# Unit information: Mathematical Methods for Computer Scientists in 2017/18

Unit name Mathematical Methods for Computer Scientists COMS10003 20 C/4 Teaching Block 4 (weeks 1-24) Professor. Eder Not open None None Department of Computer Science Faculty of Engineering

## Description

The course will demonstrate the nature and power of mathematics to students by teaching core mathematical material which is both broadly important to mathematics and computer science and illustrative of the nature of mathematics itself. It will give the students an understanding of mathematical ideas through their experience of solving mathematical problems of importance to their current and future work. The course is organized around the two key mathematical themes of proof and abstractions.

1. Mathematical objects: This part of the course recaps material the students will have encountered in school; real and imaginary numbers, polynomials and other functions, elementary calculus, set theory and relations but does this in a way that foreshadows the next two parts of the course: proof and abstraction.
2. Proof: know what you know. The power of mathematics rests on mathematical proof, the ability to decide rigorously whether a mathematical proposition is true or to decide what limits there are on the accuracy of an estimate. This is demonstrated with examples from calculus, this will include limits and convergence, differentiation and integration and power series.
3. Abstraction: abstract, construct and apply. At its heart, mathematics is about abstraction: usually with inspiration from simple examples, mathematical objects are defined axiomatically and the consequences of these axioms are derived, often leading to a rich and beautiful structure with diverse applications far away from the original inspiring example. This is demonstrated with examples from linear algebra, graph and group theory, abstract structures which nonetheless have important applications in computer science.
4. The mathematics of uncertainty. The decisive and definite nature of mathematics does not mean that it can only be applied to narrow and well defined situations and so the two themes, proof and abstraction, are brought together in a treatment of probability theory and random variables, an area with many applications in computer science. This component will provide a basis for further concepts in probability and statistics introduced at level I.

## Intended learning outcomes

On completing this course student will:

1. Have experienced mathematical ideas and the basic nature of mathematics as a discipline.
2. Have practised calculations and proofs in calculus, linear algebra and probability theory.
3. Have discovered the utility of a mathematical approach to problem solving.
4. Be able to recognise a correct proof.
5. Understand the breadth and diversity of application of abstract mathematical structures.
6. Have the confidence and numeracy to learn further mathematics from relevant sources as they required.

## Teaching details

2 lectures per week supported by problems classes

100% exam.