ECON PhD course: Mathematical Analysis

Contents
The course covers the following materials:

• Real numbers and finite dimensional spaces; proof techniques
• Convergence of real sequences and series
• Metric spaces and topology of metric spaces
• Continuity and uniform continuity
• Uniform convergence for sequence of functions
• Differentiation and integration
• Some theory of convex optimization
• Numerical methods for convex optimization problems
• Relevant results from linear algebra
• Economic applications:
  • Bellman equation
  • Walrasian Equilibrium
  • Parametrization of correlation matrices

Academic prerequisites
The student should have a basic understanding of mathematical concepts such as differentiation and integration. The student should also have a working knowledge of linear algebra such as matrix multiplication, inversion, and eigenvalues/vectors.

Prerequisites for examination participation
Six homework assignments (exercise sets) will be given, and feedback for the papers will be given. Students must hand in at least four exercises (out of six) in order to proceed to the final exam. The final grade will be based solely on the oral exam.

Literature
Johnsonbaugh, R. and Pfaffenberger, W.E. Foundations of Mathematical Analysis, Dover Publications, 2010.

Boyd, S. and Vandenberghe, L. Convex Optimization, Cambridge university press, 2004.

A selection of articles, textbooks and/or notes relevant for economic applications may also be designated/provided.

Registration
By email to Susanne Christensen, sch@econ.au.dk, no later than 1 August 2025.