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MATH40310

Academic Year 2024/2025

Functional Analysis (MATH40310)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
4 (Masters)
Credits:
5
Module Coordinator:
Dr Myrto Manolaki
Trimester:
Autumn
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

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.

About this Module

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 Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): 2 hour End of Trimester Exam End of trimester
Duration:
2 hr(s)
 Standard conversion grade scale 40% No
70
 No
Student Negotiated or Choice of Assessment: (individual/group) homework assignments or/and midterm Quiz Week 7, Week 12 Standard conversion grade scale 40% No
30
 No

Carry forward of passed components
No
 

Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Feedback individually to students, post-assessment
• 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.
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Wed 09:00 - 10:50
Autumn Tutorial Offering 1 Week(s) - Autumn: All Weeks Thurs 10:00 - 10:50
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