# Module 06-30181 (2018)

## Mathematical Foundations of Computer Science

## Level 1/C

Achim Jung | Semester 1 | 10 credits |

Paul Levy | Semester 1 | 10 credits |

### Outline

Most areas of Computer Science, from graphics to machine learning to cryptography, require specialised mathematical knowledge. Also, Computer Science as a discipline shares deep connections with the foundations of mathematics. This module introduces linear algebra (as used in graphics and machine learning), algebra (as used in cryptography), and set theory (a fundamental language of mathematics). It also deals with the formalisation of computability via (mathematical) automata, learning about regular expressions and grammars along the way, concluding with non-computability and complexity.

### Aims

The aims of this module are to:

### Learning Outcomes

On successful completion of this module, the student should be able to:

- solve mathematical problems in algebra and set theory
- apply mathematical techniques to solve a problem within a computer science setting
- explain the basics of automata theory, formal language theory, computability theory and complexity theory
- describe and use the connection between finite automata and regular language
- explain non-computability and undecidability issues

### Restrictions

### Teaching methods

Lectures, Problem Sessions

Contact hours: 66

### Assessment

Assessments: 2hr Examination (80%), Continuous Assessment (20%) Reassessment: 2hr Examination (100%)

### Detailed Syllabus

### Programmes containing this module

- BSc Artificial Intelligence & Computer Science [0144]
- BSc Artificial Intelligence & Computer Science with an Industrial Year [9502]
- BSc Artificial Intelligence & Computer Science with Study Abroad [452B]
- BSc Computer Science [4436]
- BSc Computer Science with an Industrial Year [9499]
- BSc Computer Science with Study Abroad [5571]
- MEng Computer Science/Software Engineering [4754]
- MEng Computer Science/Software Engineering with an Industrial Year [9501]
- MSci Computer Science [4443]
- MSci Computer Science with an Industrial Year [9509]
- MSci Computer Science with Study Abroad [5576]