Mathematics with Computer Science BSc

Compulsory

• Fundamentals of Mathematics

  Aims to manipulate mathematical expressions accurately, as well as recall and use mathematical formulae in areas of interest for Year 1. To develop skills in handling summation notation. To introduce students to fundamental results in mathematics. To develop an understanding of the need for rigour in definitions and proofs. To introduce the language of formal mathematics, in particular sets and functions.

• Calculus 1
  This module aims to familiarise students with the basic results, techniques and elementary functions of differential and integral calculus, to introduce students to rigorous definitions, arguments and proofs through many simple examples, to develop students’ manipulative skills in performing operations in differential calculus through work on many simple examples, and to illustrate the solution techniques of first order differential equations.
• Calculus 2

  Aims to further develop skills in differential and integral calculus and associated applications. To further develop students’ manipulative skills in performing operations in differential calculus through work on examples, including solution techniques of ordinary differential equations.

• Introductory Programming

  This module aims to provide a basic level of programming competence.  

• Linear Algebra
  This module aims to enable students to understand and become proficient in basic linear algebra and the algebra of complex numbers, to determine the eigenvalues and eigenvectors of matrices and understand their role in the theory of similar matrices and diagonalization, and to see and practice applications of linear algebra.
• Programming Applications

  This module aims to provide opportunities for students to apply fundamental programming concepts as a solution to non-trivial problems.  

Compulsory

• Fundamentals of Alogrithms

  This module aims to develop knowledge and comprehension of various valuable data structures and algorithms, to stimulate critical thinking and enhance skills in evaluating the trade-offs involved in selecting the most suitable algorithms for specific purposes. 

• Algorithms and their Applications

  This module aims to develop an understanding of a set of useful data abstractions and algorithms, to stimulate students' critical thinking and develop their ability to choose appropriate algorithms in solving practical problems and implementing them in software. 

• Calculus 3

  Aims to develop ideas and methods of multivariable calculus, including Taylor series, extrema, the use of Lagrange multipliers, and the integration of functions of several variables. To understand the extension from single variable to several variables of basic concepts such as continuity and differentiability.

• Software Development and Management

  The module aims to develop the knowledge and skills necessary for the design and implementation of software systems using recognised methodology, tools and technologies.  The module provides an introduction to software engineering and follows a development process from requirements and design through to implementation, creating a number of software artefacts. 

• Discrete Mathematics

  Graphs serve as a background for many important problems in real world applications. This gives an understanding of this area of discrete mathematics, and develops a knowledge of graph theory applications. Also, to introduce operational research optimisation modelling and problem solving and, in particular, linear programming (LP) problems. To introduce algorithms for numerical optimisation and the modelling of random events.

Compulsory

• Artificial Intelligence

  This optional module aims to develop understanding of the basic principles and techniques for the computer-based simulation and modelling of intelligent behaviour.

• Final Year Project
  This module aims to stimulate independent learning and critical thinking by the student, both as a means for studying their chosen topic and for approaching other real-life problems, to enable the student to plan and execute a major piece of work with limited input from a more experienced worker, and to give the student experience in the written communication of complex ideas and concepts and the presentation of a substantial piece of work.
• Software Engineering

  This optional module aims to provide a grounding in topics that directly influence the quality of software, an understanding of key artefacts that inform software quality from a process and product perspective (in particular, the use of and application of software metrics), and to articulate the state-of-the-art in terms of topics such as software patterns, service-oriented engineering and security issues. 

Optional

• Encryption and Data Compression
  This module aims to familiarise students with techniques widely used in data encryption and compression, and to study mathematical and algorithmic issues and their implications for encryption and compression in practice.
• Numerical Methods for Differential Equations
  This module aims to introduce numerical methods used to solve problems in financial mathematics, in particular option pricing, and implement them. Most examples treated will be taken from finance, but the module will be suitable for students mostly interested in advanced numerical methods, in particular finite differences algorithms used to approximate solutions of PDEs. The Matlab implementations of the algorithms will be an important part of the module.
• Ordinary and Partial Differential Equations
  This module aims to introduce students to the mathematics of differential equations; techniques of analysing such equations, and methods of solving them, exactly or approximately.
• Stochastic Models
  This module aims to introduce students to the concept of a stochastic process, so that they may develop an understanding of the theory underlying some of the standard models and acquire knowledge of methods of applying these models to solve problems. Students will further develop their general ability to think abstractly, to generalise, to formulate and structure stochastic problems, and to apply their knowledge of analytical and numerical mathematical techniques to solving a variety of problems in stochastic modelling.
• Decision Making in the Face of Risk
• Deep Learning

  Within this module, an in-depth introduction will be provided to the area of learning using deep neural networks. A wide variety of the architectures of deep neural networks and their learning methods will be covered, including convolutional networks, recurrent networks, generative models and deep reinforcement learning etc. The main focus of the module is to develop students’ skill in analysing of problem requirements, applying appropriate deep learning methods to real-world problems, and evaluating the effectiveness of the adopted approach.

• Practical Machine Learning
• Experimental Design and Regression
  The aim of this module is to provide an understanding of the principles of the statistical design of experiments through the study of particular design, of sampling theory for finite populations, and the concepts of survey design.