The aims of this module are:

• To give a rigorous introduction to the analytical theory underpinning calculus for functions of one real variable.
• To develop the basic ideas of real analysis in several variables.

The aim of this module is to introduce the basic ideas and methods of the classical differential geometry of curves and surfaces in three-dimensional Euclidean space.

The aims of this module are:

• To introduce basic concepts and methods of probability theory.
• To provide the requisite theoretical background for later probability and statistics modules.

The aim of this module is to introduce students to the classical results in the theory of analytic functions of a complex variable.

The aims of this module are:

• To introduce the main ideas and techniques of the qualitative theory of ODEs and the calculus of variations.
• To teach students how to apply these ideas and techniques to the study of systems of ODEs and variational problems.

The aim of this module is to give a grounding in the central ideas of topology, sufficient for the main applications in geometry, analysis and mathematical physics.

The module aims to develop students' ability to communicate mathematical content clearly and in a manner that is appropriate to the target audience.

The aims of this module are to:

• Raise students' awareness of the nature of mathematics and how this can affect learning and teaching.
• Introduce students to what it means to learn and teach mathematics.
• Encourage them to reflect critically on their own experiences.
• Consider issues that are central to effective education in mathematics.

The aims of this module are:

• To introduce fundamental statistical concepts.
• To introduce statistical methods and associated theory for design and analysis of studies and experiments.
• To develop statistical software skills.
• To reinforce skills regarding the interpretation of statistical analyses.

The aims of this module are to introduce students to modern concepts and methods of combinatorics and graph theory.

The aims of this module are to introduce the students to the basic notions and methods of classical analytical dynamics.

The aim of this module is to give a theoretical and practical knowledge of numerical methods for the approximation of ordinary and partial differential equations.

The aims of this module are:

• To introduce fundamental statistical modelling concepts.
• To introduce associated theories for statistical inference.
• To develop statistical software skills.
• To reinforce skills regarding the interpretation of statistical analyses.