# MATH06092 2018 Mathematics 4

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**Description**

This subject develops further Mathematical skills and applies some of the Mathematical skill set already developed. The module begins with a look at various integration techniques. This is followed by an application of matrices in Gaussian and Gauss Jordan elimination. There is a significant section on number theory and it's application in areas such as encryption. The concept of a group and the identification of group examples used in the current and earlier modules is then looked at. Finally the module covers coding theory, again using skills already developed previously in areas such as probability and matrices.

### Learning Outcomes

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

**1.**

Demonstrate competence in integral calculus.

**2.**

Solve problems using Gaussian and Gauss Jordon techniques.

**3.**

Apply number theory.

**4.**

Explain the concept of a group and identify examples.

**5.**

Demonstrate competence in error deection and error correction codes

### 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. Integration: Integration of polynomial, trignometric and exponential functions. Integration techniques. Approximation using Simpson's rule.

2. Gaussian elimination and Gauss Jordan elimination.

3. Number Theory: Prime Numbers, Euclidean algorithm, congruences, pseudo random number generation, encryption and decryption.

4. Group theory: Group properties, examples of groups.

5. Coding Theory: Coding schemes, block codes, Hamming distance, linear codes, parity check matrix.

### 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 6 | 1,2 |

### 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**

2017

*Maths for Computing and Information Technology*Prentice Hall