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Lecturer(s)
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Cerman Zbyněk, Mgr. Ph.D.
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Barot Tomáš, Ing. Ph.D.
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Course content
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- Propositional and predicate logic - Binary relations and algebraic structures. - Matrices, matrix operations and matrix rank. - Systems of linear equations and Gaussian elimination method. - Vector space. Linear dependence and independence of vectors. Bases and dimensions. - Determinants. Laplace expansion and Cramer's rule. - Inverse and pseudoinverse matrices. - Euclidean vector spaces. - Formulation and classification of linear programming (LP) tasks. - Methods of solving traffic problems. - Mathematical models of economic problems, transport problem, problem of production planning, division of resources, problem of mixing mixtures.
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Learning activities and teaching methods
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Lecturing, Methods for working with texts (Textbook, book), Practice exercises
- Participation in classes
- 20 hours per semester
- Preparation for course credit
- 30 hours per semester
- Preparation for examination
- 50 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| Have basic logical thinking |
| Have basic logical thinking |
| Have a basic understanding of high school mathematics |
| Have a basic understanding of high school mathematics |
| Read the materials provided and consult if there is any confusion |
| Read the materials provided and consult if there is any confusion |
| Skills |
|---|
| Regularly attend lectures |
| Regularly attend lectures |
| Answer questions at the lecture (every answer is appreciated) |
| Answer questions at the lecture (every answer is appreciated) |
| Show interest and effort in the subject |
| Show interest and effort in the subject |
| learning outcomes |
|---|
| Knowledge |
|---|
| Distinguish between propositional and predicate logic |
| Distinguish between propositional and predicate logic |
| Vyjmenovat algebraické struktury s jednou a dvěma binárními operacemi |
| Vyjmenovat algebraické struktury s jednou a dvěma binárními operacemi |
| Define a matrix over real numbers and describe matrix operations (sum, product, scalar multiplication, transpose) |
| Define a matrix over real numbers and describe matrix operations (sum, product, scalar multiplication, transpose) |
| Vysvětlit důležitost fundamentálního systému řešení homogenní lineární soustavy rovnic |
| Vysvětlit důležitost fundamentálního systému řešení homogenní lineární soustavy rovnic |
| Characterize three-dimensional vector space and describe the concept of the base of space |
| Characterize three-dimensional vector space and describe the concept of the base of space |
| Vysvětlit definici determinantu na základě permutací |
| Vysvětlit definici determinantu na základě permutací |
| Charakterizovat inverzní matici a popsat způsoby jejího nalezení |
| Charakterizovat inverzní matici a popsat způsoby jejího nalezení |
| Recognize the differences between classical vector space and Euclidean vector space |
| Recognize the differences between classical vector space and Euclidean vector space |
| Formulate a linear programming problem and outline a method by which this problem can be solved |
| Formulate a linear programming problem and outline a method by which this problem can be solved |
| Distinguish between balanced and unbalanced traffic problems and use the correct procedure to solve the corresponding problem |
| Distinguish between balanced and unbalanced traffic problems and use the correct procedure to solve the corresponding problem |
| Skills |
|---|
| Prohloubit logické myšlení (nejen v oblasti matematiky a nejen na univerzitní půdě) |
| Prohloubit logické myšlení (nejen v oblasti matematiky a nejen na univerzitní půdě) |
| Analyze an algebraic structure with one binary operation |
| Analyze an algebraic structure with one binary operation |
| Solve a system of linear equations, independent of the number of equations and unknowns, using elementary row transformations |
| Solve a system of linear equations, independent of the number of equations and unknowns, using elementary row transformations |
| Find a fundamental solution system for a homogeneous system of linear equations |
| Find a fundamental solution system for a homogeneous system of linear equations |
| Určit lineární závislost a nezávislost vektorů, a popřípadě bázi prostoru, respektive podprostoru |
| Určit lineární závislost a nezávislost vektorů, a popřípadě bázi prostoru, respektive podprostoru |
| Calculate the determinant of a matrix of degree 3 using Sarrus rule and of degree 4 and higher using Laplace development |
| Calculate the determinant of a matrix of degree 3 using Sarrus rule and of degree 4 and higher using Laplace development |
| Determine the inverse matrix to the regular matrix over the real numbers |
| Determine the inverse matrix to the regular matrix over the real numbers |
| Apply the graphical method to a linear programming problem with two variables |
| Apply the graphical method to a linear programming problem with two variables |
| Construct a transport problem and find the minimum cost |
| Construct a transport problem and find the minimum cost |
| teaching methods |
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| Knowledge |
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| Lecturing |
| Lecturing |
| Projection (static, dynamic) |
| Projection (static, dynamic) |
| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| Skills |
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| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| assessment methods |
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| Knowledge |
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| Grade (Using a grade system) |
| Written examination |
| Written examination |
| Grade (Using a grade system) |
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Recommended literature
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GROS, I. Kvantitativní metody v manažerském rozhodování 1. vydání. Praha, Grada Publishing a.s., 2003. ISBN 80-247-0421-8.
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Hasík, K. Matematické metody v ekonomii. Opava: učební text SU v Opavě, 2008.
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Hort, Daniel. Algebra I. 1. vyd. Olomouc : Univerzita Palackého, 2003. ISBN 8024406314.
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JABLONSKÝ, J. Operační výzkum. Praha: Professional Publishing, 2011. ISBN 978-80-86946-44-3.
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Jukl, Marek. Lekce z lineární algebry. Olomouc : Univerzita Palackého, 2012.
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Jukl, Marek. Lineární algebra (Euklidovské vektorové prostory, homomorfizmy vektorových prostorů)). Olomouc : Univerzita Palackého, 2010. ISBN 978-80-244-2522-1.
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Korda, B. a kol. Matematické metody v ekonomii. Praha : SNTL, 1967.
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Kozáková. Lineární algebra. Zlín: učební text FAI UTB, 2018.
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Matejdes, M. Aplikovaná matematika. Zvolen: Matcentrum, 2005. ISBN 80-89077-01-3.
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PEKAŘ, L. Optimalizace, studijní materiály, přednášky. Zlín, 2013.
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Škrášek, J., Tichý, Z. Základy aplikované matematiky I., II. Praha : SNTL, 1986.
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