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Course, academic year 2016/2017
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Algebra I - NMAI062
Czech title: Algebra I
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: Mgr. et Mgr. Jan Žemlička, Ph.D.
Class: Informatika Bc.
Classification: Mathematics > Algebra
Incompatibility : NALG026
Is co-requisite for: NMAI063
Annotation -
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.
Literature -
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.

Syllabus -
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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