100321 Introductory Algebra

Course offering details

Instructors: Dr. Stefan Maubach

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, 5. Sep. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
2 Tue, 6. Sep. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
3 Mon, 12. Sep. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
4 Tue, 13. Sep. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
5 Mon, 19. Sep. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
6 Tue, 20. Sep. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
7 Mon, 26. Sep. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
8 Tue, 27. Sep. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
9 Tue, 4. Oct. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
10 Mon, 10. Oct. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
11 Tue, 11. Oct. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
12 Mon, 24. Oct. 2011 13:15 15:30 East Hall 4 Dr. Stefan Maubach
13 Tue, 25. Oct. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
14 Mon, 31. Oct. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
15 Tue, 1. Nov. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
16 Mon, 7. Nov. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
17 Tue, 8. Nov. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
18 Mon, 14. Nov. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
19 Tue, 15. Nov. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
20 Mon, 21. Nov. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
21 Tue, 22. Nov. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
22 Mon, 28. Nov. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
23 Tue, 29. Nov. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
24 Mon, 5. Dec. 2011 14:15 15:30 East Hall 4 Dr. Stefan Maubach
25 Tue, 6. Dec. 2011 13:15 15:30 East Hall 4 Dr. Stefan Maubach
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date No
2. Final Grade No Date 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. Stefan Maubach