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%)
Home Work (30%)
Midterm Exam (30%)

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
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 Tue, 1. Sep. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
2 Mon, 7. Sep. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
3 Tue, 8. Sep. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
4 Mon, 14. Sep. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
5 Tue, 15. Sep. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
6 Mon, 21. Sep. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
7 Tue, 22. Sep. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
8 Mon, 28. Sep. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
9 Tue, 29. Sep. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
10 Mon, 5. Oct. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
11 Tue, 6. Oct. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
12 Mon, 19. Oct. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
13 Tue, 20. Oct. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
14 Mon, 26. Oct. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
15 Tue, 27. Oct. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
16 Mon, 2. Nov. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
17 Tue, 3. Nov. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
18 Mon, 9. Nov. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
19 Tue, 10. Nov. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
20 Mon, 16. Nov. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
21 Tue, 17. Nov. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
22 Mon, 23. Nov. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
23 Tue, 24. Nov. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
24 Mon, 30. Nov. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
25 Tue, 1. Dec. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
26 Th, 3. Dec. 2009 17:15 18:45 East Hall 8 Dr. Keivan Mallahi Karai
27 Mon, 7. Dec. 2009 14:15 15:30 East Hall 8 Dr. Keivan Mallahi Karai
Course specific exams
Description Date Instructors Mandatory
1. Final Exam Fri, 11. Dec. 2009 09:00-11:00 Dr. Keivan Mallahi Karai No
1. Home Work No Date No
1. Midterm Exam Time tbd No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Undergraduate Programs > Mathematics
Class Session Overview
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Instructors
Dr. Keivan Mallahi Karai