Abstract mathematics MT2116

This course is an introduction to formal mathematical reasoning, in which proof is central.

It introduces fundamental concepts and constructions of mathematics and looks at how to formulate mathematical statements in precise terms. It then shows how such statements they can be proved or disproved. It provides students with the skills required for more advanced courses in mathematics.

Prerequisites/ Exclusions

If taken as part of a BSc degree, courses which must be passed before this course may be attempted:

  • MT1174 Calculus or both MT105a Mathematics 1 and 05b Mathematics 2

This course may not be taken with MT3095 Further mathematics for economists.

Topics covered

  • Logic
  • Integers
  • Sets and functions
  • Prime numbers
  • Relations
  • Real and complex numbers
  • Greatest common divisor and modular arithmetic
  • Infimum and supremum
  • Sequences
  • Limits of sequences
  • Functions and limits of functions
  • Continuity
  • Groups

Learning outcomes

If you complete the course successfully, you should be able to:

  • Have used basic mathematical concepts in discrete mathematics, algebra and real analysis to solve mathematical problems in this subject
  • Use formal notation correctly and in connection with precise statements in English
  • Demonstrate an understanding of the underlying principle of the subjects
  • Solve unseen mathematical problems in discrete mathematics, algebra and real analysis
  • Prove statements and formulate precise mathematical arguments


Unseen written exam (3 hrs).

Essential reading

  • Biggs, Norman L. Discrete Mathematics. Oxford: Clarendon Press.
  • Eccles, P.J. An Introduction to Mathematical Reasoning; numbers, sets and functions. Cambridge University Press.
  • Bryant, Victor. Yet Another Introduction to Analysis. Cambridge University Press.

Course information sheets

Download the course information sheets from the LSE website.