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Lecturer(s)
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Plešinger Martin, doc. Ing. Ph.D.
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Course content
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Groups applied to symmetry. Cycle graph of a group. Cyclic groups, generator. Small groups and their structure. Subgroups. Inclusive graph of (normal) subgroups. Dihedral groups. Permutation groups. Direct product of groups. Normal subgroups. Factor groups. Homomorphism of groups and its kernel. Basics of lattice theory and boolean algebras. Partially ordered sets. Principle of duality. Boolean al-gebra. Applications of B-algebra. Minimization of B-functions. Propositional calculus. Seminars accompany lectures in accordance with instructions of lecturer.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Preparation for credit
- 14 hours per semester
- Preparation for exam
- 28 hours per semester
- Home preparation for classes
- 36 hours per semester
- Class attendance
- 42 hours per semester
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Learning outcomes
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Prohloubení základních znalostí obecné algebry a matematických struktur. Struktury s jednou a dvěma operacemi, uspořádané struktury, obecné algebry. Úvod do pokročilejších patrií: Liovy grupy, kvaterniony a oktorniony, boolovské algebry.
Theory, algorithms and applications of theory of groups, lattices, and Boolean algebra. Applications in geometry, symmetry, and synthesis of logical schemas.
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Prerequisites
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Algebra and geometry 1, 2.
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Assessment methods and criteria
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Combined examination, Oral exam, Written exam
Oral presentation of semester work in seminar (small groups of order at most 15, isomorphy of concrete models, applications).
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Recommended literature
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Beachy, J.A. - Blair, W.D. Abstract algebra, 3rd Edit.. Waveland Press, Inc., 2005.
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Bican, L. Algebra (pro učitelské studium). Praha, Academia, 2001. ISBN 80-200-0860-8.
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Birkhoff, G. - Bartee, T.C. Aplikovaná algebra. Bratislava, Alfa, 1981.
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Gallian, J. Contemporary Abstract Algebra. Boston, N.Y., Houlinghton Mifflin Comp., 1998. ISBN 0-618-51471-6.
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Gilbert J.:. Elements of modern algebra. PWS-KENT Publishing Company, Boston, 1988.
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Katriňák, T. aj. Algebra a teoretická aritmetika (1). Blava/Praha, Alfa/SNTL, 1985.
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Kopka J.:. Svazy a Booleovy algebry. Ústí nad Labem, UJEP, 1991. ISBN 80-7044-025-2.
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Mac Lane, S. - Birkhoff, G. Algebra. Bratislava, Alfa, 1973.
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Vild, J. - Šedý, J. Matematika II [Algoritmy a logika]. Liberec, VŠST, 1978.
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Weil, J. aj. Rozpracovaná řešení úloh z vyšší algebry. Praha, 1987.
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