Subject description - B6B01ZDM
Summary of Study |
Summary of Branches |
All Subject Groups |
All Subjects |
List of Roles |
Explanatory Notes
Instructions
| 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.htmlAnotation:
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 a brief formal construction of predicate calculus.Study targets:
The aim of this subject is the basics of combinatorics, graph and set theories and to develop logical reasoning in predicate calculus.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 a brief formal construction of predicate 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 and their characterizartion. | |
| 9. | Trees, basic properties. | |
| 10. | Weighted tree, minimal spanning tree. | |
| 11. | Bipartite graph, matching in bipartite graphs. | |
| 12. | Well-formed formula in propositional calculus. | |
| 13. | Well-formed formula in predicate calculus. | |
| 14. | Reserve. |
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 and their characterizartion. | |
| 9. | Trees, basic properties. | |
| 10. | Weighted tree, minimal spanning tree. | |
| 11. | Bipartite graph, matching in bipartite graphs. | |
| 12. | Well-formed formula in propositional calculus. | |
| 13. | Well-formed formula in predicate calculus. | |
| 14. | Reserve. |
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 in propositional calculus, well-formed 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 26.1.2025 15:51:13, semester: Z,L/2024-5, Z/2025-6, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |