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Unit information: Advanced Topics in Analysis in 2021/22

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. Jordan
Open unit status Not open
Pre-requisites

MATH20015 Multivariable Calculus and Complex Functions, MATH20006 Metric Spaces, and MATH30007 Measure Theory and Integration

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

Description including Unit Aims

Lecturers: Thomas Jordan

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.

Unit Description

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 - Level C/4 Analysis 1A and 1B, Level I/5 Metric Spaces and Multivariable Calculus, and Level H/6 Measure Theory and Integration.

Intended Learning Outcomes

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.

Teaching Information

The unit will be taught through a combination of

  • synchronous online and, if subsequently possible, face-to-face lectures
  • asynchronous online materials, including narrated presentations and worked examples
  • guided asynchronous independent activities such as problem sheets and/or other exercises
  • synchronous weekly group problem/example classes, workshops and/or tutorials
  • synchronous weekly group tutorials
  • synchronous weekly office hours

Assessment Information

75% coursework and 25% presentation.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM0020).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

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