Course detail
Practicum in Mathematics for Informatics 1
FP-PMIZAcad. year: 2022/2023
The content of this practice corresponds to the subject Mathematics 1 and gives the students the opportunity to get acquainted with the practical solution of specific tasks, to practice the difficult parts and to overcome the difficulties in the management of the curriculum.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
- fulfillment of individual tasks and written assignments,
- successful completion of control tests during the semester
Course curriculum
2. Mathematical logic (work with statements and operations with them, laws and rules)
3. Session (determining the properties of relations between sets and per set)
4. Graphs (grading classification, determining the shortest route in a rated graph)
5. Languages, grammars, automata (characteristic, hierarchy, finite automaton)
6. Matrices and determinants (matrix operations, properties and calculation of determinants)
7. Systems of linear equations (matrix rank, Frobenius theorem, Gaussian elimination method, Cramer's rule)
8. Function (determination of the functional scope, its likeness, sudity, periodicity, limitations and monotony, including consequences in the function graph, properties and graphs of elementary malfunctions - power, goniometric and cyclometric functions, exponential and logarithmic functions, general power)
9. Operations with functions (definition fields, value fields and rational operations with functions, composite, simple and inverse functions, elementary constructions, and graph shifts)
10. Polynomials and rational fracture functions (calculus of zero points - polynomial roots, polynomial decomposition using the Horner scheme, decomposition of the pure and null broken rational function into partial fractions)
11. Limit (calculation and, if appropriate, estimation of own and non-own limits at own and stepped points using the rules for calculating the limit, the limit of elementary functions and the basic limit formulas)
12. Continuity (determination of continuity and continuity discontinuities using the continuity of elementary functions and rules for counting with continuous functions)
Work placements
Aims
Objective of the course in terms of learning outcomes and competences The aim of the course is to repeat, consolidate and classify the knowledge gained in lectures and exercises in the subject Mathematics I and to develop the students' ability to solve problems independently from all the topics covered.
The student will be able to solve mathematical problems from the topics discussed and to apply mathematical procedures in solving specific problems in related subjects. Students will be acquainted with Czech and English terminology.
Specification of controlled education, way of implementation and compensation for absences
electronic materials available, including control-solved examples. The student is awarded a credit after successful completion (with at least 50% of successfully solved examples).
Recommended optional programme components
Prerequisites and corequisites
Basic literature
MEZNÍK, I. Diskrétní matematika pro užitou informatiku, Brno 2013, CERM s.r.o., 185 s, ISBN: 978-80-214-4761- 5
MEZNÍK, I.: Matematika I, , 9. vydání, Brno 2011, FP VUT v Brně, 150s, ISBN 978-80-214-3725-8
MEZNÍK, I.: Matematika II., 11.vydání, Brno 2009, CERM s.r.o., 105s, ISBN 978-80-214-3816-3
Recommended reading
JACQUES, I.: Mathematics for economics and business. Second edition. Addison-Wesley, Wokingham 1994, 485s, ISBN 0-201-42769-9
MEZNÍK, I.- KARÁSEK, J.- MIKLÍČEK, J.: Matematika I pro strojní fakulty, 1. vydání, SNTL, Praha 1992, 502s, ISBN 80–03–00313-X
Classification of course in study plans
Type of course unit
Exercise
Teacher / Lecturer
Syllabus