# Module Information

Module Identifier
CS10410
Module Title
THE MATHEMATICS DRIVING LICENSE FOR COMPUTER SCIENCE
2011/2012
Co-ordinator
Semester
Semester 1
Mutually Exclusive
Mutually Exclusive
CS10310 A level Mathematics
Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Seminars / Tutorials 10 hours
Lecture 22 Hours.

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   written exam  100%
Supplementary Assessment 2 Hours   written exam  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.

### Module Skills

Skills Type Skills details
Application of Number This module includes a substantial element of number and manipulation of numeric formulae.
Communication Reasoned argument ensures clarity of communication. Clarity of thought and validity of argument are directly addressed by this module.
Improving own Learning and Performance Contributes to capacity to comprehend and profit from courses including programming, AI, robotics and telecommunications.
Problem solving Logical reasoning is central to all problem solving. Logical reasoning is supported by mathematical reasoning. Both are directly addressed within the context of this module.
Subject Specific Skills Reasoning, clarity of expression, and skill with number and formula are developed and assessed.