Abstract Algebra (MATH 1250), Spring 2008

Old Quizzes and Homework Assignments

 

Topics:  Groups, Rings, Fields, Galois Theory and applications.

 

Textbook:  Abstract Algebra, an Introduction, by Thomas W. Hungerford, second edition.

 

Prerequisites:  Logical reasoning, some ability to write rigorous proofs, ability to handle axioms and abstract objects.


Class meets: MW  3:00-4:15pm, 1220 Benedum Hall

Instructor: Dr. Alexander Borisov

Office: 414 Thackeray Hall, phone: 624-2314

Office hours: by appointment


Grades:     Homework                  10%

                     Weekly Quizzes            20%

                     Midterm 1                    20%

                     Midterm 2                    20%

                     Final Examination         30%

 

Schedule:

All dates are approximate, and the order and selection of topics is subject to change. The section numbers refer to the textbook.

Not all topics covered are adequately represented in the book and additional materials may be used.

 

January 7            Introduction to the course. Diagnostic Test

 

January 9            Equivalence relations. (Appendix D)

 

January 14          Review of Chapter 2

 

January  16         Definitions of rings, groups and fields. (3.1, 7.1)

 

January  23        Basic examples and definitions. (3.2, 4.1)

 

January 28         Ideals and congruence. (6.1)

 

January 30        Quotient rings and homomorphisms of rings. (6.2)

 

February  4        Prime and maximal ideals. (6.3)

 

February  6        Review

 

February 11       Midterm Examination 1

 

February  13     Order of elements. Subgroups. (7.2, 7.3)

 

February  18     Group homomorphisms.  (7.4)

 

February  20     Lagrange’s Theorem. (7.5)

 

February  25     Normal subgroups, quotient groups. (7.6, 7.7)

 

February  27    Image and kernel of a group homomorphism. Isomorphism theorems.  (7.8)

 

March 3           Symmetric group, alternating group. Group ring construction.  (7.9)

      

March 5           Finite Abelian groups.  (8.1, 8.2)

 

March 17        Review

 

March 19       Midterm examination 2

 

March 24       Vector spaces and algebras. (10.1)

 

March 26       Simple extensions. Complex numbers. (10.2)

 

March 31       Algebraic extensions. (10.3)

 

April 2            Splitting fields

 

April 7            Separability. Finite fields. (10.5, 10.6)

 

April 9            The Galois Theory. (11.1, 11.2)

 

April 14          Applications: solvability in radicals, ruler/straightedge constructions. (11.3, 14)

 

April 16          Review

 

 

Final examination will be administered during the finals week.  Date, time and room will be determined later.