**Introductory courses (Introduction to University Level Mathematics and Introduction to Complex Numbers) - M&P, M&CS**

*The purpose of these introductory lectures is to establish some of the basic language and notation of university mathematics, and to introduce elements of (naive) set theory and the nature of formal proof.*

**Linear Algebra I - M&P, M&CS**

*Linear algebra pervades and is fundamental to algebra, geometry, analysis, applied mathematics, statistics, and indeed most of mathematics. This course lays the foundations, concentrating mainly on vector spaces and matrices over the real and complex number systems.*

**Analysis I: Sequences and Series - M&P, M&CS**

*In these lectures we begin a rigorous treatment of the real and complex numbers, and study their properties, particularly completeness; we define and study limits of sequences, convergence of series, and power series.*

**Introductory Calculus - M&P**

*These lectures are designed to give students a gentle introduction to applied mathematics and at the end of the course, students will be able to solve a range of ordinary differential equations (ODEs). They will also be able to evaluate partial derivatives and use them in a variety of applications. *

**Probability - M&P, M&CS**

*The aim of this introduction to probability is to develop the concept of chance in a mathematical framework. Random variables are introduced, with examples involving most of the common distributions. Probability models considered include random walks and linear difference equations.*

**Geometry **

*The course is an introduction to some elementary ideas in the geometry of euclidean space through vectors. One focus of the course is the use of co-ordinates and an appreciation of the invariance of geometry under an orthogonal change of variable.*

**Computational Mathematics**

*Many mathematicians use general-purpose mathematical software which includes tools for symbolic and numerical computation and other features such as plotting, visualization and data analysis. In this introductory course, students will explore these ideas using the popular specialist mathematics software MATLAB software.*