Module Identifier MA13310 Module Title MATHEMATICAL TECHNIQUES FOR COMPUTER SCIENCE Academic Year 2000/2001 Co-ordinator Professor T N Phillips Semester Semester 2 (Taught over 2 semesters) Co-Requisite CS12220 or CS12320, CS12420. May also be taken as part of the first year of the Ordinary Degree in Mathematics. Course delivery Lecture 22 x 1 hour lectures Practical 11 x 1 hour workshops Assessment Exam 2-hour written examination 50% Course work 2 assessed workshops. 50% Resit assessment Continuous assessment passed: same format as above; otherwise 2-hour written examination (as above). 100%

General 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.

Learning outcomes
On completion of this module, a student should be able to:

• describe some number systems;
• explain how different types of numbers can be represented in computers;
• compute with sets, relations, functions and the rates of growth of functions;
• determine properties of sequences and series;
• perform computations in propositional and predicate calculus.

Syllabus
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.