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F7AMSVKM - Selected Chapters in Mathematics

Code Completion Credits Range Language
F7AMSEMM KZ 2 1P+1S English
Lecturer:
David Vrba (guarantor), Vladimír Rogalewicz
Tutor:
Hana Děcká, Matouš Brunát
Supervisor:
Department of Biomedical Technology
Synopsis:

The course Mathematical Methods in Economics combines both theoretical knowledge and practical skills. Theoretical knowledge is necessary to formulate a mathematical model and subsequently to solve decision problems and optimal management of economic processes. Practical knowledge is trained in solving specific situations on examples, where students are introduced to specific methods and techniques of economic and mathematical data analysis.

Requirements:

Requirements of the graded assessment:

There will be small written tests during the semester - see schedule.

It is required that the student gets at lest 50% of points in each test.

It is required that the student has at least 50% of points in the sum of all small tests.

The final grade is given according to the study regulation in force.

Syllabus of lectures:

1. Mathematical solution of the optimizing problem I

Local extremes of functions of one variable, solution using derivatives. Local extremes of functions of two variables.

2. Mathematical solution of the optimizing problem II

Functions of three and more variables. Finding the local extremes of a function subject to equality constraints. Lagrange multipliers.

3. Regression analysis – linear and non-linear regression

Point and interval estimation of regression coefficients, confidence belt. General regression function. Linearization. Correlation coefficient, coefficient of determination. Interpretation. Predictive value of the regression function.

4.Regression analysis II: Multiple linear regression

5. Introduction to game theory and models of decision games. Selected game theories - Definition of game, prisoner's dilemma, oligopolies, Nash equilibrium, cake slicing (game).

6. Introduction into differential equations

Differential equations as a dynamic model. Solving ordinary differential equations.

Syllabus of tutorials:

1. Mathematical solution of the optimizing problem I

Local extremes of functions of one variable, solution using derivatives. Local extremes of functions of two variables.

2. Mathematical solution of the optimizing problem II

Functions of three and more variables. Finding the local extremes of a function subject to equality constraints. Lagrange multipliers.

3. Regression analysis – linear and non-linear regression

Point and interval estimation of regression coefficients, confidence belt. General regression function. Linearization. Correlation coefficient, coefficient of determination. Interpretation. Predictive value of the regression function.

4.Regression analysis II: Multiple linear regression

5. Introduction to game theory and models of decision games. Selected game theories - Definition of game, prisoner's dilemma, oligopolies, Nash equilibrium, cake slicing (game).

6. Introduction into differential equations

Differential equations as a dynamic model. Solving ordinary differential equations.

Study Objective:
Study materials:

Required:

Eichhorn, W., Gleißner, W. Mathematics and methodology for economics: applications, problems and solutions. New York, NY: Springer Berlin Heidelberg, 2016. ISBN 9783319233529.

ROSSER, M. J. Basic mathematics for economists. 2nd ed. New York: Routledge, 2003. ISBN 0415084253.

Recommended:

GUJARATI, Damodar N. Econometrics by example. Houndmills, Basingstoke, Hampshire ; New York: Palgrave Macmillan, 2011. ISBN 978-0-230-29039-6.

LUDERER, Bernd, Volker NOLLAU a K. VETTERS. Mathematical formulas for economists. 4th ed. New York: Springer, c2010. ISBN 9783642040795.

CHIANG, Alpha C., WAINWRIGHT, Kevin: Fundamental methods of mathematical economics. 4th ed. New York: McGraw-Hill, 2005. ISBN 978-007-123823-6.

Note:
The course is a part of the following study plans:
Downloads: