MMath (Hons) Mathematics Integrated Master's degree at Keele University

The aim of this module is to support your progress from the methods-based approach to the higher levels of understanding and rigour expected at degree level Mathematics. You will be introduced to mathematical statements, the meaning of proof, and some proof strategies. The concepts of sets and functions will then be discussed. Finally, the module will cover the algebraic development of number systems and their properties.

This module aims at deepening your understanding and appreciation of the origins of the essential techniques of elementary calculus, explaining why these methods work. Starting with developing important preliminary ideas such as the real numbers, functions, sequences and series, on a more formal basis this leads to a fundamental concept of a limit, serving as a basis for further advances in differential and integral calculus.

This module aims to provide you with a self-contained and intensive summary of all the essential methods and techniques required at the start of an undergraduate programme in mathematics. The topics covered include algebra, calculus, functions, trigonometry, and vectors and, as such, the module provides a useful refresher of these. The module also ensures that all students cover the topics to the same depth and overcomes the differences in syllabi of various pre-University qualifications.

This module is designed specifically to help you develop mathematical communication and problem-solving skills. In this module, you will be presented with unfamiliar and less structured problems that may be open to several different approaches. This module will enhance your employability skills through teamwork on several group projects and focus on mathematical communication and presentation of your results. It will also help you appreciate mathematics as a powerful method for describing and so

This module will begin with an introduction to number theory by looking at topics such as divisibility, greatest common divisors and modular arithmetic with a strong emphasis on rigour. Then you will study core concepts from linear algebra including matrix algebra, solving linear equations, determinants, eigenvalues and eigenvectors. You will also cover aspects of vector algebra with a particular emphasis of on three-dimensional vector algebra and geometry with a discussion on lines and planes,

Many real-world problems are governed by differential equations, the solution of which can help us understand their properties. For instance, oscillation of a pendulum, and the population evolution of a fish species, can all be described by ordinary differential equations. This module, being a prerequisite for several modules in the second and third years, will introduce you to the basic techniques for solving differential equations and familiarize you with multivariable calculus, including part

This module aims to provide you with a sound knowledge of core statistical concepts, skills and techniques. It will enable you with applying statistical ideas to solve problems from a wide range of disciplines; developing competency in interpreting and explaining solutions of problems in non-technical language; giving fluency in procedural skills, common problem-solving skills and strategies; using statistical tools to analyse real data sets in the statistical software environment R.

In this module you will learn to apply a variety of computational problem-solving techniques to solve problems from the real world. You will be introduced to algorithmic design strategies and learn how to analyse an algorithm to determine its correctness and efficiency, to solve problems from a variety of real-world domains. You will learn transferable skills such as interdisciplinary expertise, creativity, and problem-solving.

Differential equations are used as mathematical models describing various processes in the real world. This helps investigating problems related to population dynamics, heat dissipation in objects, vibrations of engineering structures and wave propagation, among many others. Some situations require more than one differential equation to be solved at once, e.g., modelling dynamics of two populations (e.g., foxes and rabbits). Within this module you will study a variety of methods for solving diff

Probability is the mathematics of uncertainty and randomness. You will begin with classical notions of probability associated with the analysis of games of chance using cards, dice, etc., then moving to treatment of probability of random events and further to definitions of statistical independence and conditional probability. Then, you will study discrete and continuous, univariate and bivariate, random variables, covering key concepts of expectation, variance, covariance. Applications to a wid

The aim of this module is to introduce you to the three elements of scientific computing; numerical analysis, programming and modelling. The programming element provides you with valuable transferrable skills in Python. No prior knowledge of the language is assumed or required for the module. We also aim to give you a broad appreciation of the Jupyter environment for writing Python code, displaying computational results and annotating the algorithmic developments with the underpinning mathematic

Algebra and analysis are two of the main branches of pure mathematics. Linear algebra generalises vector and matrix algebra encountered at Level 4. Mathematical analysis, dealing with the infinitely small and large, aims to provide rigorous theoretical foundations for calculus. You will study abstract vector spaces, focussing on the role of bases in describing elements. You will also cover rigorous proofs for calculus results. Each topic will be introduced via guided investigations, followed by

This module will introduce you to both vector calculus and complex variable. Vector calculus studies vector functions of one or more real variables and its techniques and results are essential tools in many areas of applied mathematics, such as fluid mechanics. Complex variable studies functions mapping complex numbers to complex numbers. In this module, you will achieve elegant results in integration which can often be used to evaluate definite integrals of real-valued functions, without any kn

Abstraction is a powerful idea in Mathematics: by focusing on the underlying properties of Mathematical systems we can identify connections and similarities that are not visible on the surface. In this module you will explore these techniques and styles of thinking. The central concept is that of a group. You will study some of the fundamental abstract results concerning groups.