# COMP11120 Mathematical Techniques for Computer Science syllabus 2014-2015

COMP11120 Mathematical Techniques for Computer Science

Level 1
Credits: 20
Enrolled students: 203

Assessment methods

• 75% Written exam
• 25% Coursework
Timetable
SemesterEventLocationDayTimeGroup
Sem 1 Lecture 1.1 Mon 12:00 - 13:00 -
Sem 1 Lecture 1.1 Tue 12:00 - 13:00 -
Sem 1 w2+ Examples G102 Fri 13:00 - 14:00 Y
Sem 1 w2+ Examples G102 Fri 14:00 - 15:00 W
Sem 1 w2+ Examples G102 Tue 14:00 - 15:00 Z
Sem 1 w2+ Examples G102 Tue 15:00 - 16:00 B+X
Sem 2 Lecture 1.1 Thu 10:00 - 11:00 -
Sem 2 Lecture 1.1 Mon 11:00 - 12:00 -
Sem 2 w2+ Examples G102 Thu 14:00 - 15:00 Y
Sem 2 w2+ Examples G102 Tue 14:00 - 15:00 B+X
Sem 2 w2+ Examples G102 Thu 15:00 - 16:00 W
Sem 2 w2+ Examples G102 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 an computational       phenomena, and enable students to apply this technique;

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

The course unit is delivered by staff from both the School of Computer Science and the School of Mathematics.

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.
• Mid semester test
• Examination
• Individual coursework
A1Have an understanding of the standard propositional logic connectives and be able to convert logical expressions into conjunctive and disjunctive normal form.
• Mid semester test
• Individual coursework
• Examination
A1 B1Have an understanding of the standard logic connectives, including universal and existential quantification, and the role they play in making precise statements.
• Mid semester test
• Examination
• 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.
• Examination
• Individual coursework
A1Have the skills to tackle simple problems on discrete probability distributions, conditional probability and independence.
• Examination
• Individual coursework
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.
• Examination
• Individual coursework