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Lecturer(s)
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Halaš Radomír, prof. Mgr. Dr.
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Cenker Václav, Mgr.
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Emanovský Petr, doc. RNDr. Ph.D.
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Botur Michal, doc. Mgr. Ph.D.
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Course content
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1. Ring of polynomials and its properties: Functional and algebraic definition from the structural point of view. 2. 3. Divisibility of polynomials over a general field: Properties of the structure (T x , +, ) concerning divisibility. 4. Properties of polynomial roots: Root of a polynomial, multiplicity of the root, the Bezout theorem, the Horner scheme, derivative of a polynomial and its application, the Basic Theorem of Algebra, decomposition of polynomials to product of irreducible ones over Q, R and C, the Viéte theorem, methods of root solving of polynomials. 5. Algebraic solvability of algebraic equations: Extension of fields using radicals, algebraic solvability of algebraic equations with respect to degree. 6. Numerical methods of solving algebraic equations: Essence of numerical methods, basic methods of separation and aproximation of real roots.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Understand bases of theory of polynomials, to master solving the typical tasks.
3. Aplication Students obtain ability to apply knowledge of theory of polynomials and algebraic equations for solving of particular equations
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Prerequisites
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unspecified
KAG/ALG1
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Assessment methods and criteria
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Oral exam, Written exam
Credit: the student has to pass one written test (i.e. to obtain at least half of the possible points in the test). Exam:
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Recommended literature
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Bican, L. (2000). Lineární algebra a geometrie. Praha, Academia.
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Blažek J. (1985). Algebra a teoretická aritmetika I. SPN Praha.
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Emanovský P. (2002). Algebra 2, 3 (pro distanční studium). VUP Olomouc.
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Emanovský P. (1998). Cvičení z algebry (polynomy, algebraické rovnice). VUP Olomouc.
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Kořínek V. (1956). Základy algebry. NČSAV Praha.
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Waerden, L. (1971). Algebra I. Springer-Verlag Berlin, Heidelberg, New York.
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