To acquire the knowledge of basic mathematical methods that are necessary for the analysis of problems in economics.

Lecture, discussion, examples

Sets: infimum and supremum; relations; partial orderMatrices; vector spaces; linear mappings (operators); projection matricesEigenvalues; singular values; decompositionsQuadratic forms; definitenessDifferentiation and integrationJensen’s inequality; Taylor’s theorem; implicit function theoremMultivariable calculusOptimization: compactness; Weierstrass theoremHyperplane separation: Minkowski’s theoremOrdinary differential equations and their solutionDifference equationsDynamic optimization: discrete and continuous timeFixed-point theorems

Knowledge of elementary mathematics

Sydsaeter K., Hammond P., Seierstad A., Strom, A. (2008). Further mathematics for economic analysis. 2nd Ed. Pearson education.Sydsæter K.,  Hammond P. J. (2012). Essential mathematics for economic analysis. 4th Ed. Pearson Education.Weir M.D., Hass J., Thomas G.B.  (2013). Thomas' calculus: early transcendentals. 12th Ed. Pearson.Roman S. (2008). Advanced linear algebra. 3rd Ed. Springer.

The exam takes place in writing and consists of a theoretical and a practical part of about 30-45 minutes each.

Theoretical part: definitions, theorems, statements.Practical part: exercises.

In order to pass the exam, at least 50% of the points (from both parts in total) must be achieved.