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Lecturer(s)
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Botur Michal, doc. Mgr. Ph.D.
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Halaš Radomír, prof. Mgr. Dr.
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Course content
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- Natural numbers. Peano axioms, arithmetic operations and ordering in NN. - Embedding of a semigroup into a group, the integers, ordering of ZZ via NN, ordered rings and their properties. - Field of fractions of an integral domain, the rational numbers, ordering of QQ. - Real numbers. Dedekind cuts and Cantor?s theory of Cauchy (fundamental) sequences. - Complex numbers. - Numeral systems, zz-adic expansions of numbers, divisibility criteria. - Hyper-complex numbers.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Understand the construction of number fields
Understanding of constructions of number systems
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral exam, Written exam
Credit:, active participation in exercises, final test. Exam: understanding the material and being able to prove the main proposition.
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Recommended literature
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Judson, T. W. Abstract Algebra: Theory and Applications.
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Silverman, Joseph H. (2013). A Friendly Introduction to Number Theory. 4th ed.. Boston: Pearson Addison-Wesley.
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Stillwell, J. (2013). The Real Numbers: An Introduction to Set Theory and Analysis. New York: Springer.
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