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7CCMMS05 Metric and Banach Spaces

7CCMMS05T (MSc Programme)/ 7CCMMS05U (MSci Programme)

Lecturer:  Professor Eugene Shargorodsky

Semester:  1

Credit level:  7       Credit Value: 15 


Mathematics MSci                                 Fourth Year

Mathematics and Physics MSci          Fourth Year

MSc Mathematics

MSc Theoretical Physics

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


To discuss some fundamental aspects of functional analysis


Various topics to be discussed include metric spaces, continuous maps, normed spaces, completeness, bounded linear maps, Banach-Steinhaus theorem, compactness, Stone-Weierstrass theorem, Hahn-Banach theorem, the dual space. Instruction is by formal lectures.

Teaching arrangements

Two hours of lectures per week plus one hour informal tutorial.


A rigorous analysis module (such as Real Analysis II or similar) and some knowledge of linear algebra.

Summative assessment
 TypeWeightMarking Model
2 hr written examination 100% Model 2

Formative assessment

Exercise sheets will be given out. Solutions handed in will be marked and difficulties discussed in class. In addition, it is essential that you work through the theory as the module progresses

Suggested reading/resource (link to My Reading Lists)


18 July 2017
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