MMath (Hons) Mathematics Integrated Master's degree at the University of Surrey

This module introduces students to the most important techniques in Calculus. In particular, the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide fundamental tools for quantitative descriptions of the real world across the entirety of applied mathematics. Tools and methods for differentiation and integration will be presented in detail. In addition, simple first and second order ordinary differential equations will be studied.

This module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.

This module is an introduction to analysis, which is the branch of mathematics that rigorously studies functions, continuity and limit processes, such as differentiation and integration. The module leads, among other things, to a deeper understanding of what it means for a sequence or series to converge. Tools such as convergence tests are presented and their validity proved, and the rigorous use of definitions and logic play a central role.

Probability is a numerical description of random events, and statistics is the science of collecting and analysing data from these random events and modelling them with random variables. Students will be introduced to the basic concepts of probability distributions, hypothesis testing and random variables. These concepts are fundamental in probability and statistics and lay the foundations for Level 5 Mathematical Statistics (MAT2013), Linear Statistical Methods (MAT2053) and Stochastic Processe

This module is an introduction to Linear Algebra, a fundamental mathematical discipline that revolves around the exploration of vector spaces as well as linear maps between these spaces. This often necessitates the solution of systems of linear equations, which are elegantly described by matrices and vectors. Techniques from Linear Algebra find application in numerous disciplines ranging from pure and applied mathematics to many fields of science, engineering, computing and economics.

Much of the way that mathematicians model the physical world today relies on the mathematical framework set out by Newton in the 17th century. In this module, we take as our starting point Newton's laws of motion and examine how they may be applied to study the dynamics of particles and mechanical systems. This module provides a foundation for MAT3008 Lagrangian and Hamiltonian Dynamics.

Programming is a companion to the modern mathematician and provides a means to tackle and provide insight into problems which are insoluble by analytical means alone. This module will first develop core programming capability and knowledge of fundamental aspects of programming, including loops, functions and conditional statements. Building on these foundations, the module will then cover aspects of the analysis and visualisation of data, including linear regression to model and interpret quanti

This module introduces students to Multivariable Calculus in two and three dimensions, and selected topics such as differential operators and line integrals in Vector Calculus. This extends students' knowledge developed in MAT1030 Calculus on differentiation and integration of single variable functions to partial differentiation, and double and triple integration of two and three-variable functions. This module provides the necessary ground work for modules such as MAT2047 Curves and Surfaces, M

Analysis is the branch of mathematics that rigorously studies functions, continuity, differentiability and integration. This module builds on Level 4 Real Analysis 1 (MAT1032) by studying these concepts in a more formal way and hence provides a deeper understanding of these concepts.

This module builds on the differential equation aspects of the Level 4 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.

This module is an introduction to the theory of complex functions of a complex variable, also known as complex analysis. We will study the continuity and differentiability of complex functions, integration along paths on the complex plane, Taylor and Laurent series expansions of complex functions with isolated singularities, and residue calculus and its applications. Complex analysis and residue calculus are widely used in many branches of Mathematics and Physics.

This module introduces a variety of commonly used techniques from Operations Research. The module leads to a deeper understanding of linear programming problems and the theory that underpins their solving. Tools such as the Simplex Method are presented and an introduction to nonlinear optimisation methods is also provided. This module supports and complements other modules where optimisation and constrained optimisation are considered.

Statistics is the science of collecting and analysing data from random events and modelling them using random variables. This module first recaps the properties of a single random variable as seen in Level 4 Probability and Statistics (MAT1033), then builds on this by considering multiple random variables simultaneously. This module also covers the transformation of random variables, as well as applications such as tail probabilities and limit theorems.

The module provides an introduction to the theory and properties of curves and surfaces in Euclidean space. Basic concepts and tools from a branch of mathematics known as differential geometry are used to study curves and surfaces, and to understand their geometric properties. This module builds on material from MAT1043 Multivariable Calculus and MAT1034 Linear Algebra. The module is recommended for students intending to select the Year 3 modules MAT3009 Manifolds and Topology, and MAT3044 Riema