Course detail

Application of mathematical and statistical methods

FP-msmPAcad. year: 2024/2025

The subject deepens and complements the theory that students learn from mathematical subjects and puts it in touch with the knowledge of economic subjects. It covers a wide range of optimization problems, statistical methods and mathematical and economical modeling.
The subject is an adjunct to the subjects Mathematics 1, Mathematics 2, and Partition Statistics most commonly needed in applications. It is intended especially for students continuing their Master's degree studies and for students planning to process different types of data in their final papers.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

Basic knowledge of Mathematics 1 and 2: properties of numbers, derivative, integral, function of one variable, function analysis of two variables
Basic knowledge of Statistics and Statistical methods and risk analysis: mean value, variance, covariance, frequency, hypothesis testing, regression and correlation analysis, time series decomposition,
Basic knowledge of economics - consumer behavior (marginal cost theory and indifference theory), producer behavior (cost and supply), market equilibrium and efficiency, portfolio.
Knowledge of work on PC, knowledge of MS Excel spreadsheet.

Rules for evaluation and completion of the course

Passing written tests with more than 50% points. Participation in exercises is controlled. Excused absence of a student from an exercise can be replaced by substitute tasks.

Aims

Learning outcomes of the course unit The aim of the course is to deepen and supplement students' knowledge of mathematics and statistics in bachelor study and to learn how to solve optimization and prediction problems resulting from managerial decision making. Emphasis is placed on understanding the possibilities of these methods and interpreting the results in order to create the prerequisites for application of acquired knowledge in other related courses.
Upon completion of the course, the student will be able to formulate and solve mathematical problems from managerial practice. Apart from the simple processing of simple statistical data, it will also be able to work together to solve more complex statistical problems, optimization and prediction tasks.
He will also be able to use Microsoft Excel special add-ins and process data data into a bachelor's thesis.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

GROS, I.; DYNTAR, J. Matematické modely pro manažerské rozhodování. 2. aktualiz. vyd. Praha: Vysoká škola chemicko-technologická v Praze, 2015. 303 s. ISBN 978-80-7080-910-5.
ZVÁRA, K.; ŠTĚPÁN, J. Pravděpodobnost a matematická statistika. 5. vydání. Praha: Matfyzpress, 2012, 230 s. ISBN 978-80-7378-218-4.

Recommended reading

HEBÁK, P. Statistické myšlení a nástroje analýzy dat. 2. vydání. Praha: Informatorium, 2015, 877 s. ISBN 978-80-7333-118-4.
KARPÍŠEK, Z. Matematika IV: statistika a pravděpodobnost. 4., přeprac. vyd. Brno: Akademické nakladatelství CERM, 2014, 171 s. ISBN 978-80-214-4858-2.
SKALSKÁ, H. Aplikovaná statistika. Hradec Králové: Gaudeamus, 2013, 233 s. ISBN 978-80-7435-320-8.

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme BAK-EP Bachelor's 2 year of study, summer semester, elective
  • Programme BAK-UAD Bachelor's 2 year of study, summer semester, compulsory-optional

Type of course unit

 

Exercise

26 hod., compulsory

Teacher / Lecturer

Mgr. Eva Michalíková, Ph.D.

Syllabus

1. Matrices and their applications: Operations with matrices, determinant of matrices

2. Matrices - sample problems: input-output models, problems on production, stocks, consumer decision-making, producer decision-making

3. Systems of linear equations and their application in practice: Direct methods (Gauss elimination method), Iterative methods (Jacobi method); Sample problems: problems leading to the determination of the equilibrium state;

4. Differential calculus of a function of one variable in applications: Application of differential calculus of a function of one variable (derivative, differential) in economics (limit quantities, elasticity of a function); Sample problems:: analysis of the income, cost and profit function;

5. Extrema of functions of several variables - bound extrema; Local extrema of functions of two variables, bound extrema of functions of two variables - substitution method, Jacobian method. conditions and restrictions;

6. Use of mathematical and statistical methods in optimization problems: Optimization models - classification of optimization models, nonlinear programming problem; Sample problems: portfolio optimization - risk and return estimation,

7. Control test

8. Markowitz model, formulation of a general nonlinear programming problem; Sample problems: portfolio optimization

9. Use of differential calculus of functions of several variables in optimization problems - sample problems: finding the extremum of economic functions for given

10. Multivariate data analysis: Introduction to selected sources of economic data; method of describing multivariate data, use of matrix algebra in multivariate data analysis, standardization, basic characteristics of multivariate data, Sample problems: economic data analysis;

11. Multivariate data analysis: principal component method, cluster analysis; Sample problems: economic data analysis;

12.Analysis of economic time series: Graphical analysis, time series adjustments, basic models of the seasonal component and methods of seasonal adjustment.Sample tasks: analysis of time series available in the Czech Statistical Office database. Estimation of future value and future development.

13.control test

Elearning

eLearning: currently opened course