University Lectureships in Pure Mathematics

Two University Lectureships in Pure Mathematics have just been in advertised here in Cambridge, to be held in DPMMS.

This is a permanent post (lying somewhere between the positions “Assistant Professor” and “Associate Professor” of the US system).

For more information, click here.

The deadline to apply is the 1st of December 2017.

Note also the fixed term Herchel Smith Research Fellowship in Pure Mathematics (3 years), for more information click here.


Analysis of Functions (Part II D-course)

The analysis of functions has its roots in the rigorous study of the equations of mathematical physics, and is now a key part of modern mathematics. This course builds on the Part II courses Linear Analysis and Probability & Measure, applying the theory of integration and the tools of functional analysis to explore such topics as Lebesgue and Sobolev spaces, the Fourier transform and the generalised derivative. These topics are important and interesting in themselves, but the emphasis is on their use in other areas of mathematics (for instance in the representation of functions and in partial differential equations), rather than their maximal generalisation. You can get an idea of the flavour of the course by browsing the Analysis by Lieb & Loss (Springer).

Prerequisites: A good understanding of the methods and results in the IB courses Linear Algebra, Analysis II and Metric and Topological Spaces is essential. Part II Linear Analysis and integration theory from Part II Probability and Measure are essential.

Chapter 1 (Integration of Functions) 2019

Chapter 2 (Vector spaces of Functions) 2018

Chapter 3 (Fourier decomposition of functions)

Chapter 4 (Generalised derivative of functions)

Mock exam questions 2017

Exam questions 2017

Exam questions 2018

Example sheet 1 2019

Example sheet 2 2019

Example sheet 3

Alternative set of notes by Paul Minter