Subjects

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Algebra II - NUMP020

Title:	Algebra II
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Mgr. Zdeněk Halas, DiS., Ph.D. RNDr. Eliška Pecinová, Ph.D.
Classification:	Mathematics > Algebra Teaching > Mathematics
Incompatibility :	NALG027, NMAI063, NMUM501
Interchangeability :	NALG027, NMUM501

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Annotation -

Last update: T_KDM (05.05.2014)

Number domains (N, Z, Q, R, C), primes, divisibility, continued fractions, geometrical applications of complex numbers. Polynomials and their roots. Groups, Galois theory and its applications.

Literature -

Last update: T_KA (14.05.2008)

T.X. Hungerford: Algebra, Springer, New York, 1974

S. Lang: Algebra, Springer, New York, 2002

S. Mac Lane, G. Birkhoff: Algebra, Providence: AMS Chelsea Publ. Co., 1999

Syllabus -

Last update: T_KA (19.05.2006)

Construction of integer, rational, real, and complex numbers, field extensions, degree of an algebraic extension, classical compass and ruler constructions and their unsolvability, constructions of regular n-gons, polynomial factorization, symbolic computation, the idea of self-correcting codes, the construction of Hamming codes, ability of codes detect and correct errors, information rate, elements of cryptography, classical ciphers, assymetric cryptography.