# Mathematics and Physics - Year 1

Mathematics at university has a different flavour from A-level mathematics. The emphasis in the analysis and algebra modules is on abstraction proof and generality. The modelling modules concentrate on the differential equations used to describe phenomena we observe and their generalisation to higher dimensions. The first year physics modules deal with the important concepts of energy, mass, electricity and heat. You will find that there is more emphasis on precise mathematical statements of the theory than is familiar from A-level.

The first year has a tight structure of integrated lectures and problem solving. The modules are supported by separate weekly examples classes, supervisions and academic tutorials. Prior to each examples class and supervision you must hand in your written attempts to the problems for marking by the class supervisor.

#### 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

#### Learning Outcomes

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