MA40057: Functional analysis
[Page last updated: 03 June 2024]
Academic Year: | 2024/25 |
Owning Department/School: | Department of Mathematical Sciences |
Credits: | 6 [equivalent to 12 CATS credits] |
Notional Study Hours: | 120 |
Level: | Masters UG & PG (FHEQ level 7) |
Period: |
- Semester 2
|
Assessment Summary: | EX 100% |
Assessment Detail: | |
Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
|
Requisites: |
Before taking this module you must take MA30252 OR ( take MA30041 AND take MA40256 )
|
Learning Outcomes: |
By the end of the unit, students should be able to:
* State and prove the principal theorems relating to Banach spaces, bounded linear operators, and dual spaces.
* Apply these notions and theorems to simple examples.
|
Aims: | To introduce and study the theory of infinite-dimensional normed vector spaces, the linear mappings between them, and spectral theory.
|
Skills: | Numeracy T/F,A
Problem Solving T/F,A
Written Communication F (on problem sheets)
|
Content: | Normed vector spaces and their metric structure. Banach spaces. Examples. Riesz Lemma. The space of bounded linear operators. Dual spaces and second duals. Uniform Boundedness Theorem. Open Mapping Theorem. Closed Graph Theorem. Zorn's Lemma. Hahn-Banach Theorem. Canonical embedding, reflexivity. Weak and weak * convergence. Banach-Alaoglu Theorem.
Applications and further topics, which might include: finite-dimensional subspaces,
projections, separating hyperplane theorems.
|
Course availability: |
MA40057 is Optional on the following courses:
Department of Computer Science
- USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
- USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
- USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Economics
- UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 3)
- UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
- UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
- UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
Department of Mathematical Sciences
- USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
- USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
Department of Physics
- USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
- USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
- USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
- USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
- USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)
|
Notes: - This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
- Courses and units are subject to change in accordance with normal University procedures.
- Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
|