ObjectivesTo offer students the opportunity to study discrete mathematics and its applications to an advanced level within an environment informed by current research. To provide students with advanced training that will be of use in a career as a worker in the general area of discrete mathematics and its applications. To provide students with training in the preparation of reports involving mathematical material, including correct referencing, appropriate layout and style. To provide students with a research-type experience that will aid them in their approach to further research activity. To enhance the transferable skills of students (including IT skills, presentation skills, problem solving abilities, numeracy and their ability to retrieve information in an efficient manner.) To provide students with information that will help them to make an informed judgement as to the appropriate methods to employ when analysing a problem of discrete mathematics and its applications.
Entry requirementsEntry Qualifications BSc degree, of Upper Second class standard or above, in Mathematics or a related subject (or an equivalent qualification). Knowledge of a computer programming language would be an advantage, but is not essential. Language requirements: IELTS 6.0 or TOEFL 540 (200) or comparable.
Academic titleMSc Discrete Mathematics and its Applications
Course description
Course Description
The MSc in Discrete Mathematics and its Applications aims to equip students with a good knowledge of discrete mathematics and an understanding of application areas of these techniques, along with other relevant skills like computing, use of algorithms and the ability to analyse data.
Modules and Options
The lists of modules below represent the range of options available for each year of study. This may not be a complete list of the options you will study, and may be subject to change, so please contact the department for further details.
Stage 1
Compulsory: COMBINATORIAL OPTIMISATION
Compulsory: CRYPTOGRAPHY AND CODES
Compulsory: GRAPH THEORY
Compulsory: MATHEMATICAL RESEARCH TECHNIQUES USING MATLAB
Compulsory: STOCHASTIC PROCESSES
Core: DISSERTATION
Core: RESEARCH METHODS
EXPERIMENTAL DESIGN
LINEAR MODELS
MACHINE LEARNING AND DATA MINING
NETWORKS: PROTOCOLS AND SECURITY
NONLINEAR PROGRAMMING
Teaching and Assessment Methods
A: Knowledge and Understanding
Learning Outcomes
A1 : A range of ideas concerning Discrete Mathematics and its applications, including methods appropriate in specialized applications and some knowledge of relevant probabilistic/statistical/computing ideas.
A2 : How to formulate algorithms to solve problems.
A3 : The power of efficient computer programs.
A4 : Some of the ways in which apparently disparate parts of the subject may interconnect.
A5 : One or more current areas of research in Discrete Mathematics and its Applications, including an awareness of the development of these areas of research.
Teaching Methods
A1-A4 are principally acquired through the coherent programmes of lectures, exercises and problem classes. These are supplemented, where appropriate, by the use of computers, computer packages, textbooks, handouts and on-line material.
In most courses there is regular set work. This work is marked and this process informs the course teacher of common difficulties that require extra attention during the subsequent problem classes.
A5 is principally acquired through the preparation of an essay and a thesis on specialized topics. During the production of their written work, students are expected to extend and enhance the basic course material concerning internet searching and the production of mathematical texts. The research guidance during the summer is a critical aspect of this training.
Assessment Methods
Knowledge and understanding are assessed through coursework, examinations, essays and the summer dissertation.
B: Intellectual/Cognitive Skills
Learning Outcomes
B1 : Analyse a mass of information and carry out an appropriate analysis of the problem material.
B2 : Express a problem in mathematical terms and carry out an appropriate analysis.
B3 : Reason critically and interpret information in a manner that can be communicated effectively.
B4 : Integrate and link information across course components.
B5 : Under guidance of a supervisor, plan and carry out a piece of research and present the results in a coherent fashion.
Teaching Methods
B1-3 These skills are developed through the regular coursework exercises. In seeking to answer these exercises students become accustomed to identifying key facts in a body of information. The problems classes provide back-up as required.
B4-5 These skills are initiated during the course of the preparation of the essay and are further developed during the course of the summer project.
Assessment Methods
The level of attainment of these skills is assessed through coursework, the summer examinations, and through examination of the summer project.
C: Practical Skills
Learning Outcomes
C1 : Model problems using discrete mathematics (and related areas of mathematics)
C2 : Construct and use algorithms.
C3 : Use computer programmes and/or packages.
C4 : Use a mathematical word-processing package.
C5 : Make an effective literature search.
C6 : Prepare a technical report.
C7 : Give a presentation and defend their ideas in an interview.
Teaching Methods
C1-C2 are developed through the programme of lectures, regular exercises and computer work.
C3-C5 are developed during the course of the preparation of the essay and the thesis.
Assessment Methods
C1-C2 is assessed by the regular coursework and examinations.
C3 is assessed in this way and also by any computer output that forms part of the summer project
C4-C7 are assessed through the MA902 essay and summer thesis.
D: Key Skills
Learning Outcomes
D1 : Write clearly and effectively
D2 : Use computer packages and/or programming languages for data analysis and computation.
D3 : Enhance existing numerical ability
D4 : Choose the appropriate method of inquiry in order to address a range of practical and theoretical problems.
D5 : Learn from feedback and respond appropriately and effectively to supervision and guidance
D6 : Work pragmatically to meet deadlines.
Teaching Methods
D1 is promoted by the supervisor of the essay and thesis work and by class teachers' feedback on written solutions to problems.
D2 results from the coursework associated with various lecture courses.
D3 is a natural consequence of courses with high numeric content.
D4 is a consequence of the coursework, problems classes, lectures and laboratory work.
D5-6 result from a tightly timetabled course of lectures and submission dates that require the student to effectively organise time to meet deadlines.
Assessment Methods
Key skills are assessed throughout the degree via coursework, examinations, the essay and the summer project.