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Lecturer(s)
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Cerman Zbyněk, Mgr. Ph.D.
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Course content
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- Propositional and predicate logic - Sets, Binary relations and Maps - Algebraic structures - Matrices and matrix operations - Systems of linear equations and Gaussian elimination method - Vector spaces: linear dependence and independence of vectors, base and dimension - Determinants: Laplace expansion and Cramer's rule. - Inverse matrices - Euclidean vector spaces - Orthogonal complement - Orthonormal basis - Perpendicular projection of a vector into a subspace - Linear programming: graphic and simplex method - Balanced and unbalanced transportation problem
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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
- 56 hours per semester
- Home preparation for classes
- 2 hours per semester
- Preparation for course credit
- 8 hours per semester
- Preparation for examination
- 34 hours per semester
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| prerequisite |
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| Knowledge |
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| Have a basic understanding of high school mathematics |
| Have a basic understanding of high school mathematics |
| Have basic logical thinking |
| Have basic logical thinking |
| Read the provided materials and consult if there is any confusion |
| Read the provided materials and consult if there is any confusion |
| Skills |
|---|
| Show interest and effort in the subject |
| Show interest and effort in the subject |
| Regularly attend lectures and exercises |
| Regularly attend lectures and exercises |
| Be active in the exercises and answer questions during the lecture (every answer is appreciated) |
| Be active in the exercises and answer questions during the lecture (every answer is appreciated) |
| learning outcomes |
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| Knowledge |
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| Distinguish between propositional and predicate logic |
| Distinguish between propositional and predicate logic |
| List algebraic structures with one and two binary operations |
| List algebraic structures with one and two binary operations |
| 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) |
| Explain the importance of the fundamental system of solutions of a homogeneous linear system of equations |
| Explain the importance of the fundamental system of solutions of a homogeneous linear system of equations |
| Characterize three-dimensional vector space and describe the concept of base of space |
| Characterize three-dimensional vector space and describe the concept of base of space |
| Explain the definition of a determinant based on permutations |
| Explain the definition of a determinant based on permutations |
| Characterize the inverse matrix and describe how to find it |
| Characterize the inverse matrix and describe how to find it |
| Recognize the differences between classical vector space and Euclidean vector space |
| Recognize the differences between classical vector space and Euclidean vector space |
| Describe the orthogonal complement in Euclidean vector spaces and its relation to the whole space |
| Describe the orthogonal complement in Euclidean vector spaces and its relation to the whole space |
| Describe the procedure for constructing an orthonormal basis using the Gramm-Schmidt orthogonalization method |
| Describe the procedure for constructing an orthonormal basis using the Gramm-Schmidt orthogonalization method |
| Explain the concept of perpendicular vector projection and in particular its use in real life |
| Explain the concept of perpendicular vector projection and in particular its use in real life |
| Formulate a linear programming problem and outline the two main methods we can use to solve it |
| Formulate a linear programming problem and outline the two main methods we can use to solve it |
| 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 |
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| Deepen logical thinking (not only in mathematics and not only on campus) |
| Deepen logical thinking (not only in mathematics and not only on campus) |
| 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 |
| Determine the linear dependence and independence of the vectors and, if necessary, the base of the space or subspace |
| Determine the linear dependence and independence of the vectors and, if necessary, the base of the space or subspace |
| 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 |
| Create an orthonormal basis from an arbitrary basis using the Gramm-Schmidt orthogonalization method |
| Create an orthonormal basis from an arbitrary basis using the Gramm-Schmidt orthogonalization method |
| Display a vector in a subspace by perpendicular projection using the Gram matrix apparatus |
| Display a vector in a subspace by perpendicular projection using the Gram matrix apparatus |
| Apply the simplex method to a linear programming problem with any number of variables |
| Apply the simplex method to a linear programming problem with any number of 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 |
| Students working in pairs |
| Students working in pairs |
| 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) |
| Individual work of students |
| Individual work of students |
| Teamwork |
| Teamwork |
| Practice exercises |
| Practice exercises |
| assessment methods |
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| Knowledge |
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| Written examination |
| Grade (Using a grade system) |
| Grade (Using a grade system) |
| Written examination |
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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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