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Lecturer(s)
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Jirsák Čeněk, Mgr.
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Koucký Miroslav, doc. RNDr. CSc.
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Course content
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Selected algebraic structures - Partially ordered set (poset), minimal/maximal, least/greatest element, lattice. - Groups (Lagrange?s theorem, normal subgroup, cyclic, symmetric group) - Rings, integral domains, fields. Polynomials over a ring/field. Generating functions - Ordinary/exponential generating functions. - Applications in combinatorics (Fibonacci, Catalan, Stirling numbers, partitions). Recurrence relations. - Solving linear (non)homogenous recurrence relations, method of generating functions. Difference equations. - Divide-and-conquer algorithms.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Preparation for exam
- 80 hours per semester
- Class attendance
- 56 hours per semester
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Learning outcomes
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Selected algebraic structures - lattices, groups, rings, fields. Generating functions - ordinary/exponential and their applications in combinatorics. Recurrence relations, solving linear (non)homogenous recurrence relations, method of generating functions. Difference equations. Divide-and-conquer algorithms.
Theoretical knowledge and ability to apply them.
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Prerequisites
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Knowledge of the secondary level mathematics
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Assessment methods and criteria
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Combined examination
Active participation in seminars, credit, knowledge according to syllabus.
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Recommended literature
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Matoušek J., Neštřil J. Kapitoly z diskrétní matematiky. Praha, Karolinum, 2009. ISBN 8024617404.
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Procházka L. Algebra. Praha, 1990. ISBN 8020003010.
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Rosen K. Discrete mathematics and its applications. McGraw-Hill, 1999. ISBN 0073383090.
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