Course detail

Mathematics 1

FP-MA1_MAcad. year: 2025/2026

The subject is a part of theoretical fundamentals. The aim is to manage calculations with numeric variables (including the use of IT) and the analysis of functions of one real variable, including their applications in economic disciplines.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

Knowledge of secondary-school mathematics.

Rules for evaluation and completion of the course

Requirements for awarding credit:

Passing control tests and achieving at least 55% of points or completing a comprehensive written paper and achieving at least 55% of points.
Awarding credit is a necessary condition for taking the exam.

Exam requirements:

The exam is written.

For all tasks in the written part, a calculation must be written, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory) and the student does not proceed to the oral part.

If the student does not achieve at least 50% of the total number of achievable points in the written paper, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory).

Completion of the course for students with individual study:
Passing the comprehensive control test and achieving at least 55% of points.
Awarding credit is a necessary condition for taking the exam.
The exam is written.
For all tasks in the written part, a calculation must be written, or the procedure described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory).
If the student does not achieve at least 50% of the total number of achievable points in the written work, the written part and the entire exam are graded "F".

Participation in seminars is checked.

Aims

The aim is for students to master numerical calculations (including the use of IT) and the analysis of functions of one real variable, including their economic applications.
Acquired knowledge and practical mathematical skills will be an important starting point for mastering new knowledge in the follow-up courses of mathematical character; they will also be essential for acquiring knowledge in courses on economy and for the correct use of mathematical software.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Marošová,M.,Mezník,I.:Cvičení z matematiky I. FP VUT v Brně, Brno 2008 (CS)
Mezník, I: Diskrétní matematika. FP VUT v Brně v Akademickém nakladatelství CERM, s.r.o. Brno, Brno 2004. ISBN 80-214-2754-X. (CS)
MEZNÍK, I. Základy matematiky pro ekonomii a management. Základy matematiky pro ekonomii a management. 2017. s. 5-443. ISBN: 978-80-214-5522-1. (CS) (CS)
Mezník,I.: Matematika II.FP VUT v Brně, Brno 2009 (CS)
Mezník,I.:Matematika I. FP VUT v Brně, Brno 2008 (CS)

Recommended reading

Not applicable.

Elearning

eLearning: currently opened course

Classification of course in study plans

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

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Bedřich Půža, CSc.
doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

Mathematical logic (statements, operations and laws, Boolean algebras and functions, representations, applications)
Relations (between sets and on sets, properties, tolerances, equivalences, ordering)
Matrices (properties, matrix operations, rank calculation and inverse matrices)
Determinants (properties, rules and determinant calculation)
Systems of linear equations (solvability, GEM and Cramer's rule)
Functions of one variable (characteristics and properties, operations with functions, composite, inverse functions, elementary functions, graphs and their constructions, roots of a polynomial and their determination, Horner's scheme)
Summary (fundamentals of mathematics, linear algebra)
Limit and continuity (proper and improper limits at proper and improper points, properties and rules, continuity at a point and on an interval, properties and rules for computing with continuous functions)
Sequences (characteristics and properties, limit)
1st-order derivative (meaning, properties and rules, derivatives of elementary functions)
Summary (properties of functions, polynomials, limit and continuity of a function)
Differential (differential and its use)
Higher-order derivatives (higher-order derivatives, l'Hospital's rule)

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.
doc. RNDr. Bedřich Půža, CSc.
doc. RNDr. Jiří Tomáš, Dr.
Natálie Rontóová, Ph.D.

Syllabus

1. Reviewing high school math
2. Mathematical logic (statements, operations and laws, Boolean algebras and functions, representations, applications)
3. Relations (between sets and on a set, properties, tolerances, equivalence, arrangement)
4. Matrices (properties, matrix operations, rank calculation and inverse matrices)
5. Determinants (properties, rules and calculation of determinants)
6. Systems of linear equations (solvability, GEM and Cramer's rule)
7. Functions of one variable, polynomials (basic characteristics of functions, properties, rational operations with functions, compound, simple, inverse function)

8. Polynomials (roots of a polynomial and their determination, Horner's scheme)

9. Sequences (bounded and monotonic sequences of real numbers, sequence limit)

10. Limit and continuity (limit at a proper point, basic properties and rules for calculation, continuity at a point and on an interval)

11. Limit at non-eigenpoint (basic properties and rules for calculation)

12. Derivation of the 1st order (meaning, basic properties and rules, derivation of elementary functions)

13. Differential (differential and its use)

Elearning

eLearning: currently opened course