MA1FM-Foundations of Mathematics

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:4
Terms in which taught: Autumn / Spring / Summer module
Pre-requisites:
Non-modular pre-requisites: A level Mathematics Grade B or higher
Co-requisites: MA1LA Linear Algebra and MA1CA Calculus
Modules excluded:
Current from: 2023/4

Module Convenor: Dr Chris Daw
Email: chris.daw@reading.ac.uk

Type of module:

Summary module description:

This module introduces fundamental topics in mathematics.

Aims:

To motivate students' appreciation for the rigorous study of mathematics and to begin that process. Emphasis will be given to the concepts of sets, functions and various familiar number systems. A central goal of this module is to understand the need for proof and develop the skills to enable the student to construct for themselves formal proofs. To develop the manipulative skills and mathematical intuition necessary for the study of mathematics at university.

Assessable learning outcomes:

By the end of the module students are expected to be ableÌý to:

• understand and use logical notation and arguments; construct simple mathematical proofs;


• perform appropriate calculations within a given numberÌý system.

Additional outcomes:

The ability to construct simple but rigorous mathematical arguments, and express correctly statements and proofs of simple mathematicalÌý theorems.

Outline content:

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

• sets and functions; relations and operations; logical arguments and proofs;


• direct proof, by induction and byÌý contradiction;


• some elementary number theory (e.g. the Euclidean algorithm); complex numbers;


• a brief introduction to group theory.

Brief description of teaching and learning methods:

Lectures supported by problem sheets and tutorials.