Course detail

Mathematics

FP-BMATEAcad. year: 2026/2027

The course provides a basic overview of linear algebra and mathematical analysis of functions of one real variable. Students become familiar with matrices, determinants, and systems of linear algebraic equations, as well as with the basic properties of functions, limits, and derivatives. Emphasis is placed on understanding fundamental concepts and methods and their application in problem solving. The course also includes applications in economically oriented disciplines and develops the ability to work with mathematical tools and software. The acquired knowledge and skills form a foundation for further study in mathematically oriented subjects.

Language of instruction

English

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Department

Institute of Informatics (ÚI)

Entry knowledge

Secondary school mathematics curriculum

Rules for evaluation and completion of the course

Requirements for awarding course credit:
Completion of continuous assessment tests and achieving at least 55% of the total points, or completion of a comprehensive written assignment and achieving at least 55% of the total points.
Awarding course credit is a necessary condition for taking the examination.

Examination requirements:
The examination consists of a written and an oral part, with the oral part being the main component.
For all tasks in the written part, a calculation must be provided, or the procedure must be described, or the result must be justified verbally.

The problems are divided into thematic groups. If a student does not achieve at least 50% of the total attainable points in each thematic group of problems, the written part as well as the entire examination is graded “F” (fail), and the student is not allowed to proceed to the oral part.

If a student does not achieve at least 55% of the total attainable points in the written part, the written part as well as the entire examination is graded “F” (fail), and the student is not allowed to proceed to the oral part.

The oral part, focused on theoretical knowledge, follows the written part and also serves to clarify any ambiguities in the written part.

Completion of the course for students with an individual study plan:
Completion of a comprehensive test and achieving at least 55% of the total points.
Awarding course credit is a necessary condition for taking the examination.

The examination consists of a written and an oral part, with the oral part being the main component.
For all tasks in the written part, a calculation must be provided, or the procedure must be described, or the result must be justified verbally.

The problems are divided into thematic groups. If a student does not achieve at least 50% of the total attainable points in each thematic group of problems, the written part as well as the entire examination is graded “F” (fail), and the student is not allowed to proceed to the oral part.

If a student does not achieve at least 55% of the total attainable points in the written part, the written part as well as the entire examination is graded “F” (fail), and the student is not allowed to proceed to the oral part.

The oral part, focused on theoretical knowledge, follows the written part and also serves to clarify any ambiguities in the written part.

Attendance in tutorials is monitored.
For students with an Individual Study Plan (ISP), the conditions are identical, except for any mandatory attendance requirements. The dates for course completion are arranged individually according to the conditions approved in the ISP.

Aims

The aim is to develop proficiency in calculations with numerical quantities, including the use of computational tools, as well as to acquire the  basic principles of algebra and the mathematical analysis of functions of one real variable, including applications in economic disciplines.

The acquired knowledge and practical mathematical skills will serve as an essential foundation for further study in subsequent mathematically oriented subjects. In particular, they will support the development of knowledge and skills in economically oriented fields and the proper use of mathematical software.

Study aids

1. JACQUES, I.: Mathematics for economics and business. Second edition. Addison-Wesley, Wokingham 1994, ISBN 0-201-42769-9;

2. HOFFMANN, D., BRADLEY, L.: . Calculus for business, economics, and the social and life sciences. 10th ed. Boston: McGraw-Hill 2007, ISBN 978-0-07-122024-8;

3. MEZNÍK, I.:  Foundations of Mathematics for Economics and Management. 2nd ed., expanded. Brno: Faculty of Business and Management, Brno University of Technology, published by the Academic Publishing House CERM, 2017. ISBN 978-80-214-5522-1.

4. KLŮFA, J., SÝKOROVÁ, I., Mathematics Textbook (2) for Students of the University of Economics. Jesenice: Ekopress, 2023. ISBN 978-80-87865-86-6;

5. WISNIEWSKI, M.: Introductory mathematical methods in economics. First edition. McGraw-Hill, London 1991, ISBN 0-07-707407-6.

Prerequisites and corequisites

Not applicable.

Basic literature

JACQUES, I.: Mathematics for economics and business. Second edition. Addison-Wesley, Wokingham 1994, 485s, ISBN 0-201-42769-9 (EN)
MEZNÍK, I.: Základy matematiky pro ekonomii a management. Vyd. 2., rozš. Brno: Fakulta podnikatelská Vysokého učení technického v Brně v Akademickém nakladatelství CERM, 2017. ISBN 978-80-214-5522-1 (CS)

Recommended reading

HOFFMANN, D., BRADLEY, L.: . Calculus for business, economics, and the social and life sciences. 10th ed. Boston: McGraw-Hill 2007, ISBN 978-0-07-122024-8 (EN)
KLŮFA, J., SÝKOROVÁ, I., Učebnice matematiky (2) pro studenty VŠE. Jesenice: Ekopress 2023. ISBN 978-80-87865-86-6.&nbsp (CS)
WISNIEWSKI, M.: Introductory mathematical methods in economics. First edition. McGraw-Hill, London 1991, 257s, ISBN 0-07-707407-6 (EN)

Classification of course in study plans

  • Programme BAK-ESBD Bachelor's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Syllabus

  1. Matrices and operations with matrices. Inverse matrix. Rank of a matrix.
  2. Determinant of a matrix. Basic properties of the determinant, computation of determinants.
  3. Systems of linear algebraic equations. Solving systems of linear algebraic equations using the Kronecker theorem.
  4. Solving systems of linear algebraic equations using the Gaussian elimination method.
  5. Polynomials of degree n. Roots of a polynomial. Horner’s scheme (algorithm) for determining the roots of a polynomial, factorization of a polynomial into linear factors.
  6.  Summary
  7. The concept of a function of one real variable. Basic properties of functions. Graph of a function. Basic transformations of the graph of a function. Composition of functions.
  8. Basic elementary functions: linear, power, exponential, trigonometric, and their inverse functions.
  9. Limit of a function, proper and improper limits. Methods for computing limits. Limit of a function and continuity.
  10. Derivative of a function. Geometric meaning of the derivative. Methods for computing derivatives.
  11. Higher-order derivatives. Asymptotes of functions. Extrema of functions and their determination using derivatives. Convexity and concavity of functions.
  12. Complete analysis of a function.
  13. Summary

Exercise

26 hours, compulsory

Teacher / Lecturer

doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Syllabus

  1. Matrices and operations with matrices. Computations with matrices, inverse matrix, determination of the rank of a matrix.
  2. Determinant of a matrix. Computation of determinants and application of their basic properties.
  3. Systems of linear algebraic equations. Solving systems using the Kronecker theorem.
  4. Solving systems of linear algebraic equations using the Gaussian elimination method.
  5. Polynomials of degree n. Roots of a polynomial. Application of Horner’s scheme, factorization of a polynomial into linear factors.
  6. Solving problems from topics 1–5.
  7. Functions of one real variable. Basic properties of functions. Sketching the graph of a function and its transformations.
  8. Elementary functions: linear, power, exponential, trigonometric, and their inverse functions. Sketching their graphs.
  9. Limit of a function. Proper and improper limits. Computation of limits. Continuity of a function.
  10. Derivative of a function. Geometric meaning of the derivative. Computation of derivatives, determination of the equation of the tangent line to the graph of a function.
  11. Higher-order derivatives. Asymptotes of functions. Determination of extrema of functions. Convexity and concavity of functions.
  12. Complete analysis of a function based on derivative computations.
  13. Solving problems from topics 7–12.

 

Professional  Knowledge
The student is familiar with the basic concepts of linear algebra, in particular matrices, determinants, and systems of linear algebraic equations, and understands their properties and significance in solving practical problems.
The student understands the fundamental concepts of mathematical analysis of functions of one real variable, including limits, continuity, and derivatives, and recognizes their importance in the context of economics and business.
The student knows the properties of elementary functions (linear, power, exponential, trigonometric, and their inverse functions) and understands their graphical representation.

Professional Competencies
The student is able to apply mathematical methods of linear algebra and mathematical analysis to solve problems in the field of economics and business.
The student is able to analyze quantitative relationships, interpret the results of calculations, and apply them in practice.
The student is able to select appropriate mathematical methods and apply them effectively in solving practical problems.

Professional Skills
The student is able to perform operations with matrices, determine the rank of a matrix, compute determinants, and find inverse matrices.
The student is able to solve systems of linear algebraic equations and work with polynomials, including determining their roots.
The student is able to compute limits and derivatives of functions of one real variable and use them to analyze the behavior of functions (monotonicity, extrema, convexity, asymptotes).
The student is able to sketch the graph of a function based on the analysis of its properties.

Self-study

50 hours, optionally

Teacher / Lecturer

doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Individual preparation for an ending of the course

54 hours, optionally

Teacher / Lecturer

doc. RNDr. Sulkhan Mukhigulashvili, CSc.