MA1FM-Foundations of Mathematics

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Terms in which taught: Autumn / Spring / Summer module
Non-modular pre-requisites: A level Mathematics Grade B or higher
Co-requisites: MA1LA Linear Algebra and MA1CA Calculus
Modules excluded:
Current from: 2021/2

Module Convenor: Dr Jani Virtanen

Type of module:

Summary module description:

This module introduces fundamental topics in mathematics.


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 able  to:

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

  • perform appropriate calculations within a given number  system.

Additional outcomes:

The ability to construct simple but rigorous mathematical arguments, and express correctly statements and proofs of simple mathematical  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 be  discussed:

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

  • direct proof, by induction and by  contradiction;

  • some elementary number theo ry (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.

Contact hours:
  Autumn Spring Summer
Lectures 20 20 4
Tutorials 9 9
Guided independent study: 69 69
Total hours by term 98 98 4
Total hours for module 200

Summative Assessment Methods:
Method Percentage
Written exam 70
Set exercise 30

Summative assessment- Examinations:

Length of examination: 3 hours

Summative assessment- Coursework and in-class tests:

 One examination and a number of assignments.

Formative assessment methods:
Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

  • where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
  • where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at:
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A mark of 40% overall.

Reassessment arrangements:

One examination paper of 3 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus coursework marks (70% exam, 30% coursework).

Additional Costs (specified where applicable):
1) Required text books:
2) Specialist equipment or materials:
3) Specialist clothing, footwear or headgear:
4) Printing and binding:
5) Computers and devices with a particular specification:
6) Travel, accommodation and subsistence:

Last updated: 8 April 2021


Things to do now