Math 203: Proving Things: Algebra

Spring 2007, Lecturer: Prof. Florian Pop. Sections 101-102
TA: Armin Holschbach
Office: 4C9
Office hours: Mon 12:00-1:00 pm, Thu 2:00-3:00 pm
Email: arminh at math.upenn.edu

Course information and resources:

Labs:
101: Tue 6:30-8:30 pm, DRL 4C2
102: Thu 6:30-8:30 pm, DRL 4C2

Homework Sample Solutions:

Solutions for Problem Set 1

Solutions for Problem Set 2

Solutions for Problem Set 3

Solutions for Problem Set 4

Homework Policy:

The homework is assigned every Friday (see link above); it is due promptly before 5 PM on the Friday of the following week. Turn in your homework either

to me personally in lab or during office hours;
in class on Friday;
my mailbox in the math office (DRL 4W1/4W2).

A word about homework:

In this course we'll touch on a wonderful assortment of mathematical topics, ranging from the very foundational (logic, set theory, and the natural numbers) to the very interesting phenomena displayed by our seemingly innocuous integers (what we call number theory) to how all of this can be exploited for for things like cryptography and quantum computing. Above all, we'll learn how to think and write about these topics in a mathematical way. One of our principal objectives in this direction is to learn how to write mathematics, and that means, how to write proofs.

Generally, a homework problem in this course (and in general any mathematical problem) will consist of two parts: the creative part and the write-up.

The creative part: This is when you "solve" the problem. You stare at it, poke at it, and work on it until you understand what's being asked, and then try different ideas until you find something that works. This part is fun to do with your friends, and during this part, if you're having trouble, you should come ask Prof. Pop or myself for hints. This part should all be done on "scratch paper."
The write-up: Now that everything about the problem is clear in your mind, you go off by yourself and write up a coherent, succinct, well-written, and grammatically correct mathematical proof. This part you should definitely NOT do with your friends. This course is about proof-writing, so use this opportunity to practice your newly learned skills of using correct mathematical and logical notation, using correct logical arguments, and creating an aesthetically pleasing solution to the problem (you'll get the hang of this.) I hope that you'll discover the pleasure of getting something down on paper "just right." This part should be done on clean sheets of paper, and should be considered a final copy, just as in any other course.

Please note that a fully correct solution requires both parts: both having "figured out" the problem, but not having written it up (or having written up something incoherent that does not express what you know) or conversely, having written up a technically perfect proof for something wrong, don't count for very much. You will be graded accordingly. Equal weight will be given for a solution that is "good" as for a solution that is "well written."