## Modules

### 4CCM115a Sequences and Series

Lecturer:  Professor David Burns

Advice/Help for this module is also available from: tbc

Semester:  1

Credit level:  4       Credit Value: 15

Programmes

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)

Aims

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.

Learning Outcomes

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.

Syllabus

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.

Teaching arrangements

Three hours of lectures each week. In addition, a one hour small group tutorial each week and one hour of large group problem classes.

Prerequisites

None

Summative assessment
TypeWeightMarking Model
2 hr written examination 80% Model 2
3 x class tests 20% Model 6

For students who fail the module at the first attempt, reassessment will be based entirely on the written exam.

Formative assessment

Exercise sheets are handed out on a weekly basis and written answers must be given in by the due date.