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Название дисциплины |
Introduction to Mathematics |
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Курс обучения |
1, Mathematics (Science-Industrial Activity) |
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Семестр обучения |
1 |
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Количество кредитов |
2 |
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Ф.И.О. лектора |
Candidate of Sciences in Psychics and Mathematics , Associate professor Kirill Kuzmin |
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Цели изучения дисциплины |
This course serves as the gateway to modern mathematics; its aim is to introduce some basic ideas and methods used in mathematics. The course contributes to three main goals. First, students are exposed to the notation as well as several important theorems and techniques of mathematics. More important, perhaps, is the role this course plays in introducing the student to the mathematical discipline. Emphasis is placed on the development of logical arguments and rigorous irrefutable proofs of mathematical truths. Beginning with very simple, rigid proofs, each student cultivates their unique style of devising proofs. Finally, in this course we prove a number of wild and mathematically interesting theorems so called paradoxes which play with different kinds of infinity and are crucial for understanding some concepts of set theory and logic. |
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Пререквизиты |
– |
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Содержание дисциплины |
Topics include: Peano axioms, mathematical induction, basic theory and manipulation of sets, Zermelo –Fraenkel set theory, cardinality concept, functions, binary relations, partial order, linear order, well-order, isomorphism, Zermelo’s theorem, Kuratowski–Zorn lemma, Banach – Tarski paradox. |
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Рекомендуемая литература |
1. Vereschagin N., Shen A. Lectures on mathematical logic and algorithms theory. Part 1. Basics of set theory – Moscow: Moscow Center for Continuous Mathematical Education, 2012. (in Russian) 2. Vilenkin N. Stories about sets – Moscow: Moscow Center for Continuous Mathematical Education, 2005. (in Russian) 3. Kononov S., Tyshkevich R., Yanchevckii V. Introduction to Mathematics. Parts 1–3 – Minsk: Belarusian State University, 2003. 4. Shen A. Mathematical induction – Moscow: Moscow Center for Continuous Mathematical Education, 2007. (in Russian)
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Методы преподавания |
Lectures, Seminars and Tutorials, Independent Study, Problem-based learning, Learning through research. |
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Язык обучения |
Russian |
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Условия (требования), текущий контроль |
To have a credit, one must obtain at least 70% in the first part of the final test or at least 67% in the second part of the final test. |
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Форма текущей аттестации |
Credit |