Unit information: Measure Theory and Integration in 2020/21

Unit name	Measure Theory and Integration
Unit code	MATH30007
Credit points	20
Level of study	H/6
Teaching block(s)	Teaching Block 1 (weeks 1 - 12)
Unit director	Dr. Slastikov
Open unit status	Not open
Pre-requisites	MATH20006 Metric Spaces
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Unit Aims

The aim of the unit is to introduce measure theory and the Lebesgue integral.

Unit Description

The course introduces the Lebesgue integral and develops the elements of measure theory. We will, (i) generalise the notions of "length", "area" and "volume", (ii) find out which functions can be integrated, and (iii) prove the main properties of the Lebesgue integral.

Relation to Other Units

This unit is an element of a sequence of courses following on Level C/4 Analysis and Level I/5 Metric Spaces and Multivariable Calculus. It is a prerequisite for the Level M/7 unit Advanced Topics in Analysis.

Intended Learning Outcomes

At the end of the course the student should know and understand the definitions and theorems (and their proofs), and should be able to use the ideas of the course in unseen situations.

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

100% Timed, open-book examination

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Reading and References

Recommended

• G. de Barra, Measure Theory and Integration, Ellis Horwood, 2003
• Robert Gardner Bartle, The Elements of Integration and Lebesque Measure, Wiley Classics Library, 1995
• Paul R. Halmos, Measure Theory, Springer-Verlag New York, 1974
• Andreĭ Nikolaevich Kolmogorov, Sergei Vasil'evich Fomin, Elements of the Theory of Functions and Functional Analysis, Dover Publications Inc., 1999