100321 Introductory Algebra

Course offering details

Instructors: Dr. Keivan Mallahi Karai

Type: Lecture

Org-unit:

Course Name Abbreviation: IntroAlgebra

Hours per week: 3

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Exam (40%)
Midterm Exam (40%)
Home Work (20%)

Official Course Description:
This course gives an introduction to three basic types of algebraic structures:
groups, commutative rings, and fields. (If time permits, a fourth one: modules.) 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.
Some examples of (important) groups. Group actions and orbit-stabilizer theorem. Possibly:
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.
Field extensions: Roots of polynomials. Irreducibiliy criteria. Finite and algebraic field
extensions. Finite fields. Possibly: Splitting fields and algebraic closure. Constructions with
straightedge and compass.
If time permits 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.

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, 1. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
2 Tue, 2. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
3 Mon, 8. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
4 Tue, 9. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
5 Mon, 15. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
6 Tue, 16. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
7 Mon, 22. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
8 Tue, 23. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
9 Mon, 29. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
10 Tue, 30. Sep. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
11 Mon, 6. Oct. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
12 Tue, 7. Oct. 2014 14:15 15:30 Research I, Seminar Room 120 Dr. Keivan Mallahi Karai
13 Mon, 13. Oct. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
14 Tue, 14. Oct. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
15 Mon, 27. Oct. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
16 Tue, 28. Oct. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
17 Mon, 3. Nov. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
18 Tue, 4. Nov. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
19 Mon, 10. Nov. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
20 Tue, 11. Nov. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
21 Mon, 17. Nov. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
22 Tue, 18. Nov. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
23 Mon, 24. Nov. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
24 Tue, 25. Nov. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
25 Mon, 1. Dec. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
26 Tue, 2. Dec. 2014 14:15 15:30 East Hall 4 Dr. Keivan Mallahi Karai
Course specific exams
Description Date Instructors Mandatory
1. Final Exam Wed, 10. Dec. 2014 09:00-11:00 Dr. Keivan Mallahi Karai No
1. Midterm Exam Time tbd No
1. Home Work No Date No
Contained in course catalogues
Course catalogue
Course Catalogue > Engineering and Science > Mathematical Sciences > Undergraduate Level Courses
Class Session Overview
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Instructors
Dr. Keivan Mallahi Karai