Math Camp 2020 Lecture Notes

  Euclidean Space

  Open and Closed Sets

  Some Notation: Set of All Functions, Set of All Subsets

  Vector Spaces

  Vector Spaces, with S&B page numbers

  Convexity; Concave and Convex Functions

  Norms and Metrics, Normed Vector Spaces, and Metric Spaces

  Sequences and Convergence

  Limits of Functions in Euclidean Spaces

  Continuous Functions

  The Bolzano-Weierstrass Property and Compactness

  Approximation and Taylor Polynomials

  Quadratic Forms

  Second-Order Conditions and Quadratic Forms with Constraints

  Unconstrained Optimization

  Derivatives and Maximization of Concave Functions

  Differentiable Quasiconcave Functions

  The Solution Function and Value Function for a Maximization Problem

  The Implicit Function Theorem

  The Envelope Theorem

  Nonlinear Programming and the Kuhn-Tucker Conditions

  Example: Linear Programming and the Kuhn-Tucker Conditions

  Example: The Pareto Maximization Problem

  Constrained Maximization vs. Constrained Minimization

  The Basic Model of Demand Theory (introduction to Econ 501A)
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