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An introduction to algebraic number theory - NMMB360

Title:	Úvod do algebraické teorie čísel
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Additional information:	https://sites.google.com/view/pyatsyna/teaching/algebraic-number-theory

Guarantor:	doc. Mgr. Vítězslav Kala, Ph.D.
Class:	M Mgr. MSTR > Povinně volitelné
Classification:	Mathematics > Algebra
Incompatibility :	NMIB053
Interchangeability :	NMIB053
Is interchangeable with:	NMIB053

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

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.

Last update: T_KA (16.05.2012)

Course completion requirements -

Oral exam

Last update: Kala Vítězslav, doc. Mgr., Ph.D. (21.02.2020)

Literature -

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.

Last update: G_M (27.04.2012)

Requirements to the exam -

Students have to pass final oral exam. The requirements for the exam correspond to what has been done during lectures.

Last update: Kala Vítězslav, doc. Mgr., Ph.D. (21.02.2020)

Syllabus -

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.

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