4CCM115a Sequences and Series
Lecturer: Professor David Burns
Advice/Help for this module is also available from: tbc
Credit level: 4 Credit Value: 15
Mathematics BSc/MSci (or with a Year Abroad)
Mathematics with Statistics BSc (or with a Year Abroad)
Mathematics with Management and Finance BSc (or with a Year Abroad)
Mathematics and Philosophy BSc (or with a Year Abroad)
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.
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.
Three hours of lectures each week. In addition, a one hour small group tutorial each week and one hour of large group problem classes.
| Type||Weight||Marking Model|
|2 hr written examination
|3 x class tests
For students who fail the module at the first attempt, reassessment will be based entirely on the written exam.
Exercise sheets are handed out on a weekly basis and written answers must be given in by the due date.
Suggested reading/resource (link to My Reading Lists)
17 August 2018