# MEng Computer Systems Engineering / Course details

Year of entry: 2021

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## Course unit details:Mathematical Techniques for Computer Science

Unit code COMP11120 20 Level 1 Full year Department of Computer Science No

### Overview

This course covers the fundamental maths required by Computer Science students in order to successfully complete the reminder of their courses as well as for a career in computer science. Topics covered include complex numbers, logic, probability, recursion and induction, relations, vectors, matrices and transformations.

### Pre/co-requisites

Students who are not from the School of Computer Science must have permission from both Computer Science and their home School to enrol.

### Aims

This is a full year course that focuses on areas of mathematics required to model and analyse the kind of problems that arise in computer science.

Probabilities are used for example in artificial intelligence, and play a vital role in machine learning, while the combinatorics required here also plays a role in the field of computational complexity. Vectors and matrices are the mathematical model underlying computer graphics. Logic is a tool used to reason about computer programs as well as the real world. Recursion is an important programming principle that comes with an associated proof rule, and other mathematical notions such as functions and relations are used routinely in computer science, for example when talking about database systems. Theoretical computer science can be considered an area of mathematics, and the unit also provides an introduction to the fundamental notions of this area.

Specifically the unit aims to

- introduce  mathematical notions relevant to computer science and their applications;

- illustrate how abstraction allows the formulation and proof of properties for real-world and computational phenomena, and enable students to apply this technique;

- give an understanding and some practice in the fundamental notion of proof.

Students are required to undertake background reading, which is supported by lectures to explain various notions and to show the application of various techniques using examples. The coursework requires the students to solve exercises each week. Feedback for and help with this work is provided in the examples classes.

### Learning outcomes

• perform the standard operations on complex numbers

• apply formal definitions and construct formal arguments based on these in the context of mathematics relevant to computer science.

• employ abstraction to move from concrete phenomena to ones which are amenable to the application of mathematical techniques.

• interpret the meaning of logical formulae as part of a natural deduction system, via the model based on truth values, or via a given intended model.

• construct logical formulae to describe aspects of a given system, and manipulate these formulae to derive properties of the system.

• apply concepts from the mathematical theory of probability to describe and analyse a variety of situations.

• use Bayesian reasoning to construct a simple algorithm for learning in a variety of situations.

• recognize recursively defined structures and define recursive operations satisfying some given specification, as well as construct inductive arguments to prove some given property for such operations.

• use vectors and matrices to describe suitable situations, such as systems of equations or operations in two- and three-dimensional space, and are able to carry out relevant calculations for these.

• choose suitable mathematical techniques to analyse questions from computer science and devise approaches to solving them.

### Teaching and learning methods

Lectures

This unit is delivered in a blended manner. Self-study materials are made available in the form of detailed notes which include exercises, as well as videos and formative self-assessment quizzes that allow students to check their understanding. Each week there is a session that allows students to ask questions about the materials and beyond, and discuss the ideas underlying the taught material. Further there are weekly examples classes to were solutions to the assessed exercises are discussed.

Students are expected to spend 4-5 hours per week engaging with the self-study materials and solving the assessed exercises.

Study hours:

Attendance: two hours per week

Self-study and solving coursework: ca 4-5 hous per week

Revision and exams: approximately 50 hours.

### Employability skills

Analytical skills
Problem solving

### Assessment methods

Method Weight
Written exam 80%
Written assignment (inc essay) 20%

### Feedback methods

Feedback is provided via marks for the weekly exercise sheets, solutions to these exercises, and the weekly examples classes, and also via the self-assessment quizzes

COMP11120 reading list can be found on the Department of Computer Science website for current students.

### Study hours

Scheduled activity hours
Assessment written exam 4
Lectures 22
Practical classes & workshops 22
Independent study hours
Independent study 152

### Teaching staff

Staff member Role
Andrea Schalk Unit coordinator