MA1FM: Foundations of Mathematics

Module code: MA1FM

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: 4

When you’ll be taught: Semester 1

Module convenor: Professor Michael Levitin , email: m.levitin@reading.ac.uk

Pre-requisite module(s): Before taking this module, you must have at least a grade B in A-Level Mathematics grade B, or equivalent. (Open)

Co-requisite module(s): IN THE SAME YEAR AS TAKING THIS MODULE YOU MUST TAKE MA1CA (Compulsory)

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2025/6

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 29 May 2025

Overview

Module aims and purpose

This module introduces fundamental topics in mathematics and it will motivate students' appreciation for the rigorous study of mathematics. Emphasis will also be given to the concepts of sets, functions and various familiar number systems. A central goal of the module is to understand the need for proofs and to develop the skills required to construct them. It will develop the skills necessary for the study of mathematics at university.

Module learning outcomes

By the end of the module, it is expected that students will be able to:

1. Understand and use logical notation and arguments;
2. Construct simple mathematical proofs;
3. Perform calculations within a given number system.

Module content

The module develops the essential skills of pure mathematics, and begins the process of learning how to think like a mathematician; in particular, how to construct logical arguments and work with definitions, theorems, and proofs. The topics discussed are likely to include: 

• sets and functions;  
• relations and operations;  
• logical arguments and proofs; direct proof, proof by induction, and proof by contradiction; 
• some elementary number theory (e.g. the Euclidean algorithm); complex numbers; 
• a brief introduction to group theory. 

Structure

Teaching and learning methods

Lectures supported by tutorials. Learning materials (lecture notes/reading lists, tutorial problem sheets, assessments) made available via Blackboard. 

Study hours

At least 50 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.