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.
BIE-LOG.21 Mathematical Logic Extent of teaching: 2P+2C Instructor: Trlifajová K. Completion: Z,ZK Department: 18105 Credits: 5 Semester: Z Annotation:
The course focuses on the basics of propositional and predicate logic. It starts from the semantic point of view. Based on the notion of truth, satisfiability, logical equivalence, and the logical consequence of formulas are defined. Methods for determining the satisfiability of formulas, some of which are used for automated proving, are explained. This relates to the P vs. NP problem and Boolean functions in propositional logic. In predicate logic, the course further deals with formal theories, such as arithmetics, and their models. The syntactic approach to mathematical logic is demonstrated on the axiomatic system of propositional logic and its properties. Gödel's incompleteness theorems is explained.
Lecture syllabus:
1. Historical introduction. Syntax and semantics of propositional logic. Proof by induction. 2. Logical equivalence. Full and minimal conjunctive and disjunctive normal forms. 3. Logical consequence. Tableau method for propositional logic. 4. Resolution method. SAT problem. P vs. NP problem. 5. Boole algebra. Boolean functions. 6. Predicate logic. Syntax. Interpretation. 7. Logical truth, satisfiability, contradictions. Logical equivalence. 8. Logical consequence. Tableau method for predicate logic. 9. Prenex normal forms. Resolution method for predicate logic. 10. First-order theories and its models. Ordering, equivalence, arithmetic. 11. Axiomatic system of propositional logic. 12. Consistency, correctness, completeness. 13. Gödel incompleteness theorems. Seminar syllabus:
1. Propositional formulas. Truth tables. Formalization. 2. Basic logical laws. Universal system of connectives. 3. Disjunctive and conjunctive normal forms. Logical consequence. 4. Tableau method. Resolution method. 5. Boole algebra: properties, counting, ordering, atoms. 6. Predicate logic. Language, terms, formulas. Formalization. 7. Three levels of truth. Logical equivalence. 8. Interpretation. Satisfiable formulas. 9. Logical consequence. Tableau method. 10. Prenex form. Resolution method. 11. Theories and their models. Isomorphism and elementary equivalence. 12. Hilbert axiomatic system. 13. Repetition. Literature:
1. Mendelson E. : Introduction to Mathematical Logic (6th Edition). Chapman and Hall, 2015. ISBN 978-1482237726. 2. Bergmann M., Moor J., Nelson J. : The Logic Book (6th Edition). McGraw-Hill, 2013. ISBN 978-0078038419. Requirements:
Knowledge of basic mathematical structures from algebra and analysis
The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester BIE-SI.21 Software Engineering 2021 V 5 BIE-PS.21 Computer Networks and Internet 2021 VO 5 BIE-PI.21 Computer Engineering 2021 V 5 BIE-IB.21 Information Security 2021 (Bachelor in English) V 5 BIE-TI.21 Computer Science 2021 PS 5 BIE-PV.21 Computer Systems and Virtualization 2021 V 5
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