Math 300(Section 2)

Fundamental Concepts of Mathematics

Fall 2010

This is the homework page for Section 2 of Math 300. Here is a link back to the main page for Math 300.

Homework
1

Homework 2

Homework 3

Homework 4

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:

II. You MUST write your solutions completely independently.

Failure to comply with these rules may result in disciplinary action. Homework will be due on Thursday at the start of lecture, unless othewise stated. Late homework will not be accepted. Please note that the lowest homework grade will be dropped.