Undergraduate Course: Real Analysis (MATH11136)
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 introduces the essentials of modern real analysis which emerged from the work of Hardy and Littlewood in the 1930's and later from the work of Calderon and Zygmund in the 1950's. Many results and techniques from modern real analysis have become indispensable in many areas of analysis, including partial differential equations. |
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 maximal functions and simple singular integrals.
2. Ability to use interpolation to reduce the study of certain linear and sublinear operators to their endpoint bounds.
3. Capacity to identify the essential features in methods and arguments introduced in the course and adapt them to other settings.
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 |
- Covering lemmas, maximal functions and the Hilbert transform.
- The Fourier Transform, L1 and L2 theory.
- Weak type estimates and Interpolation.
- Introduction to singular integrals and connections with partial differential equations. |
| Transferable skills |
Not entered |
| Reading list |
Recommended:
1. Singular Integrals and Differentiability Properties of Functions, by E.M. Stein, Princeton University Press.
2. Fourier Analysis, by J. Duoandikoetxea, Graduate Studies in Mathematics, Amer. Math. Soc. |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | RAna |
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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