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Selected Topics in Mathematics


Aims of the course

The goal of this course is to provide the students with a basic understanding of the main mathematical tools used in business and economics.

Course syllabus

1. Functions of two and more variables (Level sets, partial derivatives, gradient and Hessian, critical points, homogeneous functions)
2. Linear algebra (Systems of linear equations. Vector spaces, linear independence, linear transformations. Eigenvalues and eigenvectors, diagonalization. Vector spaces with scalar product, orthonormal basis. Symmetric matrices, quadratic forms.)
3. Optimization (General optimization problems. Convex sets, convex functions, convex problems. Linear programming problems. Standard form. Optimal, infeasible, unbounded problems. Simplex method. Two-phase simplex method, Dual problem. Complementary slackness. Network flow. Ford-Fulkerson algorithm. Extrema of functions of one variable. Extrema of functions of several variables. Constrained extrema, Lagrange multipliers. Karush-Kuhn-Tucker conditions
4. Analysis (Implicit functions. Open, closed and compact sets, continuous functions on compact sets. Correspondences. Fixed point theorems.)
5. Differential equations (definition, ordinary differential equation, partial differential equation)

Course director(s)

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