Professor John Beachy, Watson 355, 7536753
Office Hours: 11:00  11:50 (in Watson 355), or by appointment
email: beachy@math.niu.edu  My faculty homepage  My personal homepage
Syllabus  Lecture Schedule  Resources on the WEB
Assignments  Class notes  Homework hints
Some exams from previous semesters
Midterm and Final from 1993

Midterm and Final from 1999

Final solutions from 1999
Midterm from 2005
(this one looks easier than it should bewe've covered more material)

Final from 2005
PREREQUISITE: MATH 520 or consent of department
TEXT: Introductory Lectures on Rings and Modules, Cambridge University Press, and supplementary lecture notes on commutative rings. Recommended reference: Algebra, by Hungerford
SYLLABUS:
These are the topics listed for the comprehensive exam in algebra.
Rings and Modules:
Modules, simplicity, semisimplicity, chain conditions, tensor products,
Jacobson radical, density theorem, WedderburnArtin theorem,
finitely generated modules over a principal ideal domain,
canonical forms.
Unique factorization, Euclidean domains, principal ideal domains,
polynomial rings, maximal, prime, and primary ideals,
Noetherian rings, Hilbert basis theorem, LaskerNoether decomposition,
integral elements, integral closure, fractional ideals, Dedekind domains.
To prepare for these topics, I plan to cover the following sections of the text. (Chapter 5 is a set of supplementary notes available on the web, and is not included in the published version of the book). The emphasis of the book is on noncommutative rings, and so Chapter 4 covers the representation theory of finite groups as an application of the general theory developed in the previous chapters.
CHAPTER 1: RINGS (62 pages)
CHAPTER 2: MODULES (74 pages)
CHAPTER 3: STRUCTURE OF NONCOMMUTATIVE RINGS (34 pages)
CHAPTER 5: IDEAL THEORY OF COMMUTATIVE RINGS (36 pages)
MONDAY WEDNESDAY FRIDAY M Tu W Th F Week of JAN 2008 1/14 1.1 1.2 1.2 14 15 16 17 18 1/21 HOLIDAY 1.3 1.3 21 22 23 24 25 1/28 1.4 1.5 1.5 28 29 39 31 1 2/4 2.1 2.1 2.1 FEB 4 5 6 7 8 2/11 2.2 2.2 2.3 11 12 13 14 15 2/18 2.3 2.4 2.4 18 19 20 21 22 2/25 2.5 2.5 2.6 25 26 27 28 29 3/3 MIDTERM 2.6 2.6 MAR 3 4 5 5 7 SPRING BREAK 10 11 12 13 14 3/17 2.7 2.7 2.7 17 18 19 20 21 3/24 3.1 3.1 3.1 24 25 26 27 28 3/31 3.2 3.2 3.3 APR 31 1 2 3 4 4/7 3.3 3.3 5.1 7 8 9 10 11 4/14 5.1 5.1 5.2 14 15 16 17 18 4/21 5.2 5.3 5.3 21 22 23 24 25 4/28 5.4 5.4 READING DAY 28 29 30 1 2 5/5 FINAL MAY 5 6 7 8 9 FINAL EXAM: Monday, May 5, 10:0011:50 a.m.
GRADING: Semester grades will be based on 500 points:
MIDTERM: The midterm exam is tentatively scheduled for Monday, March 3.
FINAL: The final exam is scheduled for Monday, May 5, 10:0010:50 a.m.
DUE SECTION PROBLEMS Homework #8: 3.1 #2 (Correct the mistake in the question, then give the solution.) 3.2 #3,4 3.3 #2,5
Class notes: some history, solved problems, etc  Abstract Algebra OnLine
Complete books online:
Elements of Abstract and Linear Algebra, by Edwin Connell
Abstract Algebra: The Basic Graduate Year, by Robert Ash
A Course in Commutative Algebra, by Robert Ash
Top of the page  Department homepage  John Beachy's homepage