# Selected Chapters from Mathematics for Economists

- Credits: 3
- Ending: Examination
- Range: 2C
- Semester: summer
- Year: 1
- Faculty of Economics and Finance

## Teachers

## Included in study programs

**Teaching results**

Knowledge: basic knowledge of linear algebra (vectors, matrices, systems of linear equations) and basic knowledge of financial mathematics and investing in common economic practice.

Skills: to be able to solve basic problems of linear algebra with applications in economic analysis, to orientate in four basic topics of financial mathematics (interest rate, annuity, repayment and financial flows).

Competences: to acquire new knowledge independently and to actively expand one's mathematical knowledge, realizing that knowledge of the methods of financial mathematics enables the use of funds in a more prudent and efficient way.

**Indicative content**

Vectors, linear combination, linear dependence and independence, rank and equivalence of vectors, linear space and subspace, basis and dimension, elemental change bases, matrices, systems of linear equations, determinants, systems of linear inequalities. Master basic concepts and calculation methods of simple and compound interest and discounting, continuous interest, annuities and redemption. Principles of valuation of financial flows. The use of computer programs in MS Excel calculations.

**Support literature**

SAKÁLOVÁ, K. – SIMONKA, ZS. – STREŠŇÁKOVÁ, A. Lineárna algebra pre ekonómov. Bratislava: Letra Edu, 2020.

HUŤKA, V., PELLER, F.: Finančná matematika v Exceli. Bratislava: IURA Edition, 2010.

PINDA, Ľ.: Finančná matematika I. Bratislava: Letra Edu, 2021.

ŠOBA, O., ŠIRŮČEK, M.: Finanční matematika v praxi. Praha: Grada, 2017.

**Syllabus**

1. Arithmetic vector. Vector operations. Scalar product. Linear combination, dependence and independence of vectors. The rank of the vector system. 2. Linear space and subspace. Dimension and basis of linear space. Coordinates of the vector in the base Ln. Elemental change of base and change of coordinates of the vector in the base. 3. The concept of matrix, types of matrix, operations with matrix, their economic applications. Types of matrix. Inverse matrix. Matrix equations. 4. Definition of determinant. Determinants of degree n and their calculation. Use of determinants. 5. Systems of linear equations and methods of their solution. 6. Interest rate. Simple interest. The concept of discount. Mathematical and business discount. Simple interest discounting. Bills of exchange in practice. 7. Compound interest. Comparison of simple and compound interest. Discounting at compound interest. Continuous interest. 8. Financial annuities. The concept of financial annuities and types of annuities. 9. Future and present value of p-term annuities. 10. Redemption. Loan classification. 11. Redemption plan. 12. Financial flows. Financial flow analysis. Investment decision criteria. 13. Use of MS Excel computer programs.

**Requirements to complete the course**

40% semester paper,

60% written exam

**Student workload**

Participation in excercises - 26

Preparation for exercises – 13

Preparation for semester paper – 13

Preparation for exam – 26

Total study load – 78

**Language whose command is required to complete the course**

slovak

Date of approval: 10.02.2023

Date of the latest change: 15.05.2022