Module Identifier MA13310
Module Title MATHEMATICAL TECHNIQUES FOR COMPUTER SCIENCE
Co-ordinator Dr T McDonough
Semester Intended for use in future years
Next year offered N/A
Next semester offered N/A
Course delivery Lecture   22 Hours. (22 x 1 hour lectures)
Practical   11 Hours. (11 x 1 hour workshops)
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  50%
Semester Assessment coursework: 2 assessed workshops.  50%
Supplementary Assessment2 Hours [continuous assessment passed: same format as above; otherwise 2-hour written examination (as above).]  100%

#### Learning outcomes

On completion of this module, a student should be able to:
1. describe some number systems;
2. explain how different types of numbers can be represented in computers;
3. compute with sets, relations, functions and the rates of growth of functions;
4. determine properties of sequences and series;
5. perform computations in propositional and predicate calculus.

#### Brief description

This module covers the bulk of the mathematical prerequisites for the first two years of honours degree courses in Computer Science and Software Engineering. It provides a basic introduction to number systems, sets and relations, rates of growth of functions, mathematical induction, sequences and series, and propositional and predicate calcutus. The material is presented in an accessible manner and draws on examples from computer science to emphasise the importance of the concepts introduced. No prior mathematical knowledge, beyond GCSE level, is assumed.

#### Aims

To provide the mathematical prerequisites for modules in the first two years of the honours degree courses in Computer Science and Software Engineering.

#### Content

1. NUMBER SYSTEMS: Natural numbers, integers, rational numbers, real numbers. Radix r representation of integers: change of radix, representing negative and rational numbers, twos complement and computational arithmetic.
2. PROPOSITIONAL CALCULUS: Formulae, semantics, truth tables. Notions of tautology, validity, contradiction, satisfaction, equivalence and consequence. De Morgan's law. Disjunctive normal form, conjunctive normal form.
3. DIGITAL LOGIC GATES: Design and analysis.
4. PREDICATE CALCULUS: Terms and formulae, quantification, semantics.
5. SETS AND RELATIONS: Basic notation, Venn diagrams, ordered sequences, relations. Functions.
6. RATES OF GROWTH OF FUNCTIONS: Polynomials, logarithms and exponentials, and factorials.
7. SEQUENCES AND SERIES: The concepts of a sequence, a series. An application to computer science.