Module Identifier CS10410
Module Title THE MATHEMATICS DRIVING LICENSE FOR COMPUTER SCIENCE
Co-ordinator Dr Edel M Sherratt
Semester Semester 2
Other staff Dr Edel M Sherratt
Pre-Requisite NONE
Co-Requisite NONE
Mutually Exclusive NONE
Course delivery Lecture   22 Hours
Other   A paced worksheet for each of the six sections described in Content.
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Assessment2 Hours Conventional written examination  100%
Supplementary Assessment Will take the same form under the terms of the Department's policy  100%

#### Learning outcomes

On successful completion of this module students should be able to:
1. manipulate formulae, simplify expressions, draw diagrams of and state important facts about sets;

2. define properties of relations and functions, including surjectivity, injectivity, associativity, commutativity, identity; plot graphs of functions;

3. manipulate algebraic formulae and simplify basic algebraic expressions;

4. perform arithmetic in a variety of bases, express approximations to given numbers of significant figures and to given numbers of decimal places;

5. simplify expressions and manipulate formulae involving logarithms and exponents;

6. write truth tables, manipulate logical expressions, discriminate between valid and invalid reasoning.

#### Aims

Computer Science students have very diverse mathematical experiences and abilities. Less well prepared students struggle with basic concepts, even in part I, and we find ourselves advising part II students to avoid some of our most exciting part II offerings.

This module aims to provide students with the basic skills needed for successful completion of part I, and will ensure that all Computer Science students are provided with the mathematical skills needed to ensure accessibility of all our part II modules.

#### Brief description

This module is mandatory for all computer science schemes except those taking computer science as a minor part of their degree or as part of a joint degree.

CS10410 will provide students with a range of fundamental skills in mathematics and logical reasoning, which will support their learning in programming, architecture, communications, artificial intelligence, robotics and multimedia.

#### Content

1. Sets: what are sets and how do we describe them; cardinality; subset; power set; set union, intersection and difference; Cartesian product; disjoint union; universal set; complement of a set.

2. Relations and Functions: relations and their representation; injection, surjection, bijection; functions; commutativity, associativity, identity.

3. Numbers: natural numbers, integers, rational numbers, real numbers, complex numbers; arithmetic in different bases; fractions; expressing numbers to a given number of significant figures and to a given number of decimal places; graphs of functions; rates of growth of functions.

4. Basic Algebra: simplification of algebraic expressions; factors; arithmetic involving symbolic fractions; formula transposition; linear and quadratic equations.

5. Exponents and Logarithms: simplifying exponential expressions; logarithms to any base; the log and exponential functions; equations involving e and ln.

6. Logic and reasoning: truth tables for Boolean operators; unquantified propositions; using quantifiers to express statements about collections of values; manipulating quantified statements; axioms and theories; logical argument; valid and invalid reasoning.