MATHEMATICAL ECONOMICS I
These notes were developed from the lectures I gave for the Introduction to Mathematical Economics module at the University of Manchester. To bridge the gap between the "recipe-led" and "proof-based" approaches, these notes place heavy emphasis on how proofs are written and constructed. The approach taken here is inspired by and often complements the approach developed by Lara Alcock. The core topics in these notes include the following:
Logic and set theory: sets and their properties, basics of logic, proof methods,
Linear algebra: linear spaces, linear systems, matrices, quadratic forms, convexity and concavity,
Real analysis and metric spaces: sequence and series, open and closed sets, compactness, continuity, differentiability,
Multivariate calculus: Rolle's and mean value theorem, Taylor approximation, implicit function theorem,
Optimisation theory: unconstrained optimisation, constrained optimisation, envelope theorem.
You can access the online notes here.
INFORMATION ECONOMICS I
These notes form the basis of an applied game theory course for a postgraduate course in information economics. They are partly inspired by Nageeb Ali and Nima Haghpanah's graduate game theory courses that I took during my PhD at Penn State. My academic interests obviously play a major role in how the course is shaped and in the topics chosen. The (tentative) topics covered in these notes are as follows:
Revision of incomplete information games: Bayesian games, Perfect Bayesian equilibrium, Sequential Equilibrium,
Value of information: Blackwell orders
Hard Information: unravelling arguments, Dye model
Soft Information: cheap talk games, political correctness
Information design: Bayesian persuasion, limits of price discrimination.
Markets for information: digital platforms, selling cookies
You can access the online notes here.