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, 3. Sep. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
2 Tue, 4. Sep. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
3 Mon, 10. Sep. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
4 Tue, 11. Sep. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
5 Mon, 17. Sep. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
6 Tue, 18. Sep. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
7 Mon, 24. Sep. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
8 Tue, 25. Sep. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
9 Mon, 1. Oct. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
10 Tue, 2. Oct. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
11 Mon, 8. Oct. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
12 Tue, 9. Oct. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
13 Mon, 15. Oct. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
14 Tue, 16. Oct. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
15 Mon, 29. Oct. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
16 Tue, 30. Oct. 2012 13:00 15:30 East Hall 4 Dr. Stefan Maubach
17 Mon, 5. Nov. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
18 Tue, 6. Nov. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
19 Mon, 12. Nov. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
20 Tue, 13. Nov. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
21 Mon, 19. Nov. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
22 Tue, 20. Nov. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
23 Mon, 26. Nov. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
24 Tue, 27. Nov. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
25 Mon, 3. Dec. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
26 Tue, 4. Dec. 2012 14:15 15:30 East Hall 4 Dr. Stefan Maubach
27 Wed, 12. Dec. 2012 12:30 14:30 East Hall 4 Dr. Stefan Maubach
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
Dr. Stefan Maubach