Course Request Summary

Department Submitting Request: Mathematics

Request for Action: CHANGE   Effective: 200210

Course Subject Area: Mathematics

Subject Code: MAT Course Number: 250A

Descriptive Title: Algebra

Abbreviated Title: Algebra

Units: 4

Learning Activity

1st LEC 3.0 hrs/wk

2nd T-D 1.0 hrs/wk

In Progress Grading: None

Instructor Consent:

Prerequisite(s): Graduate standing in mathematics or consent of instructor.

Restrictions on Enrollment:

Course Description: Group and rings. Sylow theorems, abelian groups, Jordan-Holder theorem. Rings, unique factorization. Algebras, and modules. Fields and vector spaces over fields. Field extensions. Commutative rings. Representation theory and its applications.

  General Education: No GE Certification

     Topical Breadth:

                 Diversity:

Writing Experience:

Cross Listing: Same Course as

Repeat Credit:

Credit Limitations:

Mode of Grading: Letter

Quarters to be Offered: I Each Year

Instructors Name(s): Staff - Chair in Charge Title(s):

Remarks:
New course description more accurately reflects course content.

Expanded Course Description

1. COURSE GOALS:
   Groups are indispensable in many parts of mathematics, and the course familiarizes students with the theory of groups. This course is necessary if one is work in algebraic topology, or manifold topology, or conceptual approaches to linear algebra via matrix groups, or Lie algebras and groups, or differential geometry. By the end of the quarter students should be able to work with and should know the basic structure theory of finite groups, abelian groups, general and special linear groups.
   The last part of the course, an introduction to rings, allows students to treat more advanced topics of algebra in 250B. selected topics include dual vector spaces, multilinear functions, determinants, bilinear forms, tensor products and tensor algebras, the classification of finitely generated abelian groups and endomorphisms of finite-dimensional vector spaces, field theory and Galois theory. Time permitting also category theory.
   
2. ENTRY LEVEL:
   Graduate standing or consent of instructor.
3. TOPICAL OUTLINE:
   Group Theory: groups as symmetries, homomorphisms, subgroups and quotient groups, group actions, abelian groups. Basic concepts including group actions, Sylow's theorems, classifications of finite abelian groups and groups of small order, the Jordan-Holder theorem.
   Introduction to rings, ring homomorphisms and ideals, field of fractions of a commutative domain; polynomial rings; factorial rings; principal ideal domains and Euclidean domains; polynomial extensions of factorial domains. Unique factorization. Free groups, group representations.
    
4. READING:
   250ABC Textbook: Abstract algebra, Dummit and Foote.
   Additional reference books:
   Artin, Algebra.
   Rose, A course on group theory.
   Dixon, Problems in group theory.
   Hall, The theory of groups.
   
5. GRADING PERCENTAGES AND COURSE REQUIREMENTS:
   Discussion section and homeworks: 20%
   Midterm Exam: 30%
   Final Exam: 50%
   
6. EXPLANATION OF POTENTIAL COURSE OVERLAP:
   None
7. GENERAL EDUCATION DESIGNATION:
   None