Subject description - B6B01ZDM

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B6B01ZDM Introduction to Discrete Mathematics
Roles:P Extent of teaching:2P+2S+2D
Department:13101 Language of teaching:CS
Guarantors:Tišer J. Completion:Z,ZK
Lecturers:Tišer J. Credits:5
Tutors:Tišer J. Semester:Z

Web page:

https://math.fel.cvut.cz/en/people/tiser/vyuka.html

Anotation:

No advanced knowleges of mathematics are required at the beginning of this course. Using illustrative examples we build sufficient understanding of combinatorics, set and graph theory. Then we proceed to formal construction of propositional calculus.

Study targets:

The aim of this subject is to develop logical reasoning and to analyze logical structure of propositions. The basics form combinatorics, graph and set theories are included as well.

Content:

No advanced knowleges of mathematics are required at the beginning of this course. Using illustrative examples we build sufficient understanding of combinatorics, set and graph theory. Then we proceed to formal construction of propositional calculus.

Course outlines:

1. Basic combinatorics, Binomial Theorem.
2. Inclusion and Exclusion Pronciple and applications.
3. Cardinality of sets, countable set and their properties.
4. Uncoutable sets, Cantor Theorem.
5. Binary relation, equivalence.
6. Ordering, minimal and maximal elements.
7. Basic from graph theory, connected graphs.
8. Eulerian graphs, trees and their properties.
9. Weighted tree, minimal spanning tree.
10. Bipartite graph, matching in bipartite graphs.
11. Well-formed formula in propositional calculus.
12. Logical consequence, boolean functions.
13. Disjunctive and conjunctive normal forms, satisfiable sets, resolution method.
14. Well-formed formula in predicate calculus.

Exercises outline:

1. Basic combinatorics, Binomial Theorem.
2. Inclusion and Exclusion Pronciple and applications.
3. Cardinality of sets, countable set and their properties.
4. Uncoutable sets, Cantor Theorem.
5. Binary relation, equivalence.
6. Ordering, minimal and maximal elements.
7. Basic from graph theory, connected graphs.
8. Eulerian graphs, trees and their properties.
9. Weighted tree, minimal spanning tree.
10. Bipartite graph, matching in bipartite graphs.
11. Well-formed formula in propositional calculus.
12. Logical consequence, boolean functions.
13. Disjunctive and conjunctive normal forms, satisfiable sets, resolution method.
14. Well-formed formula in predicate calculus.

Literature:

K. H. Rosen: Discrete mathematics and its applications, 7th edition, McGraw-Hill, 2012.

Requirements:

Grammar school knowledge.

Keywords:

Permutations and combinations, bijection, countable and uncoutable sets, trees and bipatrite graphs, reltions on set, equivalence and ordering, well-formed formula of propositional calculus, logical consequence and resolution method, formula in predicate calculus.

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPSIT_2021 Common courses P 1
BPSIT4_2021 Technologie internetu věcí P 1
BPSIT3_2021 Business informatics P 1
BPSIT2_2021 Technologie pro multimédia a virtuální realitu P 1
BPSIT1_2021 Enterprise systémy P 1
BPSIT Common courses P 1


Page updated 23.7.2024 17:51:35, semester: Z,L/2023-4, Z,L/2024-5, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)