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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

BI-ZDM Elements of Discrete Mathematics Extent of teaching: 2P+2C
Instructor: Legerský J., Scholtzová J. Completion: Z,ZK
Department: 18105 Credits: 5 Semester: Z

Annotation:
Students get both a mathematical sound background, but also practical calculation skills in the area of combinatorics, value estimation and formula approximation, tools for solving recurrent equations, and basics of graph theory.

Lecture syllabus:
1. Sets, cardinality, countable sets, power set of a finite set and its cardinality.
2. Power set of the set of natural numbers - uncountable set.
3. Exclusion and inclusion, its use to determine cardinality.
4. "Pigeon-hole principle", number of structures, i.e., number of maps, relations, trees (on finite structures).
5. Function estimates (factorial, binomial coefficients, ...).
6. Relation, equivalence relation (examples of equivalence of connected/strongly connected components).
7. Relation matrix, relational databases.
8. Mathematical induction as a tool for determining the number of finite objects.
9. Mathematical induction as a tool for proving algorithm correctness.
10. Mathematical induction as a tool for solving recursive problems.
11. Structural induction.
12. Runtime complexity of recursive algorithms - solving recursive equations with constant coefficients, homogeneous equations.
13. Solving non-homogeneous recursive equations with constant coefficients.

Seminar syllabus:
1. Cardinality calculations.
2. Countability, uncountability.
3. Inclusion and exclusion principle.
4. Numbers of structures over finite sets.
5. Asymptotic function behavior.
6. Relations and directed graphs.
7. Basic proofs by induction.
8. Application of proofs by induction in combinatorics.
9. Application of proofs by induction in programming.
10. Induction and recursive algorithms.
11. Uses of induction in formal language theory.
12. Runtime complexity calculations.
13. Solving linear recurrent equations.

Literature:
1. Johnsonbaugh, R. Discrete Mathematics (4th Edition). Prentice Hall, 1998. ISBN 0130805505.

Requirements:
Students should have an adequate knowledge of basic notions of mathematics and mathematical logic as presented in previous subjects BI-ZMA, BI-MLO and BI-LIN.

Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/BI-ZDM/

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
BI-SPOL.2015 Unspecified Branch/Specialisation of Study PP Není
BI-WSI-PG.2015 Web and Software Engineering PP Není
BI-WSI-WI.2015 Web and Software Engineering PP Není
BI-WSI-SI.2015 Web and Software Engineering PP Není
BI-ISM.2015 Information Systems and Management PP Není
BI-ZI.2018 Knowledge Engineering PP Není
BI-PI.2015 Computer engineering PP Není
BI-TI.2015 Computer Science PP Není
BI-BIT.2015 Computer Security and Information technology PP Není


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška