SubjectsSubjects(version: 964)
Course, academic year 2024/2025
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Number Theory - O02310061
Title: Teorie čísel
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2018
Semester: summer
E-Credits: 5
Examination process: summer s.:
Hours per week, examination: summer s.:2/1, C+Ex [HT]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Explanation: Rok3Student zapíše jeden z kurzů Funkce více proměnných nebo Metody matematické anal
Old code: TEČÍ
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: RNDr. František Mošna, Ph.D.
doc. RNDr. Antonín Jančařík, Ph.D.
Classification: Mathematics > Real and Complex Analysis
Annotation -
The subject deals with the basic concepts of number theory. The particular types of numbers, the ways of their construction and their most important properties are concerned there.
Last update: MOSNAF/PEDF.CUNI.CZ (28.03.2009)
Aim of the course -

Purpose of the course is to make students acquainted with the elements of number theory.

Last update: MOSNAF/PEDF.CUNI.CZ (28.03.2009)
Course completion requirements - Czech

Zápočet bude udělen na základě výsledků dvou písemek. Jednu znich bude možné nahradit domácími úkoly.

Při odevzdávání materiálů v průběhu zkouškového období se musí student dostavit k ústnímu termínu zkoušky/zápočtu.

Last update: Jančařík Antonín, doc. RNDr., Ph.D. (02.02.2018)
Literature -
  • Cohen, H.: A Course in Computational Algebraic Number Theory. Springer-Verlag 1993.
  • Koblitz, N.: A Course in Numer Theory and Cryptography. Springer-Verlag 1998.
  • Korec, I.: Úlohy o veĺkých číslach. Praha : ÚV MO 1988.
  • Rosen, H.: Elementary Number Theory and Its Applications. Addison-Wesley. 2000.
  • Singh S.: Velká Fermatova věta. Praha: Academia 2000.
  • Šedivý J.: Základní poznatky z algebry a teorie čísel. Praha: SPN 1984.
  • Znám Š.: Teória čísel. Bratislava: Alfa 1977.

Last update: MOSNAF/PEDF.CUNI.CZ (28.03.2009)
Teaching methods -

Lecture and seminar

Last update: MOSNAF/PEDF.CUNI.CZ (28.03.2009)
Syllabus -
  • Natural numbers, construction, Peano axioms, adding, multiplying, order.
  • Divisibility, prime numbers, perfect numbers, Fermat theorem, Euler theorem, Gauss theorem, Tchebysew theorem - the number of prime numbers.
  • Integers, construction, operations and order.
  • Rational numbers, construction, operations and order, enumerability.
  • Real numbers, construction by means of fundamental sequences - Cantor method, supremum and infimum theorem, mention of other ways of construction - Dedekind, Kolmogorov, Conway.
  • Algebraic and transcendental numbers.
  • Euler number (e) a Ludolf number (pí), Euler constant (a), properties, relationship to sequences and series, relationship to probability.
Last update: MOSNAF/PEDF.CUNI.CZ (28.03.2009)
 
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