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Algebraic Curves - NMAG302

Title:	Algebraické křivky
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2016
Semester:	summer
E-Credits:	5
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:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. David Stanovský, Ph.D.
Class:	M Bc. MMIB M Bc. MMIB > Povinné M Bc. MMIT M Bc. MMIT > Povinné M Bc. OM M Bc. OM > Zaměření MSTR M Bc. OM > Povinně volitelné
Classification:	Mathematics > Algebra
Incompatibility :	NMIB054
Interchangeability :	NMIB054
Is interchangeable with:	NMIB054
In complex pre-requisite:	NMAG349

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Annotation -

Last update: G_M (15.05.2012)

A recommended course for Information Security and specialization Mathematical Structures within General Mathematics. This is an introductory lecture to basic algebraic geometry focused on curves. The course is concerned with the basic notions (affine and projective variety, mappings on varieties, coordinate rings), local properties of curves, Bezout theorem and elliptic curves.

Literature -

Last update: G_M (24.04.2012)

W. Fulton: Algebraic Curves: an introduction to algebraic geometry, Benjamin, Reading 1969.

B. Hassett: Introduction to algebraic geometry, Cambridge University Press, Cambridge 2007.

J. H. Silverman and J. Tate: Rational Points on Elliptic Curves, Springer, New York 1992.

I. R. Shafarevich: Basic Algebraic Geometry 1, Springer, Berlin 1994.

Syllabus -

Last update: doc. RNDr. David Stanovský, Ph.D. (20.02.2018)

Basic notions: affine and projective variety, mappings on varieties, coordinate rings.

Local properties of curves.

Bezout theorem.

Elliptic curves.

Entry requirements -

Last update: G_M (24.04.2012)

Some familiarity with basics of commutative algebra, properties of polynomial rings over a field and algebraic varieties.