Math 112: Abstract Algebra II
Spring 2004
Instructor: Ben Davis
Email: bldavis@stmarys-ca.edu
Web: http://galileo.stmarys-ca.edu/bldavis/
Office: Galileo 103 D
Office Phone: 631-8048
Office Hours: M 3-4, Tu 9:10-11:20, or by appointment.

Texts: Homework: There will be a weekly homework assignment due at the beginning of class on Wednesdays. I expect you to write a complete solution to every assigned problem. If you get stuck on a problem, or if you are not confident in your solution, please confer with fellow students and come ask me in office hours. Late homework may be accepted due to unavoidable circumstances, and only at my discretion. Missing homework will receive a score of zero.
Exams: There will be two take-home midterms and a proctored final exam. Each exam will emphasize the material of homeworks and lectures since the previous exam.
Grades: Your grade is based on homework and exams. Homework is worth 25% and the exams are each worth 25%. The following distribution will be used to assign course grades: 100-93% = A, 92-90% = A-, 89-86% = B+, 85-83% = B, 82-80% = B-, 79-76% = C+, 75-73% = C, 72-70% = C-, 69-66% = D+, 65-63% = D, 62-60% = D-, Below 60 % = F.
Academic Honesty: The Saint Mary's policies regarding academic honesty detailed in the student handbook apply to this course. I encourage you to work with other students on the homework, but your write-up should be in your own voice, and consist largely of your own work. Where your argument depends heavily on another's work, say so.
Course Calendar: The course calendar lists the section we will cover on each day of class. I encourage you to read the section before attending lecture.

The original goal of algebra was to solve polynomial equations. In this course, we study polynomial equations from a modern standpoint. We develop the abstract machinery of vector spaces, rings, fields, ideals, and varieties used to attack the problem of solving polynomial equations. We develop an ``algebra-geometry dictionary" that relates algebraic properties of a given system of equations to geometric properties of the set of solutions. We develop the computational method of Groebner bases and use Groebner basis computer packages to solve concrete problems in algebra and geometry. This course moves very quickly, and the topics pile up rapidly. I will try to deliver clear lectures and be enthusiastic and approachable. For your part, I expect a fair level of mathematical maturity. For example, you may need to look to the texts for details that we don't have time to cover in lecture. Do your best to stay on top of things, and don't hesitate to come visit me in office hours.
Homework and Announcements
Assignment 9 due Fri May 14
You will need to use Mathematica to do some of the problems. Come to my office hours and we will go up to the lab.
C2.7#2, read pp.90-93 of Cox, Little O'Shea, then do C2.7#9,11
C2.8#1-4
C3.1#2,3,6,7
Assignment 8 due on Cinco de Mayo, Wed May 5
C2.3 #1,6
C2.4 #1,4,9,11
C2.5 #1,5,6,7
C2.6 #3,5,8
Exam 2 due at beginning of class on Mon Apr 26.
Assignment 7 due Wed Apr 21
C2.1 #1,2,4
C2.2 #1,2,10,11,12
The math 112 final exam is scheduled for Tuesday, May 18 from 1:00-3:00 in Dante 114.
Assignment 6 due Wed Mar 31
F29 #4,6,18,30
F30 #1,2,27
F31 #2,4,25,27,31
Exam 1 due at beginning of class on Mon Mar 15.
Assignment 5 due Saint Patrick's Day, Wed Mar 17
F27 #5,6,7
C5.1 #2,8 (Hint for #2: Find all polynomials g(u,v,w) in R[u,v,w] such that g(x^2-y,y^2,x-3y^2)=0.)
C5.2 #4,6,16,17
C1.5 #5,8,9 (For #8, the command "PolynomialGCD" in Mathematica can be used. The Mathematica lab is in Galileo 210A. The lab will be open Monday 3:00-4:00 and Tuesday 9:00-11:00, and I will be there to help you with Mathematica. If you cannot make these times, please let me know.)
Assignment 4 due Wed Mar 10
C1.4 #1,3,5,7,15
F26 #3,22,24,26
F27 #1,4,15,24,28
Assignment 3 due Wed Mar 3
F23 #13,14,16-19,27,28,34
C1.1 #2,4,5
C1.2 #1,5,6,7,8
Revised Assignment 2 due Wed Feb 25
F21 #1,4(justify),5
F22 #1,7,13,21,22
F23 #1,3,9
Monday office hours have been change to 3-4 pm.
Assignment 1 due Wed Feb 18
F18 #3,10,16,19,22,23,24,25
F19 #1,3,10,14,29
F20 #1,5,9,29