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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 2013 to 2017
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:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Is provided by:	OKB2310097
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

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

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

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.

Aim of the course -

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

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

Literature -

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

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.

Teaching methods -

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

Lecture and seminar

Syllabus -

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

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.