Undergraduate Course: Functional Analysis (MATH11135)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This course will cover the foundations of functional analysis in the context of normed linear spaces The Big Theorems (Hahn-Banach, Baire Category, Uniform Boundedness, Open Mapping and Closed Graph) will be presented and several applications will be analysed. The important notion of duality will be developed in Banach and Hilbert spaces and an introduction to spectral theory for compact operators will be given. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
1. Facility with the main, big theorems of functional analysis.
2. Ability to use duality in various contexts and theoretical results from the course in concrete situations.
3. Capacity to work with families of applications appearing in the course, particularly specific calculations needed in the context of Baire Category.
4. Be able to produce examples and counterexamples illustrating the mathematical concepts presented in the course.
5. Understand the statements and proofs of important theorems and be able to explain the key steps in proofs, sometimes with variation. |
Assessment Information
| Coursework 5%, Examination 95% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
- Review of linear spaces and their norms.
- The Hahn-Banach, Baire Category, Uniform Boundedness Principle, Open Mapping and Closed Graph theorems.
- Duality in Banach and Hilbert spaces.
- Spectral theory for compact operators on Hilbert spaces. Fredholm alternative.
- Weak topologies, Banach-Alaoglu and the Arzela-Ascoli theorem. |
| Transferable skills |
Not entered |
| Reading list |
Recommended:
1. Functional Analysis, Sobolev Spaces and Partial Differential Equations, by Haim Brezis. Universitext, Springer.
2. Elements of Functional Analysis, by Robert Zimmer, University of
Chicago Lecture Series. |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | FAna |
Contacts
| Course organiser | Dr Thomas Leinster
Tel: (0131 6)50 5057
Email: Tom.Leinster@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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