Subjects

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Algebra 2 - NMAI076

Title:	Algebra 2
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	summer
E-Credits:	4
Hours per week, examination:	summer s.:2/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Michael Kompatscher, Ph.D. Liran Shaul, Ph.D.
Class:	Informatika Bc.
Classification:	Mathematics > Algebra
Co-requisite :	NMAI062
Incompatibility :	NMAI063
Interchangeability :	NMAI063, NMAX063
Is incompatible with:	NMAI063
Is interchangeable with:	NMAI063

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (08.06.2022)

The second part of course in basic algebra is concerned with divisibilty in commmutative domains, extensions of fields and basic properties of the notion variety.

Course completion requirements

Last update: Michael Kompatscher, Ph.D. (19.02.2024)

To pass the practicals and get "Zápočet", one needs to obtain a minimal amount of points in three written homework assignments.

Literature -

Last update: Michael Kompatscher, Ph.D. (07.02.2023)

The course will follow the lecture notes of David Stanovsky, an English translation will be uploaded throughout the semester on Michael Kompatscher's website https://www2.karlin.mff.cuni.cz/~kompatscher/.

Other resources:

S. Lang. Algebra, 3rd ed. New York 2002, Springer.

S. MacLane, G. Birkhoff. Algebra 3rd ed, Providence 1999, AMS Chelsea publishing company.

Stanley N. Burris, H.P. Sankappanavar. A Course in Universal Algebra, The Millenium Edition, Waterloo 2012. URL: https://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html

Requirements to the exam -

Last update: Michael Kompatscher, Ph.D. (07.02.2023)

In order to be admitted to the exam, one needs to pass the practicals first (and obtain "zápočet").

The exam is oral and will cover all material discussed in the lecture.

Syllabus -

Last update: Michael Kompatscher, Ph.D. (07.02.2023)

1. Homomorphisms (group homomorphism, quotient groups, ring homomorphisms, ideals, classification of finite fields)

2. Number fields (ring and field extensions, algebraic elements, and finite degree extensions)

3. Algorithms in polynomial arithmetic (fast polynomial multiplication and division, decomposition)

4. Further algebraic structures (lattices and Boolean algebras)

Entry requirements

Last update: Michael Kompatscher, Ph.D. (07.02.2023)

The material covered in Algebra 1, and basic knowledge of linear algebra.