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Lecturer(s)
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Halaš Radomír, prof. Mgr. Dr.
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Course content
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1. Natural numbers. The Peano axioms, basic operations and ordering on natural numbers. 2. Embeddability of semigroups into groups, integers, ordering on Z by means of N, linearly ordered rings and their properties. 3. Fields of quotients of integral domains, the rational numbers, ordering on Q. 4. Real numbers. Dedekind cuts and the Cantor's theory of fundamental sequences. 5. Complex numbers. 6. z-adic expressions of natural numbers and rationals. Criteria of divisibility by natural 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 building of number systems. Understand basics of classical number theory with applications in solving problems at secondary schools.
Understanding of constructions of number systems. Learns important problems from number theory.
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Prerequisites
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unspecified
KAG/KALII and KAG/KALI
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Assessment methods and criteria
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Oral exam, Written exam
Exam: the student has to understand the subject and be able to prove the principal results.
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Recommended literature
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Balcar B., Štěpánek P. (1986). Teorie množin. Academia Praha.
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Blažek J. (1985). Algebra a teoretická aritmetika I. SPN Praha.
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Botur, M. (2011). Úvod do aritmetiky. UP Olomouc.
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Halaš, R. (1997). Teorie čísel. VUP Olomouc.
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Ireland M. (1987). Klasický úvod do moderní teorie čísel. Mir Moskva.
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Little C. H. C., TEO K. L., Van Brunt B. (2003). The numbersystems of analysis. World Scientific.
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Nathanson, M. B. (2000). Elementary methods in number theory. Springer.
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