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Module MA3486: Fixed Point Theorems and Economic Equilibria

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2015-16
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
Prof. David Wilkins
Learning Outcomes
On successful completion of this module, students will be able to:
    using the simplex method;
  • describe and justify with reasoned logical argument basic properties of convex sets in finite-dimensional spaces;
  • describe and justify with reasoned logical argument basic properties of simplices and simplicial complexes;
  • describe in reasonable detail how techniques from real analysis and low-dimensional topology can be applied to investigate the existence and properties of equilibria in simple economic models.
Module Content
  • Review of results from real analysis
  • Properties of convex subsets of finite-dimensional spaces
  • Simplices and simplicial complexes
  • Barycentric subdivision and the Simplicial Approximation Theorem
  • The Brouwer and Katukani Fixed Point Theorems
  • Mathematical models of simple economies.
  • Proof of the existence of equilibria in economic modules
 
Module Prerequisite
MA1124 or MA2223.
Assessment Detail
This module will be examined in a 2-hour examination in Trinity term.