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Introduction

The language of mathematics is extensively used to analyse problems in economics and finance, and mathematical models, theories, and methods are extensively used to solve problems. The mathematical requirements of a doctoral student go beyond the material usually taught in courses at the bachelor and master level, and this course will teach the beginning doctoral student more advanced mathematical models, theories, and methods. Topics include linear algebra and matrix methods, introduction to function spaces and functional analysis, optimisation in several real variables, differential and difference equations, optimal control theory, and fixed point theory.

The course is designed for students in the following programmes:
Ph.D. specialisation in Economics
Ph.D. specialisation in Finance

Course content

The course will be based around the following topics:

• Sets and point set topology
• Vectors and linear algebra
• Real analysis in one and several variables
• Unconstrained and constrained optimization
• Correspondences and fixed points
• Differential equations and dynamical systems
• Control theory in continuous and discrete time