Introduction to Pure Mathematics - MAT00013C
Module summary
This module introduces students to university-level pure mathematics through a selection of topics, developing a range of tools and techniques to equip students for their degree.
Related modules
Co-requisite modules
Additional information
Post-requisite modules:
All Pure Mathematics modules
Elective Pre-Requisites
These pre-requisites only apply to students taking this module as an elective.
Semester 1, Prerequisites: A or above in A-level Maths
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Semester 1 2025-26 |
Module aims
In this module you will encounter topics from several core areas of Pure Mathematics, including Number Theory, Analysis, Algebra and Discrete Mathematics. Together we will explore properties of the integers, rational and real numbers, develop our understanding of how to deal with the infinitely big and the infinitesimally small, and study symmetry and graph theory.
The module will also act as a showcase for some of the pure mathematics on offer in the department through invited lectures from colleagues doing research related to the topics covered in the course.
A key aim of the module is to help you make the transition to university mathematics by emphasising the rigorous development of mathematics. Through completing the coursework assignments, you will develop your ability to communicate your mathematical ideas to others successfully and precisely. This rigorous point of view is especially characteristic of pure mathematics, but the tools developed in this module will be of use across your programme of study.
Module learning outcomes
By the end of this module, students will be able to:
- work with foundational concepts and tools in pure mathematics and use these when solving problems at an appropriate level;
- use various proof techniques;
- write clear mathematical statements and rigorous proofs;
- distinguish correct from incorrect or sloppy mathematical reasoning.
Module content
The module is based around 4 core topics:
The Integers: an introduction to number theory. Euclid’s algorithm, divisibility and primes, modular arithmetic.
The Rationals and the Reals: an introduction to analysis. Sequences and convergence, how to construct the reals, continued fractions.
Groups: an introduction to algebra. Examples of symmetry in mathematics, permutations and symmetric groups.
Graph Theory: an introduction to discrete mathematics. Examples of graphs, Eulerian and Hamiltonian cycles, the Euler characteristic.
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 80.0 |
| Essay/coursework | 20.0 |
Special assessment rules
None
Additional assessment information
The assessed coursework component mark will be calculated from written assignments and online tests, weighted 1:1 respectively. The reassessment for the coursework component will consist of a single written task covering similar ground.
Due to the pedagogical desire to provide speedy feedback in seminars, extensions to the written coursework are not possible.
To mitigate for exceptional circumstances, the written coursework grade will be the best 4 out of the 5 assignments. If more than one assignment is affected by exceptional circumstances, an ECA claim must be submitted (with evidence)
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 80.0 |
| Essay/coursework | 20.0 |
Module feedback
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
The module will draw from a variety of sources. There is no one book covering everything in the exact same way as in the module. Good sources include:
Alcock L. How to study for a mathematics degree . 1st ed. EBSCOhost, editor. Oxford ; Oxford University Press; 2013.
Liebeck MW. A concise introduction to pure mathematics . 4th edition. Boca Raton ; London :; Boca Raton ; London : CRC Press; 2016.
Hirst KE. Numbers, sequences and series . London : E Arnold; 1995.