Mathematical Foundations for Computing

Overview

Mathematics provides the formal structures and reasoning tools that underpin computer science. Mathematical Foundations for Computing introduces core topics essential for problem-solving, algorithm design, and theoretical computing. You will explore sets and set theory, number systems and bases, functions, and relations—building a toolkit to model data, describe systems, and reason about computational processes. Each module connects abstract mathematics to practical computing contexts, from binary representation and function mapping to relational models. By the end of the course, you will not only understand these concepts theoretically but also know how to apply them to programming, algorithms, and data structures. This course is part of the Essential Mathematics for Computer Science specialisation, preparing you for advanced topics in logic, algorithms, and computational complexity.

Syllabus

Module 1: Sets and Set Theory

This week you will be learning about two key concepts: the definition of a set, set notation, and membership tables.

Module 2: Number Systems and Bases

In this module, we will cover three key concepts: an introduction to number bases, the conversion of non-integer numbers, and operations with binary numbers. You will gain an understanding of how number bases work and learn how to perform arithmetic in different bases.

Module 3: Functions and Their Properties

This week you will learn about four key concepts: the definition of a function; properties of one-to-one and onto functions; proving correctness if a function is one-to-one or onto; and plotting functions.

Module 4: Relations

In this week you will learn about three key concepts: the definition of a relation and how it is different from a function; a relation digraph; and reflexive, symmetric, anti-symmetric and transitive relations.