The Single Honours course in Mathematics provides an opportunity for breadth of study that more traditional Single Honours Mathematics courses do not allow. In particular, it has a high content of statistics and operational research, the quantitative analysis of decision-making, and experience of these fields enriches and widens mathematical study significantly. Whilst providing a firm foundation in pure mathematics, applied mathematics and statistics, the course has a strong element of flexibility; for example, in the final year it is possible for students to concentrate in any of these areas.
The aim of the first part of this module is to introduce students to the fundamental mathematical concepts of logic, numbers, sets and functions in a setting that will be unfamiliar in its level of abstraction, but that will provide an essential grounding for later modules. Progressing to complex numbers, polynomials and divisibility in the set of integers, this module also introduces students to the Fundamental Theorems of Arithmetic and Algebra. The concept of rigorous proof is central to all of the material in this module.
Dr. D. Bedford and Neil Turner
This module forms a bridge between A-level and University level mathematics. Many of the topics covered will be familiar, but the emphasis will be different, focusing on understanding and tackling some of the more technical issues necessarily left unresolved at A-level. Starting with a brief look at the real number system, the module then examines real-valued functions and, in particular, the trigonometric, exponential and logarithmic functions. Moving on to the notion of a ‘limit’, the module then discusses infinite series, differentiation and integration in a rather more careful and precise way than at A-level. The module closes with an introduction to differential equations.
Lecturers : Prof. D.A. Quinney and Andrew Looms
This module will expose students to numerical methods for solving algebraic and differential equations, iteration techniques and numerical integration. One aim of the module is to familiarise students with appropriate technology for solving problems numerically and, in particular, to introduce and provide a working knowledge of Mathematica®, a powerful software package useful in many diverse areas of mathematics.
This module introduces students to formal analysis, and its core concept of a limit, in the context of sequences, infinite series and functions. Extending these ideas to the definition of continuity of functions, students will see how a rigorous foundation for differential calculus is achieved.
The first two-thirds of this module concentrate on an introduction to linear algebra. Topics studied are systems of linear equations, matrices and their algebra, determinants, vectors in 2-, 3- and n- dimensional Euclidean space and a brief introduction to some of the basic concepts of general vector spaces. The emphasis is on precise derivation of results and drawing together apparently disparate areas of mathematics. The final third combines elements of geometry and linear algebra to examine the important optimisation technique of linear programming. This is used extensively in organisational and manufacturing contexts.
Building on the foundations of Calculus I, this module is largely techniques based, with much of the material being essential for second and third year applied and methods modules. Divided into three parts, the first topic of study is that of ordinary differential equations, including linear and nonlinear first-order equations and certain classes of second-order linear equations. The second part of the module studies the theory and application of Taylor series, whilst the third part introduces students to functions of two variables, including partial differentiation and double integration techniques. There is also a brief introduction to partial differential equations.
This module in pure mathematics, which is available to Single Honours students only, explores a subject that has become virtually extinct in the school curriculum. The module begins with a detailed examination of the geometry of the Euclidean plane, as first explored by the mathematicians of ancient Greece. It then progresses to examine straightedge and compasses constructions, constructible numbers, isometries of the plane, together with some non-Euclidean geometries, such as projective geometry and hyperbolic geometry. A study of the symmetries of polygons and polyhedra will introduce students, in an intuitive way, to an algebraic structure called a group. The module concludes with a brief treatment of knots.
This module is designed to assist students’ appreciation of mathematics as a tool for describing and solving real-world problems. In addition it aims to help students to make the transition from A-level to undergraduate mathematics; as such it concentrates on mathematical problem solving that moves away from the examples-based methods encountered at A-level towards the more sophisticated approaches expected at degree level and in employment. Physical or computer experiments will be used to motivate the study of a number of phenomena. The mathematical and problem solving ideas will be developed throughout the module by means of group projects.
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