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

Seminar work.
Passing a written test with more than 50% points earnings.
Participation in exercises is controlled.
Explained absence from the student on the 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.

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

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

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: steady-state roles;
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 :: analysis of revenue, cost and profit functions;
4.Extremes of multiple variables - bound extremes; The local extrema of the function of two variables bound by the extremes of the functions of the two variables - the positioning method, the Jacobian method. conditions and constraints;
6.Control test
7.Use of mathematical and statistical methods in optimization tasks: Optimization models - classification of optimization models, the role of non-linear programming; Sample tasks: portfolio optimization - risk and return estimates,
8.Markowitz model, formulation of the general task of nonlinear programming; Sample Tasks: Portfolio Optimization
9. Utilization of Differential Number of Multiple Variable Functions in Optimization Tasks - Demonstration Tasks: Finding Extreme Economic Functions in Given
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.Variometric Data Analysis: Main Component Method, Cluster Analysis; Sample Tasks: Analysis of Economic Data;
12.Analysis of economic time series: Graphical 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 measured quantity - analysis of time series available in CZSO database