# COMP11120 Mathematical Techniques for Computer Science syllabus 2015-2016

COMP11120 Mathematical Techniques for Computer Science

Level 1
Credits: 20
Enrolled students: 185

• 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 Tue 12:00 - 13:00 -
Sem 1 Examples G102 Fri 13:00 - 14:00 B+X
Sem 1 Examples G102 Fri 14:00 - 15:00 W
Sem 1 Examples G102 Tue 14:00 - 15:00 Z
Sem 1 Examples G102 Tue 15:00 - 16:00 Y
Sem 1 w1-5,7,9-12 Lecture Hum Bridge St CORDINGLEY TH Mon 12:00 - 13:00 -
Sem 1 w8 Lecture Crawford House TH 1 Mon 13:00 - 14:00 -
Sem 2 Lecture 1.1 Wed 09:00 - 10:00 -
Sem 2 Lecture 1.1 Thu 10:00 - 11:00 -
Sem 2 w2+ Examples G102 Thu 14:00 - 15:00 Y
Sem 2 w2+ Examples LF15 Tue 14:00 - 15:00 B+X
Sem 2 w2+ Examples G102 Thu 15:00 - 16:00 W
Sem 2 w2+ Examples LF15 Tue 15:00 - 16:00 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
A1Have basic familiarity with complex numbers and the standard operations for these.
• Individual coursework
• Examination
• Mid semester test
A1Have an understanding of the standard propositional logic connectives and be able to convert logical expressions into conjunctive and disjunctive normal form.
• Examination
• Individual coursework
• Mid semester test
A1 B1Have an understanding of the standard logic connectives, including universal and existential quantification, and the role they play in making precise statements.
• Examination
• Mid semester test
• Individual coursework
A1 B1Understand the basics of using a formal logical system, equivalence of logical formulae, and conjunctive and disjunctive normal forms.
• Mid semester test
• Examination
• Individual coursework
A1 B1Understand the principle of recursion and the accompanying proof principle of induction, including carrying out standard indutive proofs.
• Individual coursework
• Examination
• Mid semester test
A1 B1Be familiar with the general concept of binary relation, equivalence and order relations and methods of combining relations; be familiar with the standard graphical representations of relations.
• Examination
• Individual coursework
A1Have a good appreciation of the basic laws of probability.
• Individual coursework
• Examination
A1Have the skills to tackle simple problems on discrete probability distributions, conditional probability and independence.
• Individual coursework
• Examination
A1Have an understanding of vectors and matrices and their associated operations.
• Examination
• Individual coursework
A1Be able to use vectors and matrices to solve simple geometrical problems.
• Individual coursework
• Examination
A1 B1Have an understanding of the role of vectors and matrices in graphics-based computation.
• Individual coursework
• Examination

TitleAuthorISBNPublisherYearCore
Applied statistics and probability for engineers (5th edition)Montgomery, Douglas C. and George C. Runger9780470505786Wiley2010
Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences (4th edition)Jordan, D.W. and P. Smith9780199282012Oxford University Press2008
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
Discrete mathematics with applications (5th edition)Epp, Susanna S.9780357114087Cengage Learning2018
How to think like a mathematician: a companion to undergraduate mathematicsHouston, Kevin9780521719780Cambridge University Press2011