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Higher School of Economics vía Coursera
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Mathematics for economists

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  • The basics of the set theory. Functions in Rn
    • Week 1 of the Course is devoted to the main concepts of the set theory, operation on sets and functions in Rn. Of special attention will be level curves. Also in this week introduced definitions of sequences, bounded and compact sets, domain and limit of the function. Also from this week students will grasp the concept of continuous function.
  • Differentiation. Gradient. Hessian.
    • Week 2 of the Course is devoted to the main concepts of differentiation, gradient and Hessian.
      Of special attention is the chain rule. Also students will understand economic applications of the
      gradient.
  • Implicit Function Theorems and their applications.
    • Week 3 of the Course is devoted to implicit function theorems. In this week three different
      implicit function theorems are explained. This week students will grasp how to apply IFT
      concept to solve different problems.
  • Unconstrained and constrained optimization.
    • Week 4 of the Course is devoted to the problems of constrained and unconstrained optimization.
      Of special attention are quadratic forms, critical points and their classification.
  • Constrained optimization for n-dim space. Bordered Hessian.
    • Week 5 of the Course is devoted to the extension of the constrained optimization problem to the
      n-dimensional space. This week students will grasp how to apply bordered Hessian concept to
      classification of critical points arising in different constrained optimization problems.
  • Envelope theorems. Concavity and convexity.
    • Week 6 of the Course is devoted to envelope theorems, concavity and convexity of functions.
      This week students will understand how to interpret Lagrange multiplier and get to learn the
      criteria of convexity and concavity of functions in n-dimensional space.
  • Global extrema. Constrained optimization with inequality constraints.
    • Week 7 of the Course is devoted to identification of global extrema and constrained optimization
      with inequality constraints. This week students will grasp the concept of binding constraints and
      complementary slackness conditions.
  • Kunh-Tucker conditions. Homogeneous functions.
    • Week 8 of the Course is devoted to Kuhn-Tucker conditions and homogenous functions. This
      week students will find out how to use Kuhn-Tucker conditions for solving various economic
      problems.