MA3486 - Fixed Point Theorems and Economic Equilibria Module MA3486, Hilary Term 2016 — Relevant lecture notes from previous years Dr. David R. Wilkins

Notes from Previous Years in Related Modules

Module MA2321, Michaelmas Term 2015, Section 6

A significantly edited version of the notes for Section 6 of the current MA2321 module should provide the basis for part of the introductory section of module MA3486 in Hilary Term 2016.

Module MA2321, Michaelmas Term 2015, Additional Notes, Section 9

Subsections 9.1 and 9.4 of the “additional notes” for MA2321, and, in particular, results concerning the existence of Lebesgue numbers for open covers of closed bounded subsets of Euclidean spaces should also be incorporated into the initial section of module MA3486 in Hilary Term 2016.

Module MA421, Michaelmas Term 2002

The material for MA3486 should expand upon the material covered in Sections 4 and 5 of the MA421 notes for Michaelmas Term 2002. However these notes do presume knowledge of some results of real analysis (or point set topology) relating to compactness, which include the Lebesgue Lemma. The first section of module MA3486 should supply the necessary background material. Section 5 of these MA421 notes states and proves an existence theorem for an equilibrium in a simple economic model. This is a topic that should be pursued in greater depth in MA3486.

Module MA3428, Hilary Term 2011, Sections 3 to 5

Section 3 of the MA3428 notes for Hilary Term 2011 contains a more detailed treatment of the geometry of simplicial complex, with more concrete examples and diagrams. And edited version of Section 3 of these notes should provide the basis for material covering the geometry of simplicial complexes, barycentric subdivision and the simplicial approximation theorem taught in MA3486 in Hilary Term 2016.

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Dr. David R. Wilkins, School of Mathematics, Trinity College Dublin.