Discrete Mathematics is a new degree course offered jointly by the Department of Computer Science and the Warwick Mathematics Institute.

Discrete Mathematics is a rapidly growing area of mathematics with many current and emerging applications. It is the study of mathematical structures that are "discrete" (in contrast to "continuous"); these are graphs, trees, networks, etc.

The importance of Discrete Mathematics today lies in its numerous practical and relevant applications. It plays an essential role in modelling the natural world (e.g., the genome) and the technological world (e.g., the Internet), and in designing efficient solutions such as Internet routing protocols. It is commonly used in cryptography, computer security, electronic banking and auctions, coding theory, algorithms, theory of computing, telecommunication, web search engines, etc. It is also in the core of modern Computer Science and Operational Research.

The degree in Discrete Mathematics aims to present the area of discrete mathematics in depth and to discuss its various applications, especially in algorithms and Computer Science. The principal intellectual objectives for the course are:

• to present an academic perspective on discrete mathematics that addresses the key principles relating to mathematics, discrete structures, and applications in algorithms, optimisation problems, and computer science;
• to develop mathematical maturity and to train students in four essential skills: understanding mathematical reasoning, ability to perform combinatorial analysis, knowledge about discrete structures, and excellence in algorithmic thinking;
• to provide students with the foundations that are needed to use discrete mathematics effectively in various applications, such as algorithms, computing, operational research, telecommunication, economics, etc.;
• to train graduates for careers in computing and business that require expertise in discrete mathematics: this degree could lead on to one of the many postgraduate courses offered in this area the graduates of which are in high demand.
  

Course Content

The objective of the First Year modules is to provide the background knowledge and skills necessary for a deeper understanding of the discipline, as well as a motivation for the breadth of topics to be covered later in the course. Students will learn basic concepts in university mathematics (like proofs, formal arguments, rigour and calculations), exercise mathematical reasoning, perform combinatorial analysis, and acquire knowledge about discrete structures. There is opportunity to develop transferable skills, and the flexibility inherent in the Warwick system allows students to follow their interests in a variety of allied fields, especially in Mathematics and Computer Science.

The core includes two key modules devoted to discrete mathematics and its applications. These are complemented by the core modules in Mathematics that are most relevant to discrete mathematics together with key modules that are an essential part of a university mathematics programme, and by two core modules in Computer Science that introduce the essential theoretical knowledge and practical knowledge required to design and implement abstract algorithms, the central area of applications of discrete mathematics.

The objective of the Second Year modules is to integrate the mathematical and computational perspectives that underpin Discrete Mathematics. The modules provide a broader theoretical base for Discrete Mathematics students, and help to equip them for different kinds of specialisation in the advanced study of discrete structures and algorithms. The core modules cover the areas of combinatorics, graph theory, and the design of algorithm and data structures, as taught jointly in Mathematics and Computer Science.

In the final Third Year the main focus is on applications of discrete mathematics to computer science. Students take an individual project in discrete mathematics together with advanced modules relating to algorithms. Options are chosen from a range of modules which reflect both the research strengths within the departments as well as the wider context of advances in the discipline.

A detailed listing of the course structure is available: for the 1st year, the 2nd year, and the 3rd year.

Entry Requirements

A-level grades A*AA (or equivalent) including A* in either Mathematics or Further Mathematics.

Further Questions?

If you have further questions, please look at our page of Frequently Asked Questions about Discrete Mathematics admissions.

If you have any questions about the new degree which are not answered on the web pages or FAQs then please contact the following (please include 'BSc Discrete Mathematics' and your UCAS ID number in the subject line of your email):

• For queries about the BSc Discrete Mathematics: dmaths@dcs.warwick.ac.uk.
• For queries regarding your current offer or to request a change to BSc Discrete Mathematics: ugadmissions@warwick.ac.uk.

What is Discrete Mathematics ?

Discrete Mathematics on Wikipedia

The Puzzle Toad page from Carnegie Mellon University lists a number of puzzles that describe well the flavour of some subjects in Discrete Mathematics

You can play Planarity Game that describes one of the central concepts in discrete mathematics of planarity of graphs: for a given set of points in the plane with the links between the points, place the points so that the links don't intersect!