Introduction to Abstract Mathematics

This information is for the 2021/22 session.

Teacher responsible

Prof Peter Allen, Prof Amol Sasane and Dr Emilio Pierro


This course is compulsory on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics and BSc in Mathematics with Economics. This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.


Students should have taken, or be taking concurrently, the course Mathematical Methods (MA100).

Course content

The course is an introduction to the use of formal definitions and proofs in mathematics, and to basic results of elementary set theory, number theory, linear algebra, algebra and analysis. Specific topics covered are as follows: Logic, sets and functions, relations, real numbers, infimum and supremum, sequences, limits and continuity, integers, prime numbers, greatest common divisor and modular arithmetic, complex numbers, groups and vector spaces.


This course is delivered through a combination of classes and lectures totalling a minimum of 80 hours across Michaelmas Term and Lent Term. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos.

Formative coursework

Students will be expected to produce 20 problem sets in the MT and LT.

Written answers to set problems will be expected on a weekly basis.

Indicative reading

Students may wish to have one of the recommended textbooks: N L Biggs, Discrete Mathematics (2nd edn) or P J Eccles, An Introduction to Mathematical Reasoning, but these are not required. Further background reading can be found in R Allenby, Numbers and Proofs; M Liebeck, A Concise Introduction to Pure Mathematics; V Bryant, Yet Another Introduction to Analysis; R Bartle & D Sherbert, Introduction to Real Analysis and H Anton, Elementary Linear Algebra.


Exam (90%, duration: 3 hours) in the summer exam period.
Continuous assessment (10%) in the MT and LT.

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Important information in response to COVID-19

Please note that during 2021/22 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the differing needs of students in attendance on campus and those who might be studying online. For example, this may involve changes to the mode of teaching delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2020/21: 188

Average class size 2020/21: 12

Capped 2020/21: No

Value: One Unit

Guidelines for interpreting course guide information

Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Communication
  • Application of numeracy skills
  • Specialist skills