CSMMA21NU-Mathematics and Statistics

Module Provider: Computer Science
Number of credits: 20 [10 ECTS credits]
Level:7
Semesters in which taught: Semester 1 module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2023/4

Module Convenor: Dr Fazil Baksh
Email: m.f.baksh@reading.ac.uk

NUIST Module Lead: Yin Han
Email: 002123@nuist.edu.cn

Type of module:

Summary module description:

This module is a maths and stats primer module containing key mathematics and statistics concepts.

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Aims:

The module aims to bring students up to the appropriate level as regards the mathematics and statistics necessary for the modules taught as part of the MSc in Advanced Computer Science. It contains a number of topics and students will focus on those they have not met before and which are most relevant to their degree.

Assessable learning outcomes:

Students will be able to:

• understand and use appropriate mathematical notation and concepts; understand mathematical and statistical techniques for data analytics;


• apply appropriate mathematical and statistical techniques for small-scale and well-defined data analytics and tasks.

Additional outcomes:

Outline content:

The module covers the topics of Calculus, Vectors and Matrices, Probability and Statistical Modelling. It also includes an introduction to a mathematical/statistical computing package.

• Introductory Lecture – setting scene.


• Matrices and Vectors: basic operations; linear independence; rank of a matrix; determinants and inverses; linear systems of equations; eigenvalues and eigenvectors; positive definite and negative definite matrices; dotand cross products; singular values, vector and matrix norms. linear vector spaces; open, closed and compact sets.


• Calculus: reminder of differentiation; integration; differential equations; numerical solution of ODEs; functions of several variables; vector functions; partial differentiation; gradient vector; Jacobian and Hessian matrices; Taylor series expansions; unconstrained optimisation of differentiable functions of several variables.


• Probability and Distribution Theory: • Introduction to combinatorics; conditional probability; independence; Bayes theorem; random variables; distributions; expectation; co-variance; sums of random variables; approximation theorems.


• Basic statistical modelling: hypothesis testing; linear and non-linear regression; Analysis of variance (ANOVA); Linear discriminant analysis (LDA); Principal component analysis (PCA).

Recommended Textbooks:

Engineering Mathematics Through Applications (5th edition), Kuldeep Singh, Palgrave, ISBN: 0-333- 92224-7.

Mathematics for Engineers (3rd edition), Anthony Croft and Robert Davison, Pearson, ISBN: 978-0-13- 205156-9.

Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal and Cheng Soon Ong, Cambridge University Press, ISBN: 978-1-10-847004-9.

Modern Engineering Mathematics (3rd edition), Glyn James, Prentice Hall., ISBN: 0-13-018319-9.

Brief description of teaching and learning methods:

The module comprisesÌýlectures introducing the topics with appropriate tutorial support for learning the material. Practical time is provided where students can use a mathematical/statistical computing package to practice and further develop their understanding of the material covered.ÌýÌý