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.
BIK-DML.21 Discrete Mathematics and Logic Extent of teaching: 14KP+4KC Instructor: Pernecká E. Completion: Z,ZK Department: 18105 Credits: 5 Semester: Z Annotation:
Students will get acquainted with the basic concepts of propositional logic and predicate logic and learn to work with their laws. Necessary concepts from set theory will be explained. Special attention is paid to relations, their general properties, and their types, especially functional relations, equivalences, and partial orders. The course also lays down the basics of combinatorics and number theory, with emphasis on modular arithmetics.
Lecture syllabus:
1. Propositional logic. Formulas. Truth tables. Logical equivalence. Basic laws. 2. Disjunctive and conjunctive normal forms. Full forms. Logical consequence. 3. Predicate logic. Formalization of language. Types of mathematical proofs. 4. Mathematical induction. 5. Sets, relations, functions. Basic number sets. Cardinalities of sets. 6. Binary relations (properties, representations). Composition of relations. 7. Equivalence and ordering. 8. Enumerative combinatorics and its basic principles. 9. Classical definition of probability. 10. k-combinations with repetition, permutations with repetition, Stirling numbers, properties of binomial coefficients. 11. Fundamentals of number theory, modular arithmetic. 12. Properties of prime numbers, Fundamental theorem of arithmetic. 13. Diophantine equations, linear congruences, Chinese remainder theorem. Seminar syllabus:
1. Introduction to mathematical logics. 2. Formulas, truth tables. Tautology, contradiction, satisfiability; consequence and equivalence. 3. Universal systems of connectives. Disjunctive and conjunctive normal forms, minimalization, Karnaugh maps. 4. Syntax of predicate logic. Language, terms, formulas. 5. Formalization of language. Types of mathematical proofs. 6. Mathematical induction. 7. Sets and maps. 8. Binary relation (properties, representation), composition of relations. 9. Equivalence and order. 10. Application of combinatorial principles. 11. Advanced combinatorial problems, probability, 12. Divisibility. Diophantine equations solution. 13. Solution of linear congruences and their systems. Literature:
1. Mendelson E.: Introduction to Mathematical Logic (6th Edition); Chapman and Hall 2015; ISBN 978-1482237726 2. Chartrand G., Zhang P.: Discrete Mathematics; Waveland;2011; ISBN 978-1577667308 3. Graham R. L., Knuth D. E., Patashnik O.: Concrete Mathematics: A Foundation for Computer Science (2nd Edition); Addison-Wesley Professional; 1994; ISBN 978-0201558029 4. Trlifajová K., Vašata D.: Matematická logika; ČVUT2017; ISBN 978-80-01-05342-3 5. Nešetřil J., Matoušek J.: Kapitoly z diskrétní matematiky; Karolinum2007; ISBN 978-80-246-1411-3 Requirements:
None.
The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester BIK-IB.21 Information Security 2021 (in Czech) PP 1 BIK-SPOL.21 Unspecified Branch/Specialisation of Study PP 1 BIK-PV.21 Computer Systems and Virtualization 2021 (in Czech) PP 1 BIK-PS.21 Computer Networks and Internet 2021 (in Czech) PP 1 BIK-SI.21 Software Engineering 2021 (in Czech) PP 1
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