Subjects(version: 849)
Algebra I - NMAI062
Title in English: Algebra I Department of Algebra (32-KA) Faculty of Mathematics and Physics from 2019 to 2019 winter 6 winter s.:2/2 C+Ex [hours/week] unlimited unlimited taught Czech, English full-time http://msekce.karlin.mff.cuni.cz/~zemlicka/
Guarantor: Mgr. Jan Šaroch, Ph.D.Liran Shaul, Ph.D. Informatika Bc. Mathematics > Algebra NALG026 NMAI063
 Annotation - ---CzechEnglish
Last update: T_KA (20.05.2009)
The course in basic algebra is devoted to fundamental algebraic notions that are demonstrated on basic algebraic structures. Notions include closure systems, operations, algebras (as sets with operations), homomorphisms, congruences, orderings and the divisibility. Lattices, monoids, groups, rings and fields are regarded as the basic structures. The course also pays attention to modular arithmetic and finite fields.
 Course completion requirements - ---CzechEnglish
Last update: Mgr. Jan Šaroch, Ph.D. (12.10.2017)

To obtain "Zápočet", the student has to have an amount of 60 points. These can be gained either from two written tests (maximal 50 points per each), or by correctly solving homework problems (here, the point rating varies).

 Literature - ---CzechEnglish
Last update: T_KA (17.05.2010)

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

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

 Requirements to the exam - ---CzechEnglish
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (09.10.2017)

The exam will be oral. It will consists of three questions; one general asking to overview certain topic, for example, symmetric groups or unique factorization domains, one more specific, for example, to formulate and prove the Lagrange theorem for groups, and one testing the understanding, for example, to find a non-trivial normal subgroup of the group A4 . Students will get time to prepare the answers.

 Syllabus - ---CzechEnglish
Last update: T_KA (17.05.2010)

1. Monoids, groups and subgroups. Factorization of groups and normal subgroups.

2. Cyclic groups and RSA.

3. Basic notions of universal algebra: algebra, homomorphism, congruence.

4. Lattices and Boolean algebras.

5. Rings and ideals. Fields of fractions. Construction of finite fields.

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