Links to Homeworks: Please note that occasionally I discover typos in homework assignments, thanks to alert readers. When that happens, I update the hw and change the "date last modified" field. So during the week check back occasionally to see if there have been any modifications.
Homework 1 (pdf) HW1 is due on Thursday February 3rd. (Last UPDATED 1/29/05, 06:52; reworded 5(a) so as to be more helpful with 5(b))
Homework 2 (pdf) HW2 is due on Thursday February 10th. (Last UPDATED 2/8/05, 01:43; more notes were added and slightly modified; problem 6 acquired a part viii; extra credit problem slightly rephrased. previously: 2 regular problems added at the end, one extra credit problem added).
Homework 3 (pdf) HW3 is due on Thursday February 17th. Last UPDATED 2/14 11:51; minor modifications to notes. Previous update 2/14 01:58 flaw in discussion of inverse functions fixed. Previous Update 2/13 9:09. Problems 6, 7 and 12 contained glaring errros that have now been corrected. First posted 2/12 11:42.
Homework 4 (pdf) HW4 is due on Thursday February 24th. First posted 2/17 18:18. The notes will undergo slight modification. There are fewer problems than usual. The notes contain some material which will not be covered on the exam, but all the problems should help you prepare for the exam. Note that the exam HAS BEEN MOVED TO THURSDAY MARCH 3.
Exam 1 Sample
No Homework Due the week of Feb 28-March 4, STUDY FOR EXAM
For your convenience, I am providing solutions to most of the homework problems up to now. Please note that these are provided as a guide to help you study: these were typed quickly and may contain errors.
HW 1 Solutions HW 2 Solutions HW 3 Solutions HW 4 Solutions HW 5 Solutions HW 6 Solutions HW 7 Solutions HW 8 Solutions HW 9 Solutions

Homework 5 due March 24. Last UPDATED March 14 14:00. Notes slightly modified. Modified March 14, 12:10, added notes, problems did not change. First posted March 10.
Homework 6 due March 31. First posted March 24.

Homework 7 due April 12. Last updated April 13, 23:42; corrected minor typos. March 31, 17:40. Modified some problems, added some extra credit problems. March 31, 12:41; changed the due date to April 12 instead of April 7, fixed typos, added some notes. March 29: dded a bunch to the notes, typos fixed. First posted March 28, 3:00.

Homework 8 due May 3. Last updated March 30, 12:43 typos fixed. March 28, 16:00: Notes and problems added, typos fixed. First posted March 28, 3:00.

Exam 2 Review Contains sample exam and description of what the exam will cover.

Homework 9 due May 10. Last UPDATE: May 6 10:40. Added HINT to 4b. CORRECTED TYPO IN DEFINITION OF w in 7. April 28, 17:00. Added more notes. Modified April 28, 15:01. More notes and more problems (Yikes!) added. This assignment is rather long. Get started soon on these problems. First posted April 28, 3:05.

Final Exam Review Contains sample exam and description of what the exam will cover.

General remarks (with thanks to Tom Braden): 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.

All the various texts for this class are on the accessible side for an abstract math course, but they all will 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: that is what is expected.  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 in the various texts, in the Extra Credit Problems I will assign.

Homework Rules and Guidelines: 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: