Mathematical Logic 360-MS2-2LM
Course profile: academic
Form of study: stationary
Course type: obligatory
Academic discipline: Mathematics, field of study in the arts and science: mathematics
Year: 2, semester: 4
Prerequisities: none
lecture 30 h. exercise class 30 h.
Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups.
ECTS credits: 5
Balance of student workload:
attending lectures15x2h = 30h
attending exercise classes 15x2h = 30h
preparation for classes 15h
home work 15h
consultations 12h
preparation to tests 10h
preparation to final exam 10h
final exam 3h
Quantitative description
Direct interaction with the teacher: 75 h., 3 ECTS
Practical exercises: 50 h., 2 ECTS
Course coordinators
Type of course
Mode
Learning outcomes
The student knows the basic syntactic notions of the classical propositional logic and the classical calculus of quantifiers, the language of logic, Hilbert – style proof system, a thesis, a derivable rule, the syntactic consequence operation: KA7_WG02, KA7_WG04.
The student knows the basic logical notions connected with the matrix semantics of the classical propositional logic and the standard semantics of the classical calculus of quantifiers (the classical predicate calculus): KA7_WG04.
The student knows the essence of metamathematical properties of a logical system, such as: soundness, completeness, consistency, decidability: KA7_WG02, KA7_WG04.
The student knows the basic theorems of the classical propositional logic and the classical calculus of quantifiers: the deduction theorem, Lindenbaum’s theorem, Post - completeness theorem, Gödel’s completeness theorem: KA7_WG02, KA7_WG04, KA7_WG06.
The student knows how to construct Hilbert – style proofs. The student knows how to prove the properties of the logical notions presented during the lectures (e. g. the notion of the syntactic consequence). The student knows how to prove the non difficult metamathematical properties of logical systems: KA7_UW02, KA7_UK01, KA7_UW03.
The student knows how to apply the definitions and theorems in formal proofs: KA7_UW02, KA7_UW03.
The student knows how to apply the truth – table method for checking if a given propositional formula is a tautology: KA7_UW02, KA7_UK01, KA7_UW03.
The student is able to present examples of valid, satisfiable and unsatisfiable formulas of the classical propositional logic and of the classical calculus of quantifiers (the classical predicate calculus): KA7_UW02, KA7_UK01, KA7_UW03.
The student is able to precisely formulate questions while seeking the missing details in argumentation and developing his knowledge of a studied subject: KA7_UU01.
Assessment criteria
The overall form of credit for the course: final exam
Bibliography
A. Grzegorczyk, An outline of mathematical logic, PWN, Warszawa 1974
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: