# COMP11120 Mathematical Techniques for Computer Science syllabus 2018-2019

COMP11120 materials

COMP11120 Mathematical Techniques for Computer Science

Level 1
Credits: 20
Enrolled students: 224

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

Assessment methods

• 75% Written exam
• 25% Coursework
Timetable
SemesterEventLocationDayTimeGroup
Sem 1 Lecture 1.1 Thu 11:00 - 12:00 -
Sem 1 Examples G41 Mon 14:00 - 15:00 Z
Sem 1 Examples G41 Thu 15:00 - 16:00 W
Sem 1 Examples G41 Mon 15:00 - 16:00 Y
Sem 1 Examples G41 Thu 16:00 - 17:00 X
Sem 1 w1-5,7,9-12 Lecture 1.1 Mon 17:00 - 18:00 -
Sem 1 w8 TEST G36 Mon 11:00 - 12:00 -
Sem 1 w8 TEST Uni Place TH B Mon 11:00 - 12:00 -
Sem 2 Lecture Sam Alex SAMUEL ALEXANDER TH Mon 11:00 - 12:00 -
Sem 2 Lecture 1.1 Thu 14:00 - 15:00 -
Sem 2 w2+ Examples G41 Wed 09:00 - 10:00 W
Sem 2 w2+ Examples G41 Wed 10:00 - 11:00 X
Sem 2 w2+ Examples G41 Mon 15:00 - 16:00 Y
Sem 2 w2+ Examples G41 Mon 16:00 - 17:00 Z

## 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.

## 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.

## Teaching methods

Lectures

44 in total, 2 per week

Examples classes

22 in total, 1 per week

Study hours

Attendance: 3 hours per week

Self-study and solving coursework: ca 4 hours per week

Revision and exams: ca 45 hours

## Feedback methods

One to one feedback will be provided during examples classes. Written feedback will be provided on the marked homework and exam papers. End of semester and end of year feedback on exam performance will also be provided.

## Study hours

• Assessment written exam (4 hours)
• Lectures (44 hours)
• Practical classes & workshops (22 hours)

## Employability skills

• Analytical skills
• Problem solving

## Learning outcomes

Programme outcomeUnit learning outcomesAssessment
A1 D6Have basic familiarity with complex numbers and the standard operations for these.
• Examination
• Individual coursework
• Mid semester test
A1 D6Apply formal definitions and construct formal arguments based on these in the context of mathematics relevant to computer science.
• Mid semester test
• Examination
• Individual coursework
A1 B1 D6Employ abstraction to move from concrete phenomena to ones which are amenable to the application of mathematical techniques.
• Examination
• Individual coursework
A1 B1 D6Interpret 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.
• Individual coursework
• Mid semester test
• Examination
A1 B1 D6Construct logical formulae to describe aspects of a given system, and manipulate these formulae to derive properties of the system.
• Examination
• Individual coursework
A1 B1 D6Apply concepts from the mathematical theory of probability to describe and analyse a variety of situations.
• Examination
• Individual coursework
A1 B1 D6Use Bayesian reasoning to construct a simple algorithm for learning in a variety of situations.
• Individual coursework
• Examination
A1 B1 D6Recognize 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.
• Examination
• Individual coursework
A1 B1 D6Are able to 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.
• Individual coursework
• Examination
A1 B1 D6Choose suitable mathematical techniques to analyse questions from computer science and devise approaches to solving them.
• Examination
• Individual coursework

TitleAuthorISBNPublisherYearCore
Linear alegbra: a modern introduction (4th edition)Poole, David9781285463247Brooks/Cole2014
Discrete mathematics for new technology (2nd edition)Garnier, Rowan and John Taylor9780750306522Taylor & Francis2001
Discrete mathematics for Computer Scientists (2nd edition)Truss, J.K.0201360616Addison-Wesley1999
Interactive computer graphics: a top-down approach with WebGL (7th edition)Angel, Edward and Dave Shreiner9781292019345Pearson2015
Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences (4th edition)Jordan, D.W. and P. Smith9780199282012Oxford University Press2008
How to think like a mathematician: a companion to undergraduate mathematicsHouston, Kevin9780521719780Cambridge University Press2011
Discrete mathematics with applications (5th edition)Epp, Susanna S.9780357114087Cengage Learning2018