The goal of this course is to present many of the mathematical tools that you will typically encounter throughout your first year at the PhD program.
Keep in mind that this course should serve as a warm-up for the challenging first year that you'll have. We expect that, at the end of the Math Camp, students will be familiarized with the theory presented and will be able to apply it throughout the first year.
Finally, many of the topics we will cover will be presented in a “Cookbook” way, perhaps without the details a rigorous and formal student ideally would want. A more rigorous presentation of the topics we will expose will come shortly (ECON 2010).
You can download a PDF copy of the full syllabus here.
The topics covered are as follows: proofs and logic, functions, countability, metric spaces, introduction to topology, and limits. There's also a final section titled "Fun Remarks" with some fun math facts.
You can download a PDF copy of Lecture 1 notes here.
The topics covered are as follows: sequences, continuous functions, continuity characterizations, and the Intermediate Value Theorem. There's also a final section titled "Fun Remarks" with some fun math facts.
You can download a PDF copy of Lecture 2 notes here.
The topics covered are as follows: compactness, the Heine-Borel Theorem, Weierstrass' Extreme Value Theorem, sequential characterizations of compactness, correspondences, hemicontinuity, Berge's Theorem of the Maximum, some fixed point theorems, and an appendix with a useful economics application.
You can download a PDF copy of Lecture 3 notes here.
The topics covered are as follows: differentiation, the Mean Value Theorem, Taylor's Theorem, partial derivatives, the Implicit Function Theorem, and unconstrained optimization problems.
You can download a PDF copy of Lecture 4 notes here.
The topics covered are as follows: Constrained optimization with equality constraints, constrained optimization with inequality constraints, the Karush-Kuhn-Tucker conditions, a 2-dimensional Cobb-Douglas utility maximization problem, the Envelope Theorem, and a 2-dimensional cost minimization problem.
You can download a PDF copy of Lecture 5 notes here.
The topics covered are as follows: vector spaces, linear transformations, matrix inverses, rank, determinant, and eigenvalues/eigenvectors.
You can download a PDF copy of Lecture 6 notes here.