Homework 5 = Sample Exam 1 Please Note type on #11 in Part II; the function g should be from Y to X not from X to Y.
Handout On Relations and Induction
Homework 6 Due Thursday October 21.
Homework 7 Due Thursday October 28.
Homework 8 Due Thursday Nov. 4.
Homework 9 Due Tuesday Nov. 16.
Exam 2 Sample You don't turn this one in.
Notes on Groups (by Prof. Cattani)
Complete Copy of Prof. Cattani's notes, including more sections on groups
Homework 10 Due Tuesday Dec. 7th. [This short problem set will be collected on Dec. 7th, but it's highly advisable that you complete these problems by this Thursday Dec. 2nd, if you can, so as to make sure you are keeping up with the material.] Homework 11 will be due on Thursday Dec. 9th.
Homework 11 Due Thursday Dec. 9th.
Sample Final Exam . You don't turn this one in. The final is cumulative, and will be (very approximately): 25% groups, 25% material from Exam 1, 50% material from Exam 2.
Please Read the following carefully; it is very important to comply with the Rules discussed below.
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: