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Mathematical Logic

General data

Course ID: 0600-MS2-2LM Erasmus code / ISCED: 11.101 / (unknown)
Course title: Mathematical Logic Name in Polish: Logika matematyczna
Department: (in Polish) Instytut Matematyki
Course groups: (in Polish) 2L stac. II st. studia matematyki - przedmioty obowiązkowe
ECTS credit allocation (and other scores): 5.00
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Language: Polish
Type of course:

obligatory courses

Short description:

Course objectives: To convince the students of the necessity of making the language precise while studying the foundational problems in mathematics. To convince the students of the necessity of analysing the formal aspects of mathematical proofs. To presents to the students two formal languages: the language of propositional calculus and the language of the predicate calculus. To presents to the students the basic theorems of mathematical logic: the completeness theorem for propositional logic, the completeness theorem for the predicate calculus, the deduction theorem.

Full description:

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 7x3h = 21h

completing notes after exercises and lectures 7x2h = 14h

consultations 12x1h = 12h

the final examination: preparation.and take 12h + 3h = 15h

control works: repeating the material and preparation 3x4h = 12h

Quantitative description

Direct interaction with the teacher: 75 h., 3 ECTS

Practical exercises: 77 h., 3 ECTS

Learning outcomes:

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).K_W02, K_W04

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).K_W04

The student knows the essence of metamathematical properties of a logical system, such as: soundness, completeness, consistency, decidability.K_W02, K_W04

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.K_W02, K_W04, K_W07

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.K_U01, K_U02, K_U03

The student knows how to apply the definitions and theorems presented during the lectures, in formal proofs.K_U01, K_U03

The student knows how to apply the truth – table method for checking if a given propositional formula is a tautology.K_U01, K_U02, K_U03

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).K_U01, K_U02, K_U03

The student is able to to formulate precisely the questions used for seeking the missing details in argumentation and for developing his knowledge of a studied subject.K_K02

Assessment methods and assessment criteria:

The overall form of credit for the course: final exam

Classes in period "Academic year 2017/2018" (in progress)

Time span: 2017-10-01 - 2018-06-30
Choosen plan division:


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Type of class: Individual Classes more information
Coordinators: Krzysztof Belina-Prażmowski-Kryński
Group instructors: Krzysztof Belina-Prażmowski-Kryński
Students list: (inaccessible to you)
Examination: Examination
Course descriptions are protected by copyright.
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