# Mathematics and Statistics Group

## MAT911: Discrete Structures

**SCQF Level: **8

**Availability: **Semester module, Autumn

**Course Prerequisite: **SCE Standard Grade pass in
Mathematics, GCSE Mathematics or equivalent

**Credit Value: **22 (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%.