| Unit name | Advanced Topics in Analysis |
|---|---|
| Unit code | MATHM0020 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Netrusov |
| Open unit status | Not open |
| Pre-requisites |
MATH20900 Calculus 2, Metric Spaces (Analysis 2) and Measure Theory and Integration (Analysis 3) |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit aims
The aim of the unit is to give an introduction to several topics of modern analysis such as Fourier analysis, Harmonic analysis, distributions, Sobolev spaces, and geometric measure theory.
General Description of the Unit
The course contains the following parts: 1.Introduction to Fourier analysis 2.Introduction to Function spaces 3.Introduction to Geometric measure theory
Sobolev spaces play a major role in modern analysis, spectral theory and partial Differential Equations. As of today, Bristol is one of the few places in the UK, offering a course in Sobolev spaces to undergraduates.
In addition, the course covers such fundamentals of modern analysis as the Fourier transform, distributions, Sobolev inequalities, Hausdorff dimension, Hardy-Littlewood maximal operators etc. The main thrust of the course is to prepare students so that the body of modern analysis literature, such as monographs, research papers becomes accessible to them.
Relation to Other Units
This is the final element of a sequence of Analysis courses at Levels C/4, I/5, and H/6.
After taking this unit, students should be equipped to read some of the current research in Analysis. In addition, the unit is aimed to give students basic skills of making mathematical presentations. This is a rare opportunity important for their future development.
Lectures, guided reading from a textbook for student presentations, discussion of problems, and student seminars.
80% coursework & 20% participation in seminars (including presentation)
E.B.Davis: Spectral Theory and Differntial Operators, Graduate text, Cambridge University Press , 1995 E.H.Lieb, M.Loss: Analysis, Graduate Studies in Mathematics Volume 14, AMS, 1997 V.Maz'ya, S. Poborchi: Differentiable functions on bad domains, World Scientific, 1997
