atomic length scales in quantum physics. In all the modules, you will find that there is more emphasis on finding and analysing precise mathematical statements of the underlying phenomena than is normal at A-level.

Everyone on the joint honours Mathematics and Physics course has A-levels (or equivalent) in mathematics and physics and some have further mathematics A-level. However, there is a lot of variation between the syllabuses set by the various boards and everyone has different strengths. An essential part of the first year is therefore to revise important elements from A-level.

The actual mechanisms of teaching are very different at university. Most new material is introduced in lectures, which can involve up to three hundred and fifty students in some first year classes. There is therefore no real opportunity in the lectures themselves to interrupt and ask questions. Instead there are separate supervisions in mathematics and examples classes in physics which support the lectures. There are also tutorials with your personal tutor. The tutorials/supervisions are the place to ask questions and go through difficulties associated with any of the material presented in lectures. The tutors also help you with the problem sheets handed out in conjunction with the lectures and mark some of your answers. These marks are recorded and form part of the overall assessment of your work.

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

#### Aims

- To introduce the language and style of mathematics
- To introduce the three main areas of mathematics: Analysis, Algebra and Applied Mathematics
- To introduce the core areas of physics (Quantum & Classical Mechanics, Electricity & Magnetism, Thermodynamics) which are the basis of many future modules
- To introduce computers as an essential tool in any scientific environment
- To revise important elements of the A-level syllabuses in the two subjects

#### Objectives

At the end of the first year, you should

- Be familiar with vector spaces and set theory and their use in describing relations and functions
- Understand the significance of limit processes and important definitions and theorems relating to continuity, differentiability and Taylor's theorem
- Be competent in solving differential equations and the use of calculus in more than one dimension
- Be familiar with concepts in classical and quantum mechanics, electromagnetism and classical thermodynamics
- Be familiar with Python