470-6301/01 – Discrete Mathematics (MDM)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantordoc. Mgr. Petr Kovář, Ph.D.Subject version guarantordoc. Mgr. Petr Kovář, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEI, USPIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
KOV16 doc. Mgr. Petr Kovář, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Combined Examination 28+0

Subject aims expressed by acquired skills and competences

Each student is supposed to - analyze real life problems - express them using discrete mathematics formulation - solve the problem using methods of discrete mathematics - give an interpretation of the theoretical results in the terms of the original problems At the same time he should decide what are the limits of an ideal theoretical solution in contrast to the real situation.

Teaching methods

Lectures
Individual consultations
Tutorials
Project work

Summary

The scope of the course are selected topics of Discrete mathematics (combinatorics, graph theory and Combinatorial Designs. Applications vary from real life problems to application of one field in other branch of discrete mathematics (such as coding theory and error correcting codes).

Compulsory literature:

D. B. West, Introduction to graph theory - 2nd ed., Prentice-Hall, Upper Saddle River NJ, (2001). Hill: A First Course in Coding Theory, Clarendon Press, Oxford, reprinted 2009. C.C. Lindner, C.A. Rodger, Design Theory second edition, CRC Press, Boca Raton FL, (2009)

Recommended literature:

Rosen K.: Discrete Mathematics and Its Applications - 6th ed., McGraw-Hill NY, 2007, 0-07-288008-2 Norman L. Biggs: Diskrete Mathematics Revised Edition, Oxford University Press, 1994, ISBN 019-853427-2

Way of continuous check of knowledge in the course of semester

Active participation during lectures. Project - progress consulting. The exam has a written and oral part.

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures (chosen among the following topics) 1) Sets, relations and functions. Algorithms and their complexity. Mathematical induction. Permutations and k-permutations, binomial coefficients and combinatorial identities. Inclusion and exclusion principle. 2) Recurrence relations. Applications, constructions and solving recurrence relations. Generating functions. 3) Pigeon-hole principle and its applications. 4) graphs and introduction to graph theory. 5) Communication networks, shortest/widest path, network flows, bipartite graphs, trees and spanning trees. Searching trees, algorithms. Bridges and articulations, Vertex and Edge-connectivit, blocks. Oriented and weighted graphs, networks and flows, cuts and max-flown min-cut theorem. 6) Planar and non planar graphs. 7) Main coding theory problem. Equivalence of codes, necessary and sufficient conditions of the existence of (n, M, d) - codes, Hamming bound, perfect codes. 8) Finite fields and vector spaces Orthogonal Latin squares, projective planes. 9) Codes and Latin squares. Latin squares and mutually orthogonal Latin squares. 10) Introduction to combinatorial designs. Symmetric designs, Application in coding theory. 11) Steiner triple systems. Constructions and relation to graph decompositions. During the semester each student prepares one or two projects.

Conditions for subject completion

Combined form (validity from: 2013/2014 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
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2018/2019 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
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2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
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2017/2018 (P2658) Computational Sciences (2612V078) Computational Sciences K Czech Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
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2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
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2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
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2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
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2010/2011 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

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