Math Camp

Materials from the Brown Economics PhD math camp.

• Syllabus

  Course Description

  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 ahead. We expect that, at the end of Math Camp, students will be familiarised with the theory presented and be able to apply it throughout the first year.

  Many topics are presented in a "cookbook" way — a more rigorous treatment will follow in ECON 2010.

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• Lecture 1 — Proofs, Metric Spaces, & Topology

  Covers proofs and logic, functions, countability, metric spaces, introduction to topology, and limits.

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• Lecture 2 — Sequences & Continuity

  Covers sequences, continuous functions, continuity characterisations, and the Intermediate Value Theorem.

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• Problem Set 1 — Download (PDF)
• Lecture 3 — Compactness, EVT, & Correspondences

  Covers compactness, the Heine-Borel Theorem, Weierstrass' Extreme Value Theorem, sequential characterisations of compactness, correspondences, hemicontinuity, Berge's Theorem of the Maximum, some fixed point theorems, and an economics application.

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• Lecture 4 — Differentiation, IFT, & Unconstrained Optimisation

  Covers differentiation, the Mean Value Theorem, Taylor's Theorem, partial derivatives, the Implicit Function Theorem, and unconstrained optimisation.

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• Problem Set 2 — Download (PDF)
• Lecture 5 — Constrained Optimisation & Envelope Theorem

  Covers constrained optimisation with equality and inequality constraints, Karush-Kuhn-Tucker conditions, a 2-dimensional Cobb-Douglas utility maximisation problem, the Envelope Theorem, and a 2-dimensional cost minimisation problem.

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• Lecture 6 — Linear Algebra

  Covers vector spaces, linear transformations, matrix inverses, rank, determinant, and eigenvalues/eigenvectors.

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• Problem Set 3 — Download (PDF)