University of Massachusetts, Amherst
Math 411 Homework Page
Introduction to Abstract Algebra I
Fall Semester 2009 (Section 2)

Homework 1: is due Tuesday September 22.

Homework 1 Solutions to selected problems.

Homework 2: is due Th Oct. 1.

Homework 2 Solutions to selected problems.

Homework 3: is due Th Oct. 8.

HW 3.5 = Sample Exam 1: is due Th Oct. 15. This Sample exam also serves as homework number 4. It is due at the start of class on on Oct. 15, just before the exam starts.

Homework 4: is due Th Oct 29, but will be accepted until Tue Nov. 3.

Homework 5: is due Th Nov. 5, but will be accepted until Tue Nov. 10.

Homework 5.5=Sample Exam 2: is due Tues Nov. 17.
NOTE: Exam 2 is scheduled for Thurs. Nov. 19, in class.

Homework 5.5=Sample Exam 2 Solutions: is due Tues Nov. 17 but accepted until Nov. 19.

NOTE: Exam 2 is scheduled for Thurs. Nov. 19, in class.

Homework 6: is an optional HW assignment purely for Extra Credit. Details to be explained in class. It is due Tuesday Dec. 8th. No extensions given on this one.

Homework 7: is due Th Dec. 10 but will be accepted until Friday December 11.

Sample Final Exam: is not to be turned in.

General remarks and Rules for Homework Assignments: For many of you this will be your first mathematics class where concepts and proofs are more important than algorithmic computation.  Do not make the mistake of treating this like a calculus class!  You will need to be much more active in your learning.  In order to really understand the concepts, you should ask lots of questions like: What happens if I change this definition in some way? What goes wrong if I leave out an assumption from this theorem? Are there any other examples that work like this?  Is this like something I've already seen?  You should do this in class, while reading the book, and while working on homework problems.

The book is fairly accessible for an abstract math book, but it is still has many more ideas per page than your average calculus book.  Don't be discouraged if you must read slowly, or read many passages more than once.  I strongly encourage you to read the material for a lecture before you come to class.  Read actively -- when the book gives examples to illustrate an abstract definition, spend some time to convince yourself that they do in fact work, try to think of other examples of the same type, etc.

Doing plenty of examples is essential for attaining a solid understanding of any abstract theory.  We will do some examples in class, but it is not possible to do enough and still cover all the material.  The homework problems I will assign should only be taken as a starting place; there are lots of interesting problems of various levels of difficulty all through the book. If you are hungry for more resources beyond your book, try typing "abstract algebra" in google.

Why are you are attending a University instead of studying on your own? So that you can be part of an interacting academic community. So, when you get stuck, seek help from your instructor, other students, classmates ...! I especially recommend that you work with your fellow students in groups. If you are stuck on a problem and seek help from an instructor or a fellow student, you owe it to yourself to aim for an understanding of the concepts and ideas that come up in the discussion (do not just memorize the series of steps leading to the solution). Then, go home and reconstruct the argument for yourself in the privacy of your own brain, to make sure you are not merely reproducing mindlessly something you have not thought through. Remember that during tests and quizzes, you will have to rely on your own understanding of the material.

Here are the rules for collaborating on homework problems:

I. You must list the names of all people with whom you discussed each specific problem.
II. You MUST write your solutions completely independently.

Failure to comply with these rules may result in disciplinary action.