Course objectives:
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The aim of this course is to introduce the students to the basics of mathematical logic. The course covers the propositional calculus as well as the first-order predicate calculus and includes an overview of the incompleteness results of K. Gödel.
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Requirements on student
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Oral examination only. The student is assigned one topic from the list in the course overview.
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Content
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1. The language of propositional logic, truth values
2. Deduction in propositional logic, the Deduction Theorem
3. The completeness theorem for propositional logic
4. The language of predicate logic
5. Structures and models
6. Deduction in predicate logic
7. The completeness theorem for predicate logic
8. Gödel's incompleteness theorem for arithmetic
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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52
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Preparation for an examination (30-60)
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32
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Total
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84
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
The only prerequisite is a moderate level of experience with mathematical thinking and proof techniques. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
Upon completion of this course, students will acquire basic orientation in the subject and become capable of independent study of the literature. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
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