# Module Information

#### 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 Exam | 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

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

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

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. |

### Reading List

**Recommended Text**

Croft, A and Davison, R Foundation Maths A Croft and R Davison Foundation Maths Addison-Wesley ISBN 9780131979215;ISBN 0131979213 Addison-Wesley Primo search

**Supplementary Text**

Rosen, K H Discrete Mathematics and its Applications K H Rosen Discrete Mathematics and its Applications McGraw-Hill ISBN 9780071167567;ISBN 0071167560;ISBN 0072899050 McGraw-Hil Primo search

### Notes

This module is at CQFW Level 4