Show/hide main menu

Modules

6CCM321a Real Analysis II

Lecturer:  Professor Eugene Shargorodsky

Semester: 1

Credit Level: 6       Credit Value: 15

Programmes

Mathematics BSc/MSci  Third Year

Mathematics with a Year Abroad BSc  Third Year

Mathematics with Management and Finance BSc  Third Year

Mathematics and Physics BSc/MSci  Third Year

Mathematics and Philosophy BA  Third Year

Graduate Diploma

Advice/Help for this module is also available from: Dr Alexander Pushnitski

Aims

The main aims of the module are:

to extend your knowledge and appreciation of analysis to a wider range of situations and introduce you to the important concepts that are applicable in these more general cases;

to establish the central results on continuity in this more general context;

to demonstrate some applications of the theory to other parts of mathematics.

Syllabus

Metrics and norms. Open and closed sets. Continuity. Bounded linear maps. Cauchy sequences. Completeness. Absolutely convergent series in complete normed spaces. Contraction mapping theorem. Connectedness and path connectedness. Totally disconnected metric spaces. Compactness. Compact and sequentially compact sets. Uniformly continuous functions. Stone--Weierstrass theorem. Integration (rigorous definition via uniform approximation by step functions). Integrals depending on a parameter. Picard's existence theorem for first order differential equations

Teaching arrangements   

Three hours of lectures each week and occasional tutorials.

Prerequisites

5CCM221A Analysis I

Summative Assessment

Type WeightMarking Model
2hr written examination 100% Model 2

Formative Assessment : Exercise sheets will be given out

Suggested reading/resources (link to My Reading Lists)

Sitemap Site help Terms and conditions Privacy policy Accessibility Modern slavery statement Contact us

© 2017 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454