Mathematics for Computing
Module aims
This module is designed for students on the MSc Computing conversion programme who have had limited or no exposure to mathematics content in their undergraduate degree. The aim of this optional autumn‑term module is to refresh your A‑level mathematics and to provide you with core knowledge in selected topics from linear algebra, calculus and, probability and statistics.
This foundation should prepare you to pursue more specialised optional modules in the spring term, such as Machine Learning, Computer Vision, Graphics, and Algorithms.
Soft prerequisite: A‑level Mathematics or an equivalent mathematical background.
Learning outcomes
By the end of the module, you will be able to:
1. Appraise and apply foundational mathematics in formulating and solving mathematical methods used in computing and engineering;
2. Perform key matrix and vector operations frequently employed in machine learning algorithms and computer graphics;
3. Systematically analyse functions and series using established techniques from calculus;
4. Solve problems in probability and statistics and demonstrate scientific reasoning in interpreting results.
Module syllabus
The planned syllabus for this module aims to cover the following topics:
Maths foundation: topics in pre-calculus such as numbers, algebra, geometry, functions, data handling, visualisation and descriptive statistics;
Vector and matrix algebra: scalars and vectors, vector operations: dot product, cross product, vector projection, vector norms and distances, linear independence, elementary and special matrices, matrix operations, determinants, inverse matrix, solution of liner equations, rank, eigenvalues and eigenvectors, matrix decomposition, other topics and applications;
Calculus: limits, continuity, differentiation, integrations, sequences and series, functions of several variables, gradient-based optimisation and applications;
Probability and statistics: sample space, events, Bayes' rule, random variables, important practical distributions, other topics and applications;
Fundamentals of signals and systems, convolution, Fourier analysis (if time permits).
Teaching methods
The module content will be delivered through timetabled lectures. Tutorial exercises, tightly coupled to the topics covered in the lectures, will help you reinforce your leaning through self-paced problem solving. Collaborative leaning will be facilitated through online discussion tool. Optional maths support session will include GTA‑guided problem solving and offer a more personalised learning experience.
Assessments
There will be in-class tests 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. Normally, resit students will be assessed through a single written examination.
Timetabled teaching sessions will provide opportunities for live interaction with the lecturing staff. Marked class tests will be returned at regular intervals for you to assess your continuous learning and to adapt your study plan for the final written exam. Additionally, an online discussion tool, monitored by the GTAs and lecturing staff, will allow you to ask questions and receive answers from fellow students. Feedback on tutorial exercises will be provided through solutions to the problems. You will also receive cohort feedback for the final written examination.