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Course, academic year 2019/2020
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An introduction to algebraic number theory - NMMB360
Title in English: Úvod do algebraické teorie čísel
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information: https://sites.google.com/site/vitakala/teaching/18uatc
Guarantor: Mgr. Vítězslav Kala, Ph.D.
Class: M Bc. MMIB
M Bc. MMIB > Doporučené volitelné
M Bc. MMIT
M Bc. MMIT > Doporučené volitelné
Classification: Mathematics > Algebra
Incompatibility : NMIB053
Interchangeability : NMIB053
Annotation -
Last update: T_KA (16.05.2012)
A recommended elective course for bachelor's program in Information security. The lecture introduces notions of algebraic number theory. Beside the theory of Dedekind domains, which will be deepened and illustrated, the lecture will be focused on number fields, ideal class groups and quadratic fields.
Course completion requirements - Czech
Last update: Mgr. Vítězslav Kala, Ph.D. (11.06.2019)

Ústní zkouška

Literature -
Last update: G_M (27.04.2012)

E.I. Borevič, I.R. Šafarevič: Number Theory, Academic Press 1966;

H. Cohen: A course in computational algebraic number theory, Springer-Verlag, Berlin 1996.

A. Frőhlich, M.J. Taylor, Algebraic number theory, Cambridge University Press, Cambridge 1991.

R.I.Harold, M. Edwards: Higher arithmetic: an algorithmic introduction to number theory, AMSociety, Providence 2008.

H. Matsumura, Commutative Ring Theory, W. A. Benjamin, 1970.

V. Shoup: A computational introduction to number theory and algebra, Cambridge University Press, Cambridge 2009.

Requirements to the exam - Czech
Last update: Mgr. Vítězslav Kala, Ph.D. (14.02.2018)

Zkouška bude ústní s 30-60 minutami na přípravu jedné nebo dvou otázek, odpovídajících probrané látce na přednáškách.

Syllabus -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (26.09.2012)

1. Fractional ideals of Dedekind domains, absolute norm of ideals, the finiteness of class groups.

2. Lattices. Blichfeldt's lemma.

3. Units of rings of algebraic integers, Dirichlet's Unit Theorem.

4. Quadratic and cubic fields, selected Diophantine equations.

 
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