# MATH40310 Functional Analysis

Functional analysis plays an important role in many areas of mathematics such as Probability, Stochastic processes, Differential Equations, Measure Theory, Mathematical physics, Topology and many others. Topics included in the module will cover normed spaces, Banach spaces, finite and infinite dimensional examples of these spaces, continuity, linear operators, linear functionals, the dual space of a Banach space and the Hahn-Banach theorem. Time permitting a brief introduction to Hilbert spaces may be given.

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Curricular information is subject to change

Learning Outcomes:

On completion of this course, the student should have a firm grasp of the topics listed above, namely the fundamentals of normed spaces and Banach spaces. In more general terms, on completion of this module the student is expected to be able to master the following mathematical skills.

IN TERMS OF THEOREMS: the student should know what constitutes a proof and what does not, and should be familiar with different types of proof. The student should know why a theorem is relevant or interesting, and know its underlying motivation. The student should also be able to construct simple proofs themselves and to reconstruct proofs from those given in class.

IN TERMS OF EXAMPLES: the student must be familiar with examples given in class and know their purpose, and must also be able to produce their own examples.

IN TERMS OF CONCEPTS: the student must understand the ideas/motivation behind the definitions\theorems\examples and be able to explain the concepts involved.

Student Effort Hours:
Student Effort Type Hours
Lectures

24

Tutorial

6

Specified Learning Activities

36

Autonomous Student Learning

34

Total

100

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
Incompatibles:
MATH40030 - Functional Analysis

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Continuous Assessment: In-trimester assignments Unspecified n/a Standard conversion grade scale 40% No

30

Examination: Final Examination 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

70

Carry forward of passed components
No

Resit In Terminal Exam
Autumn Yes - 2 Hour
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.

Spring

Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Thurs 09:00 - 09:50
Lecture Offering 1 Week(s) - 20, 21 Wed 10:00 - 11:50
Lecture Offering 1 Week(s) - 22, 23 Wed 10:00 - 11:50
Lecture Offering 1 Week(s) - 24 Wed 10:00 - 11:50
Lecture Offering 1 Week(s) - 25 Wed 10:00 - 11:50
Lecture Offering 1 Week(s) - 26, 29 Wed 10:00 - 11:50
Lecture Offering 1 Week(s) - 30, 31, 32, 33 Wed 10:00 - 11:50
Spring