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

Annotation

English

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.

Last update: T_KDM (05.05.2014)

Czech

Číselné obory (N, Z, Q, R, C), prvočísla, dělitelnost, řetězové zlomky, aplikace komplexních čísel v geometrii. Polynomy a jejich kořeny. Grupy, Galoisova teorie a její aplikace.

Last update: T_KDM (05.05.2014)

Literature

English

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

Last update: T_KA (14.05.2008)

Czech

Stanovský: Základy algebry. Matfyzpress, 2010.

Blažek, Calda, Koman, Kusová: Algebra a teoretická aritmetika I, SPN Praha 1983

Blažek, Koman, Vojtášková: Algebra a teoretická aritmetika II, SPN Praha 1985

Ráb M.: Komplexní čísla v elementární matematice. 2. přeprac. vyd. MU, Brno, 1996.

Tignol J.-P.: Galois' Theory of Algebraic Equations. World Scientific Publishing, Singapore, 2001.

Last update: Halas Zdeněk, Mgr., DiS., Ph.D. (29.04.2014)

Syllabus

English

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.

Last update: T_KA (19.05.2006)

Czech

Číselné obory (N, Z, Q, R, C), prvočísla, dělitelnost, řetězové zlomky, aplikace komplexních čísel v geometrii.

Polynomy a jejich kořeny. Grupy, Galoisova teorie a její aplikace.

Last update: Halas Zdeněk, Mgr., DiS., Ph.D. (29.04.2014)