Logic and Mathematics for Computing

Module aims

This module is specifically designed for students on a conversion MSc Computing programme with limited (or no) logic and/or mathematics content in their undergraduate degree. The aim of this Term 1- selective module is to provide you with the core knowledge of the selected topics in logic and mathematics required to pursue more specialised spring term selective modules, such as Logic-based Learning, Introduction to Machine Learning, Computer Vision and Graphics. 

Learning outcomes

By the end of the module you will be able to:
- Formalise English sentences in logic
- Provide formal arguments regarding consequences and semantics of logical theories
- Appraise and apply foundational mathematics and statistics used in computing
- Perform key matrix/vector operations frequently employed in machine learning algorithms and computer graphics
- Apply mathematics for signals and systems (e.g. convolution, Fourier analysis) relevant to computer vision and graphics

Module syllabus

This module covers the following topics: 

*** Logic ***
Propositional and predicate logic: syntax, semantics
Semantic consequence and proof techniques for propositional and predicate logic

*** Mathematics ***
Foundation: number, algebra, geometry, functions, complex numbers
Vector and matrix algebra:  Cartesian coordinates, scalars and vectors, vector operations, complex numbers as vectors, scalar (or dot/inner) product, vector (or cross) product, basic matrix operations, determinants, inverse matrix, solution of liner equations, rank, eigen values and eigen vectors
Calculus: sequences/series, limits, integrations, differentiation, functions of several variables – concept of gradient-based optimisation
Data handling, statistics and probability: experiments and sampling, data types, visualization of qualitative and quantitative data, probabilities of random events, random variables, practical distributions
Fundamentals of signals and systems, convolution, Fourier analysis

Teaching methods

The module content will be delivered through timetabled lectures. Coursework exercises, tightly coupled to the topics covered in the lectures, will reinforce self-paced learning through problem solving. Active and collaborative leaning will be facilitated through online discussion tool.

Assessments

There will be coursework exercises that contribute 20% of the marks for the module.  There will be a final written exam, which will count for the remaining 80% of the module marks. Regular formative exercises will enable you to reinforce your understanding of the material taught in the class.

Timetabled teaching sessions will provide opportunity for live interaction with the lecturing staff. Written feedback, primarily formative in nature, will be returned for the submitted coursework exercises through departmental e-marking platform.  Additionally, online discussion tool, monitored by the teaching assistants/staff, will allow students to ask questions and receive answers from fellow students. Feedback on formative exercises will be given through solution to exercise problems and by problem solving in the class.

Reading list

Section 1 (Logic)

Section 2 (Mathematics)

Module leaders

Dr Fariba Sadri
Dr Pancham Shukla

Reading list

View the module reading list (Leganto)