Content

One definition of equilibrium is "the condition of a system in which competing influences are balanced, resulting in no net change" while a definition of fixed point is "a value which is unchanged by a function or other mapping". Equilibria are important in physics, chemistry, biology, economics and other subjects. In the early 1950's it was discovered that, unlike physical and chemical equilibria, which were often treated via maximum principles, economic equilibria are often best understood in terms of fixed points of functions or correspondences.

This module is mostly concerned with the mathematics underlying fixed point theorems, but will also discuss simple economic applications.

After a quick introduction the topics considered will be:

Text

There is no textbook for the course, but there are extensive notes written by David Wilkins, who used to teach this module before his retirement.

I will also post my slides after lectures.

MondayTuesdayWednesday
Week 0 Lecture 0 Lecture 1 Lecture 2
Week 1 Lecture 3 Lecture 4 Lecture 5
Week 2 No Lecture
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9

Exams

There will be single exam in the usual exam period, worth 100% of your module mark.

Assignments

There are no assignments for this module.

Tutorials

There are no tutorials for this module.

Past Module Webpages

This module is taught in alternate years. In 2024 and 2022 it was taught by David Wilkins. There doesn't appear to be a web page for 2022. In 2020 it was taught by me. In 2018 and previously it was taught be David Wilkins under the module code MA3486. Knowing the old module code is useful if you want to look at past exam papers. The content isn't exactly the same from year to year but it is fairly stable.