100321 Introductory Algebra

Course offering details

Instructors: Prof. Dr. Ivan B. Penkov

Type: Lecture

Org-unit:

Course Name Abbreviation: IntroAlgebra

Hours per week: 3

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Grade

Official Course Description:
Algebraic structures can be found everywhere in mathematics; it is therefore important to become familiar with them. This course gives an introduction to four basic types of structures: groups, commutative rings, modules and
fields. Here is a more detailed list of topics to be covered.

Group Theory: Definitions and key examples. Cosets and Lagrange's theorem.
Group homomorphisms and basic constructions including quotient groups, direct and semi-direct products. Group actions and orbit-stabilizer theorem. Sylow theorems.

Commutative Rings: Definitions and elementary properties. Ideals, ring homomorphisms and quotient rings. Domains, Euclidean domains, principal ideal domains and unique factorization. Polynomial rings.

Modules: Definitions and basic constructions. Linear maps and exact sequences. Direct products and sums. Structure theory for finitely generated modules
over a principal ideal domain.

Field extensions: Roots of polynomials. Irreducibiliy criteria. Finite and algebraic field extensions. Splitting fields and algebraic closure. Finite
fields. Constructions with straightedge and compass.

Literature
Primary Text
  • A first course in abstract algebra
Required Reading (To view a list click a category.)
Recommended Reading (To view a list click a category.)
Appointments
Date From To Room Instructors
1 Mon, 2. Sep. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
2 Tue, 3. Sep. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
3 Mon, 9. Sep. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
4 Tue, 10. Sep. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
5 Mon, 16. Sep. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
6 Tue, 17. Sep. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
7 Mon, 23. Sep. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
8 Tue, 24. Sep. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
9 Mon, 30. Sep. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
10 Tue, 1. Oct. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
11 Mon, 7. Oct. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
12 Tue, 8. Oct. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
13 Mon, 14. Oct. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
14 Tue, 15. Oct. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
15 Mon, 28. Oct. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
16 Tue, 29. Oct. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
17 Mon, 4. Nov. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
18 Tue, 5. Nov. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
19 Mon, 11. Nov. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
20 Tue, 12. Nov. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
21 Mon, 18. Nov. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
22 Tue, 19. Nov. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
23 Mon, 25. Nov. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
24 Tue, 26. Nov. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
25 Mon, 2. Dec. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
26 Tue, 3. Dec. 2013 14:15 15:30 East Hall 4 Prof. Dr. Ivan B. Penkov
27 Wed, 11. Dec. 2013 16:00 18:00 East Hall 4 Prof. Dr. Ivan B. Penkov
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Mathematical Sciences > Undergraduate Level Courses
Class Session Overview
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Instructors
Prof. Dr. Ivan B. Penkov