An introduction to sets and functions: defining sets, subsets, intersections and unions; injections, surjections, bijections. Compositions and inverses of functions. An introduction to mathematical logic and proof: logical operations, implication, equivalence, quantifiers, converse and contrapositive; proof by induction and contradiction, examples of proofs. Then these ideas will be applied in the context of the real numbers to make rigorous arguments with sequences and series and develop the notions of convergence and limits.
|Semester 1 only students will be set an alternative assessment in lieu of in-person exams in January.
Full year students will complete the standard assessment.
Educational aims & objectives
This module aims to introduce the ideas and methods of university level pure mathematics. In particular, the module aims to show the need for proofs, to encourage logical arguments and to convey the power of abstract methods. This will be done by example and illustration within the context of a connected development of the following topics: real numbers, sequences, limits, series.
Understand and be able to apply basic definitions and concepts in set and function theory. Understand the nature of a logical argument and a mathematical proof and be able to produce examples of these. Understand the definitions of limits and convergence in the context of sequences and series of real numbers. Be able to compute limits of sequences involving elementary functions. Be able to prove simple statements involving convergence arguments.
Three hours of lectures and one hour of tutorial per week throughout the term
Suggested reading list
Indicative reading list - link to Leganto system where you can search with module code for lists