Mathematics for economists Training

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 are explained. This week students will grasp how to apply IFT concept to solve different problems. 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.

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.
with inequality constraints. This week students will grasp the concept of binding constraints and complementary slackness conditions.
week students will find out how to use Kuhn-Tucker conditions for solving various economic problems.

Implicit Function Theorems and their applications.

Week 3 : of the Course is devoted to implicit function theorems. In this week three different

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

Envelope theorems. Concavity and convexity.

Week 6 : of the Course is devoted to envelope theorems, concavity and convexity of functions.

Global extrema. Constrained optimization with inequality constraints.

Week 7 : of the Course is devoted to identification of global extrema and constrained optimization

Kunh-Tucker conditions. Homogeneous functions.

Week 8 : of the Course is devoted to Kuhn-Tucker conditions and homogenous functions. This