# MATH06090 2018 Mathematics 2

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**Description**

This subject adds further to the Mathematical skills set for students in the computing area. The module begins with a section on relations and functions and properties associated with these. The middle section covers matrix algebra and also covers probability, combinations and permutations. In the latter stage of the module time is spent on developing competence in trigonometry, complex numbers and quaternions.

### Learning Outcomes

*On completion of this module the learner will/should be able to;*

**1.**

Distinguish and classify properties of relations and functions.

**2.**

Show competence in performing matrix operations and solving matrix equations.

**3.**

Demonstrate competence in calculating probabilities.

**4.**

Utilize trigonometric functions and solve trignometric equations.

**5.**

Demonstrate competence in the use of complex numbers and quaternions.

### Teaching and Learning Strategies

The student will engage with the content of the module through lectures and tutorials.

The student will work on practical examples and exercise sheets to develop and apply their learning.

### Module Assessment Strategies

Written examination at end of semester and also a written examination around mid-semester.

### Repeat Assessments

The repeat assessment will involve a repeat examination.

### Indicative Syllabus

1. Relations: Properties such as domain, range, restriction, anti-restriction, composition, inverse, reflexive, symmetric, transitive and equivalence. Functions: properties such as injective, surjective, bijective, composition, inverse.

2. Matrices: operations, determinant, inverse, solution of equations.

3. Probability: sample space, mutually exclusive events, independent events, conditional probability, Bayes theorem, probability trees, expected value, combinations and permutations.

4. Trigonometry: angles, trignometric functions, inverse trignometric functions, trignometric identities, trignometric equations, polar co-ordinates.

5. Complex numbers and quaternions: Cartesian, polar and exponential form, conjugate, arithmetic operations, DeMoivre's theorem.

### Coursework & Assessment Breakdown

**Coursework & Continuous Assessment**

**End of Semester / Year Formal Exam**

### Coursework Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
---|---|---|---|---|---|---|

1 | Continuous assessment breakdown | Coursework Assessment | Closed Book Exam | 30 % | Week 7 | 1,2,3 |

### End of Semester / Year Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | End of term exam | Final Exam | Closed Book Exam | 70 % | End of Term | 1,2,3,4,5 |

### Full Time Mode Workload

Type | Location | Description | Hours | Frequency | Avg Workload |
---|---|---|---|---|---|

Lecture | Lecture Theatre | Lecture | 3 | Weekly | 3.00 |

Tutorial | Flat Classroom | Tutorial | 1 | Weekly | 1.00 |

Independent Learning | Not Specified | Independent Learning | 3 | Weekly | 3.00 |

### Required & Recommended Book List

**Recommended Reading**

2017

*Discrete maths for Computing*Palgrave MacMillan

**Recommended Reading**

2016

*Foundation Mathematics*Pearson

**Recommended Reading**

2017

*Maths for Computing and Information Technology*Prentice Hall