# MATU9D1 - Discrete Structures

SCQF Level: 8
Availability: Semester module, Autumn
Course Prerequisite: SCE Standard Grade pass in Mathematics, GCSE Mathematics or equivalent
Credit Value: 20 (1 module)

### Aims

Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. Discrete mathematics has become more prominent in recent years because of its relevance to Computing Science. This introduction to discrete mathematics covers mathematical concepts in a rigorous fashion and with the attention to detail necessary to promote clear and logical thinking. Algebraic arguments will be used and backed up by a range of visualisation techniques. The module is relevant to all those who want to understand Mathematics as well as use it - whether they are from the Natural, Human or Management Sciences.

### Learning Outcomes

Students should be able to: convert numbers between different bases; solve logic problems and simplify logical expressions involving truth tables, Venn diagrams and switching circuits; write down the converse, negation and contrapositive of a proposition; use a variety of methods of proof including induction, counterexample and contradiction; determine the validity of an argument; work with relations and functions; carry out matrix algebra; construct graphs and their adjacency matrices; perform algorithms for traversing graphs.

### Content

• Set theory and Venn diagrams
• Truth tables and Boolean algebra
• Logic and methods of proof
• Number bases
• Relations and functions
• Matrix algebra
• Graph theory
• Algorithms

### Transferable Skills

Effective time-management, methodical working, competency in presentation and communication.

### Bibliography

There is no set text for this course, but lecture notes will be available. For background reading:
Kevin HOUSTON, "How to Think Like a Mathematician", Cambridge University Press.
A. CHETWYND & P. DIGGLE, "Discrete Mathematics"
R. J. McELIECE, R. B. ASH, C. ASH, "Introduction to Discrete Mathematics", McGraw-Hill
K. H. ROSEN, "Discrete Mathematics and its Applications", McGraw-Hill
will be available in the Reserve Book Room of the Library.

### Teaching Format

4 one-hour lectures and a 1.5 hour tutorial per week.

### Assessment

Coursework (including 2 class tests) 40%, examination 60%.

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