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:

  • use mathematical notation to formulate mathematical concepts and statements precisely
  • recall key important definitions and results
  • use logical argument and various proof techniques to prove or disprove mathematical statements
  • use techniques learned in the course to solve a variety of standard problems in discrete mathematics, analysis and algebra
  • approach and solve new, unseen, problems in an analytical and logically precise way.

Assessment

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.