MA0FMNU-Foundations of Mathematics

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Terms in which taught: Spring term module
Non-modular pre-requisites: High School Mathematics
Co-requisites: MA0MANU Mathematical Analysis
Modules excluded:
Current from: 2020/1

Module Convenor: Dr Calvin Smith


Type of module:

Summary module description:

This module focuses on introducing basic mathematical techniques such as proof by induction, and basic concepts such as Set Theory and Group Theory.

The Module lead at NUIST is Dr John Evans.


To help the students transition from pre-university mathematics to university mathematics. To introduce them to the idea of definition, theorem and proof, and to rigorously cover topics they should have mostly seen in high school

Assessable learning outcomes:

By the end of the course, students are expected to be able to:

  • State several key definitions and important results;

  • Understand basic concepts of propositional and predicate logic;

  • Effectively use various methods of proof, e.g. proof by induction and proof by contradiction;

  • Handle sets and the functions between them. In particular, students should know what is meant by injective, surjective and bijective functions;

  • Understand and work with the supremum and infimum of a set;

  • Perform basic number theory computations;

  • Understand the concept of a group and a subgroup. Be comfortable working with various finite groups such as cy clic groups, dihedral groups and symmetric groups.

Additional outcomes:

Outline content:

The module will focus on the following areas and topics:

  • Logic and proof

  • Sets and functions

  • Real numbers

  • Basic number theory

  • Group theory

Brief description of teaching and learning methods:

Lectures enhanced by self-study and peer-group learning.

Contact hours:
  Autumn Spring Summer
Lectures 45
Tutorials 16
Guided independent study:      
    Wider reading (independent) 20
    Wider reading (directed) 7
    Exam revision/preparation 12
Total hours by term 0 0
Total hours for module 100

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

Summative assessment- Examinations:

2 Hours

Summative assessment- Coursework and in-class tests:

A number of assignments.

Formative assessment methods:

Problem sheets.

Penalties for late submission:

The Module Convenor 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[1] (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 re-examination paper of 2 hours duration in August - 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):

Last updated: 4 April 2020


Things to do now