MATH 462, Section 1: Abstract Algebra II
Spring 2009 Homework Assignments

Listed here (by date) is the homework assigned in our Abstract Algebra class. Make sure you keep an eye on this page, and keep yourself up to speed!

If you have any questions about these assignments, please don't hesitate to contact me.

• Wednesday, January 14th. Here are the several topics on which you will be asked to prepare a brief presentation for Friday:
  • group
  • symmetric group (S_n)
  • modular group (ℤ_n)
  • subgroup
  • group homomorphism
  • normal subgroup
  • quotient group
  • First Homomorphism Theorem
  • ring (with identity)
  • integral domain
  • field
  • polynomial ring
  • field of fractions
• Friday, January 16th. Read Section 3.3 of your textbook in order to be ready to discuss polynomial rings next week!
• Monday, January 19th. Martin Luther King, Jr. Day: no class, and therefore no homework!
• Wednesday, January 21st. Do the homework contained on the handout on polynomial rings. Here is the schedule for this homework:
  • Monday, January 26th. Committee problems due.
  • Wednesday, January 28th. The committees will present their reports.
  • Friday, January 30th. Final drafts of all problems due.
• Friday, January 23rd. Nothing new! I will hand out some new homework from Section 3.4 of your text (on ring homomorphisms and ideals) on Monday.
• Monday, January 26th. We should get to the point where you can do the two (non-committee) problems on the handout on ideals. This is due on Friday, January 30th.
• Wednesday, January 28th. Nothing new! How sad...
• Friday, January 30th. Here are a few new problems on ideals, including a committee problem or two for Monday. Here is the schedule for this homework:
  • Monday, February 2nd. Committee problems due.
  • Wednesday, February 4th. The committees will present their reports.
  • Friday, February 6th. Final drafts of all problems due.
• Monday, February 2nd. There are three new, mostly computational, problems at the end of the handout on Division Algorithm. These problems (none of which are committee problems) are due on Friday, February 6th.
• Wednesday, February 4th. SNOW DAY: CLASS CANCELED!
• Friday, February 6th. Nothing new! You have quite a bit to keep you busy for now.
• Monday, February 9th. There are three problems on the handout on PIDs. These, none of which are committee problems, are due on Friday, February 13th.
• Wednesday, February 11th. For Friday, come up with one potential question for Exam 1. Your question may be computational or theoretical, and deeply involve one or more of the concepts we have talked about so far this semester.
• Friday, February 13th. Nothing new! Monday brings the first exam.
• Monday, February 16th. Exam 1! See the schedule for the exam on the main page for the course.
• Wednesday, February 18th. Nothing new! Keep cracking on the exam.
• Friday, February 20th. Nothing new. Monday will bring more fun!
• Monday, February 23rd. There are five homework problems at the end of the handout for today. The last three of these are "modified" committee problems: please complete them by class on Wednesday; those who have done so will get committee credit when their submissions are shared and analyzed in class. This homework is due on Friday, February 27th, along with revisions for Exam 1.
• Wednesday, February 25th. Here is the schedule for the homework problems from the handout on congruences and quotients (modified to account for the snow day!); note that there are two committee problems:
  • Wednesday, March 4th. Committee problems due.
  • Friday, March 6th. The committees will present their reports.
  • Monday, March 16th. Final drafts of all problems due.
• Friday, February 27th. See the previous entry for the homework schedule! Here was another one we added on the spur of the moment:
  4. Prove that if R=ℤ_n and k in R is given, then ℤ_n/(k) is isomorphic to ℤ_(n,k).
• Monday, March 2nd. SNOW DAY: CLASS CANCELED! Thus, no new homework.
• Wednesday, March 4th. Time to choose your own adventure™! Check out the choice at the bottom of the handout for today, and make your decision. Choose wisely! Oh, and we added one more question for Friday:
  5. Prove that if X is a given set and A is a subset of X, then P(X)/P(A) is isomorphic to P(X-A), as rings.
• Friday, March 6th. Nothing new. Enjoy your break!
• Monday, March 9th through Friday, March 13th. Spring Break! Nothing new!
• Monday, March 16th. Do the two exercises at the end of the notes on congruences in universal algebras. These exercises are due on Friday, March 20th.
• Wednesday, March 18th. Nothing new. You should start to think about the topic you would like to speak on for your final presentation.
• Friday, March 20th. Here is the schedule for the homework problems from the handout on universal algebra homomorphisms:
  • Monday, March 23rd. Committee problem due.
  • Wednesday, March 25th. The committee will present its report.
  • Friday, March 27th. Final drafts of all problems due.
• Monday, March 23rd. Nothing new. Do I look like a sadist? You have an exam coming up!
• Wednesday, March 25th. Hmmmm...I may have to rethink my not handing out homework, if your exam is put off until Monday...
• Friday, March 27th. Spring Undergraduate Research Symposium: no class, therefore no new homework!
• Monday, March 30th. No homework, but I will pass out a copy of Exam 2!
• Wednesday, April 1st. Nothing new! Work on that exam!
• Friday, April 3rd. No class, ergo nothing new, encore! The Mathematica notebook FindingIrreducibles might help you with the exam.
• Monday, April 6th. Finally: there are a few simple (non-committee) problems at the end of the handout for today, due on Friday, April 10th.
• Wednesday, April 8th. Aaaaaah! More committee problems (all four of them!): do the problems at the end of the second handout on Galois theory. Here is a schedule for the committee stuff:
  • Monday, April 13th. Committee problems due.
  • Wednesday, April 15th. The committees will present their reports.
  • Friday, April 17th. Final drafts of all problems due.
• Friday, April 10th. Nothing new!
• Monday, April 13th. Nothing new.
• Wednesday, April 15th. Nothing new.
• Friday, April 17th. There are two problems at the end of the latest handout on Galois theory. These problems are due on Friday, April 24th.
• Monday, April 20th. Nothing new; see the previous entry for the handout with the two problems due on Friday, April 24th.
• Wednesday, April 22nd. Nothing new: brace for the impact of Exam 3 next week!
• Friday, April 24th. Nothing new.
• Monday, April 27th. Nothing new, from here on out!