Course detail

# Application of mathematical and statistical methods

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.

Learning outcomes of the course unit

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.

Prerequisites

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.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

SKALSKÁ, H. Aplikovaná statistika. Hradec Králové: Gaudeamus, 2013, 233 s. ISBN 978-80-7435-320-8.
ZVÁRA, K.; ŠTĚPÁN, J. Pravděpodobnost a matematická statistika. 5. vydání. Praha: Matfyzpress, 2012, 230 s. ISBN 978-80-7378-218-4.
KARPÍŠEK, Z. Matematika IV: statistika a pravděpodobnost. 4., přeprac. vyd. Brno: Akademické nakladatelství CERM, 2014, 171 s. ISBN 978-80-214-4858-2.
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.
HEBÁK, P. Statistické myšlení a nástroje analýzy dat. 2. vydání. Praha: Informatorium, 2015, 877 s. ISBN 978-80-7333-118-4.

Planned learning activities and teaching methods

Předmět je vyučován formou cvičení, v rámci kterých jsou vysvětleny základní principů a nezbytná teorie a je zaměřeno především na praktické zvládnutí látky probrané a řešení ilustrativních příkladů.

Assesment methods and criteria linked to learning outcomes

Seminar work.
Passing a written test with more than 50% points earnings.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

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.
1. Matrices and their application: Operations with matrices, matrix determinants; Sample tasks: input-output models, production tasks, inventory, consumer decision making, manufacturer decisions.
2. Systems of linear equations and their application in practice. Direct methods (Gaussian elimination method), Iteration methods (Jacobi method); Sample tasks: The roles leading to the equilibrium state.
3. Differential number of functions of one variable in applications: Application of the differential function of one variable (derivative, differential) in economy (limit values, function elasticity). Sample Tasks: An Analysis of Revenue, Cost, and Profit.
4. Extremes of function of multiple variables-bound extremes. The local extremes of the function of the two variables bound by the extremes of the function of the two variables-setting method, the Jacobian method.
6. Control test.
7. Utilization of mathematical and statistical methods in optimization problems: Optimization models - classification of optimization models, role of nonlinear programming;
8. Markowitz model - formulation of the general task of nonlinear programming;
9. Markowitz model - sample tasks: risk and yield estimation, portfolio optimization.
10. Multidimensional data analysis: getting acquainted with selected sources of economic data; method of description of multidimensional data, use of matrix algebra in multidimensional data analysis, standardization, basic characteristics of multidimensional data, Sample tasks: analysis of economic data.
11. Multivariate data analysis: main component method, cluster analysis; Sample Tasks: Analysis of Economic Data.
12. Analysis of economic time series: Graphic analysis, time series adjustment, seasonal component base models and seasonal adjustment methods. Sample tasks: analysis of time series available in the CZSO database.
13. Analysis of economic time series. Examples of time series processing, including estimation of future value and future development of the measured quantity - analysis of time series available in the CZSO database.

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.

Specification of controlled education, way of implementation and compensation for absences

Participation in exercises is controlled.
Explained absence from the student on the exercise can be replaced by substitute tasks.

Classification of course in study plans

• Programme BAK Bachelor's

branch BAK-EP , 3. year of study, winter semester, 3 credits, compulsory-optional

#### Type of course unit

Exercise

26 hours, compulsory

Teacher / Lecturer