Introduction to Geometry, Algebra, and Number theory

The details
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Undergraduate: Level 4
Monday 13 January 2025
Friday 21 March 2025
10 May 2024


Requisites for this module



Key module for

BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
MMATG198 Mathematics,
MSCIG199 Mathematics and Data Science

Module description

For students outside of the Department, an appropriate A level in Mathematics (or equivalent) is required for this module. If you are unsure if you meet these criteria, please contact before attempting to enrol.

This is a problem-based module that will reinforce aspects of Euclidean geometry, the algebra of equations, and introduce elementary number theory techniques.

Module aims

The aims of this module are:

  • To further develop mathematical skills in order to solve several problems that are varied in nature and difficulty.

  • To learn to write mathematical arguments that explain why their calculations allow the question to be fully answered.

Module learning outcomes

By the end of this module, students will be expected to be able to:

  1. Be adept at solving general mathematical problems that arise in which the student does not know in advance what specific mathematical skills are needed.

  2. Be able to justify through mathematical argument how a given mathematical calculation leads to solution of a problem.

  3. Become sure-footed in the use of algebraic techniques that arise throughout mathematics.

Module information


  • Circle Theorems and derivation of trigonometric identities.

  • Arithmetic and Geometric progressions.

  • The Euclidean algorithm.

  • Primes and divisors.

  • Remainder and Rational root theorems.

  • General solution of the Cubic.

  • Modular arithmetic and solution of linear congruences.

  • Linear Diophantine equations.

  • Fermat's lemma.

Learning and teaching methods

Teaching in the department will be delivered using a range of face to face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.


The emphasis throughout will be on the student tackling a large number of varied problems.


This module does not appear to have a published bibliography for this year.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Assignment 1     
Coursework   Assignment 2     
Coursework   Assignment 3     
Coursework   Assignment 4     
Coursework   Assignment 5     
Exam  Main exam: In-Person, Open Book (Restricted), 90 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 90 minutes during September (Reassessment Period) 

Additional coursework information

There will be five fortnightly summative homework counting for 10% each.

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
50% 50%


Coursework Exam
50% 50%
Module supervisor and teaching staff
Prof Peter Higgins, email:
Prof. P Higgins & Dr Jessica Claridge



External examiner

No external examiner information available for this module.
Available via Moodle
Of 33 hours, 33 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.


Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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