Applied Mathematical Methods for Computing

Overview

Mathematics underpins every aspect of computing, from algorithms and artificial intelligence to data analysis and cryptography. Applied Mathematical Methods for Computing equips you with essential tools in algebra, vectors, matrices, sequences, series, combinatorics, probability, and statistics. These methods provide the structure and reasoning needed to solve complex computational problems. Across four modules, you’ll explore advanced techniques, practise solving real-world examples, and build the confidence to apply mathematics in programming, algorithms, and data science. By the end, you’ll have a comprehensive toolkit for modelling systems, analysing uncertainty, and reasoning rigorously about computational tasks. Whether you’re preparing for advanced studies in computer science or strengthening your foundations for professional roles, this course offers the mathematical depth you need to succeed.

Syllabus

Algebra, vectors and matrices

In this module, we will introduce algebra, vectors and matrices. This week, we will introduce vectors and vector spaces and look at how to perform basic operations with vectors. We will then introduce linear transformations and their representation via matrices. We will use matrices to describe and capture geometrical transformations (rotations, contractions, shear and projections). We will use a trick (using an extra dimension) to deal with translations.

Sequence and Series

In this module, we will cover the key concepts of sequences, series and the principle of mathematical induction. We will understand what a sequence is and look at its convergence and divergence. We will also introduce the concept of series.

Combinatorics

In this module, we will cover the following key concepts: counting, permutations, combinations, inclusions, exclusions and the Pigeonhole Principle.

Probability and Statistics

This week, we will introduce basic concepts of statistics. We will look at how to estimate probabilities from data and how to define and extract important measures from data, like mean, median and variance.