SubjectsSubjects(version: 955)
Course, academic year 2023/2024
Mathematics - AB501094
Title: Mathematics
Guaranteed by: Department of Economics and Management (837)
Faculty: Central University Departments of UCT Prague
Actual: from 2022
Semester: both
Points: 8
E-Credits: 8
Examination process:
Hours per week, examination: 3/4, C+Ex [HT]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
you can enroll for the course in winter and in summer semester
Guarantor: Vozárová Pavla Ing. Mgr. Ph.D., M.A.
Romanenko Viktoriia doc. Ph.D.

Sydsæter, K., Strøm, A., & Berck, P. (2005). Economists' mathematical manual (Vol. 3). Berlin: Springer.


Sydsæter, K., & Hammond, P. J. (2008). Essential mathematics for economic analysis. Pearson Education.

Bronshtein, I. N., & Semendyayev, K. A. (2013). Handbook of mathematics. Springer Science & Business Media.

Vinogradov V. (1999). A Cook-book of Mathematics. CERGE-EI.

Last update: Cibulková Jana (19.12.2022)

1. High school mathematics revision.

2. Mathematical logic and notation.

3. Linear algebra (1) Matrices and matrix operations. Determinants. Eigenvalues. Positive and negative definite matrices.

4. Linear algebra (2) Singular and regular matrices, inverse matrices, systems of linear equations. Frobenius theorem, Gaussian elimination, Cramer's rule.

5. Linear algebra (3) Vector space, linear independence, basis and dimension.

6. Functions of one variable (1) Domain of definition, range. Properties of functions. Limit and continuity.

7. Functions of one variable (2) Elementary functions, their properties and graphs. Complex functions. Bijective and inverse functions.

8. Functions of one variable (3) Derivative – definition and meaning. Rules for calculating the derivative. Derivatives of complex and inverse functions. Derivatives of higher orders.

9. Functions of one variable (4) Monotonicity and local extrema. Global extrema. Convexity, concavity, inflection points.

10. Functions of one variable (5) L'Hospital's rule. Taylor’s polynomial. Tangent to graph of a function.

11. Functions of one variable (6) Asymptotes. Sketching the graph of a function.

12. Functions of multiple variables (1) Domain, limit and continuity. Visualisation using the section method.

13. Functions of multiple variables (2) Differential calculus, partial derivatives. Gradient, directional derivative. Total differential.

14. Functions of multiple variables (3) Implicitly specified functions of multiple variables and their derivatives. Derivatives of higher orders, convex and concave functions, quasi-convex and quasi-concave functions.

Last update: Cibulková Jana (19.12.2022)
Course completion requirements

Requirements for assessment: A combined result of three tests written during the semester of at least 50%, conditional on the teaching assistant agreement to grant credit on the basis of active participation during exercies sessions.

Exam requirements: The grade will be awarded based on the result of the written exam followed by an oral discussion.

Last update: Cibulková Jana (19.12.2022)
Teaching methods
Activity Credits Hours
Účast na přednáškách 1.5 42
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 3.5 98
Příprava na zkoušku a její absolvování 1 28
Účast na seminářích 2 56
8 / 8 224 / 224