MA13310 - MATHEMATICAL TECHNIQUES FOR COMPUTER SCIENCE

Module Identifier	MA13310
Module Title	MATHEMATICAL TECHNIQUES FOR COMPUTER SCIENCE
Academic Year	2001/2002
Co-ordinator	Professor T 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	Course work	2 assessed workshops.	50%
	Exam	2-hour written examination	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.

Reading Lists

Books
** Recommended Text
R P Grimaldi. (1999) Discrete and Combinatorial Mathematics. 4th. Addison-Wesley 0201304244
J K Truss. (1999) Discrete Mathematics for Computer Sciences. 2nd. Addison-Wesley 0201360616