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.