MATH 280, Section 1: Foundations of Mathematics

As ever, here's a bad joke to start things off:

The function party is going smoothly: the music is groovy, the food is great, and everyone is having a good time and getting along... everyone except for e^x, who is just kind of hanging out in the corner gloomily. tan(x), whose party it is, sees him sulking and decides to try to cheer him up.

"Hey, everybody!" she shouts, "how about we all differentiate?" Cheers rise from all around, and everyone gets in on the action, differentiating themselves, taking first derivatives, second derivatives, using the Chain Rule...there is even some implicit differentiation going on on one side of the room.

But e^x is still just sitting there morosely. tan(x) is disappointed, so she goes over to him. "Hey," she says consolingly, "why not join in on the fun? See, everyone is differentiating, you could do it too!"

"Why bother?" asks e^x, "it won't change anything."

Want class resources? Here ya go:

Syllabus and course description
Course schedule
Homework assignments, by date
Here is a stylesheet that will give you an idea as to what I look for in high-quality mathematical writing.
Advice on surviving MATH 280, given to you by the students in the Spring 2008 MATH 280 course

Greatest Hits: the best of the homework solutions

Exams!

Exam 1: first draft due on Friday, September 25th, final draft due on Friday, October 2nd.
Exam 2: first draft due on Friday, November 6th, final draft due on Friday, November 13th.

Resources for using the LaTeX typesetting language:

Getting started with LaTeX: where to find the software you need online
The basics of mathematical typesetting: a LaTeX-created PDF document with many useful math symbols
The basics of mathematical typesetting (raw code): the .tex file corresponding to the previous .pdf file
Using LaTeX to typeset math papers: a LaTeX-created sample math article
Using LaTeX to typeset math papers (raw code): the .tex file corresponding to the previous .pdf file
Links to free LaTeX compilers:
- MiKTeX (for PCs)
- MacTeX (for Macs)
Here is a link to a free LaTeX text editor: TeXMaker; it works for all computer platforms, but Mac users will probably just want to use the TexShop front end that comes with MacTeX when downloaded from the link above.

Day-by-day goings-on:

Monday, August 17th. First day of class! You will prove your first "theorem," having been given the data on this worksheet. A debriefing will then be in order. Before Wednesday, you will read over this example and be ready to discuss it in class.
Wednesday, August 19th. We begin by discussing this example handed out on Monday, and from there move on to a more mathematical example. We will also spend a bit of time talking about the structure of the class as outlined on the syllabus, and you will get your first class-guiding worksheet!
Friday, August 21st. We will start into our first in-class worksheet, on making mathematical statements.
Monday, August 24th. We continue with statement-making, using the worksheet begun last week; see the previous entry for a link to the worksheet. Also, here is a link to the next handout, on forming compound statements.
Wednesday, August 26th. We will have an in-class LaTeX workshop. If you have a laptop, please bring it along, and have LaTeX installed on it by now.
Friday, August 28th. We will begin working on forming compound statements. (Please note that today is the last day to add/drop, with instructor permission!)
Monday, August 31st. We finish off compound statements and get started on the next section, on basic proof techniques.
Wednesday, September 2nd. We will continue talking about methods of proof, and the second homework committees will start us off with their reports!
Friday, September 4th. More on basic proof techniques! No new handouts.
Monday, September 7th. Labor Day: no class!
Wednesday, September 9th. Time to talk about induction, an incredibly useful method of mathematical proof. Read over the handout for Friday; we will spend most of the day today playing with L-tiles.
Friday, September 11th. More induction: we begin officially, with the handout contained in the previous entry.
Monday, September 14th. Induction, encore! And here is a handout with more induction examples. Enjoy!
Wednesday, September 16th. Class canceled! I am sick as a dog.
Friday, September 18th. We finally wrap up induction. The next handout will get us talking about the basics of sets.
Monday, September 21st. Sets are the order of the day. You can read all about them in the handout contained in the previous entry.
Wednesday, September 23rd. More on sets. In case we finish the first handout on this topic, here is the second one.
Friday, September 25th. We will definitely finish up the first handout on sets. See the previous entry for the next one, which I will hand out today.
Monday, September 28th. More on sets, continuing with the handout two entries back.
Wednesday, September 30th. Onward, continuing with the second handout on sets.
Friday, October 2nd. More on sets!
Monday, October 5th. We will begin our next handout, the first on combinatorics.
Wednesday, October 7th. We continue with the first handout on combinatorics.
Friday, October 9th. We should wrap up the first combinatorics handout and get ready to dive into the second one!
Monday, October 12th. Fall Break: no class!
Wednesday, October 14th. We continue with the second combinatorics handout, obtainable above. Also, please see this handout on k-combinations for a careful proof of the trickiest of the theorems on the handout.
Friday, October 16th. Finishing up the second combinatorics handout, we begin the third one!
Monday, October 19th. We may be able to finish up the final combinatorics handout (above) and begin our first of two on relations.
Wednesday, October 21st. We continue talking about relations; see the previous entry for the handout.
Friday, October 23rd. No class! I will be out of town. More on Monday...
Monday, October 26th. More on relations! See the handout from last Monday.
Wednesday, October 28th. We will finish up the first handout on relations, and I will hand out the second, on order relations.
Friday, October 30th. More on relations. You will also receive your second exam on this day!
Monday, November 2nd. We continue our discussion of order relations.
Wednesday, November 4th. More on order relations; you will receive a handout on functions.
Friday, November 6th. Finishing our discussion of relations in general, we turn to that special kind of relation, functions. See the previous entry for the handout.
Wednesday, October 21st. Last day to withdraw from a course.
Wednesday, November 25th and Friday, November 27th. Thanksgiving Break: no class!
Friday, December 4th. Last day of class!