Math 510

Math 510, Introduction to the Foundations of Geometry
(5:35-6:50 MW in C-10)

Grades are posted. You may see your scores on Blackboard and final grade on Webportal.

Syllabus: Here is the syllabus.

Online resources:

I use Blackboard to post your grades periodically throughout the semester

Homework:

Assigned	Due date	Read	Exercises
1/28	2/4	Your syllabus Ch 1, pp. 1-23	Study your syllabus. There will be a quiz on it on Mon, 2/2. No exercises yet, I'll assign some on Mon.
2/2	2/9	Ch 1, pp. 15-25	1.1, 2, 7, 14, 15
2/9	2/16	Ch 1, pp. 23-29	1.3-5, 9
2/16	2/23	Ch 1, pp. 30-42	1.6, 8, 10, 13, 16
2/23	3/2	Ch 1, pp. 34-42	1.9 Major exercises 1.2, 4
3/2	3/9	Ch 2, pp. 53-71	Major exercises 1.1, 3
3/9	3/16	Ch 2, pp. 72-88	2.2-6
3/16	3/23	Ch 2, pp. 76-91	2.7, 9, 11, 17, 19
4/8	4/13		2.10, 12, 14
4/13	4/20		Complete the proofs of Theorems 3 and 4 and finish writing up your discovery notes up to Theorem 4.
4/20	4/27	Your own discovery notes	Prove Theorems 5-7 and finish the proof of Theorem 8 (i.e. Lemmas 3-5). Your discovery notes should now be complete up to Axiom 14.
4/27	5/4	Your own discovery notes	Prove Theorems 12-15. Your discovery notes should now be complete through Theorem 15.
5/4	5/11	Your own discovery notes	Prove Theorems 16-18 and complete the proofs that the model of Rⁿ as defined in class satisfies Axioms 0-3. Your discovery notes should now be complete through Theorem 18.
5/11	5/16	Your own discovery notes	Complete and write up the proofs that the model of Rⁿ as defined in class satisfies Axioms 4-9.

Discovery notes: In the second part of the course, you compile your own notes from the work we do in class and the you do for the homework. You will use your own notes to prepare for the exams, so it is in your best interest to keep them neat, organized, and above all complete and correct. To start you off and give you an idea of what is expected of you, here is the first page of my notes with some of our first definitions, axioms, theorems, and proofs. I recommend that you use your computer to keep your notes. This will make it much easier to edit and revise them as you grow wiser about axiomatic geometry. The question is what software to use. While it's possible to use MS Word, typing mathematical formulas in Word is slow, troublesome, and the possibilities are quite limited. Also, the output is ugly, although this is probably the least of your concern now. You are welcome to stick with Word, but I do have a better suggestion for you.

Most mathematicians (and physicists and computer scientists) use LaTeX. The basic principle of Latex (it should be LaTeX, but that's annoying to type) is quite different from MS Word. In Word, you see your document exactly the way it will look when you print it. You format it yourself. In Latex, you edit the content, but leave a lot of the formatting to the computer. If you have edited an internet page directly in html, you know what I mean. If not, never mind, you'll see it shortly. The disadvantage of Latex is that it takes some time to learn how to use it, the advantage is that once you've gained some experience with it, it makes it very convenient to typeset mathematics. It produces professional quality output too. In fact, this is the same software publishers use to print math textbooks and journals. Since Latex is the gold standard in typesetting mathematics, if you are planning a career in math, you might as well get started on learning it. Even if your career plans revolve around teaching math in high school, I don't think you'll regret learning Latex. It's easy enough to find a free implementation of Latex for your computer. In fact, if you are running Linux, you most likely already have Latex on your computer. But you're probably running Windows. No problem, you can download MiKTeX.

You can get a start by looking at the source code of the first page of my notes. In fact, you may want to start your own lecture notes by editing this file. You can use any text editor, such as Notepad on Windows, to view and edit it. If you aren't ready to take the plunge, and would like a more gentle transition to Latex, you may want to check out LyX (free) or Scientific Workplace (commercial) below, which let you edit your documents a little closer to WYSIWYG style and produce the Latex code for you. Here are some links:

MiKTeX is a free implementation of Latex for Windows
Texmaker is a free text editor for Latex documents. If you set it up right, it also spares you the trouble of having to type latex math510lecturenotes.tex into DOS window, which is so 1980s.
LyX is a free document processor built on top of Latex which let's you edit your document a little more like MS Word and produced the Latex code for you.
Scientific Workplace (and Scientific Word) are similar to LyX, but with more features. It's quite popular. It's commercial software, so it costs $, but you could perhaps find some discounted deal at the campus bookstore.
To find a zillion online tutorials for Latex, just google Latex tutorial.
I have even found an online manual for Latex.
Our library has a book on Latex.
If you need a quick reference on how to use this or that in Latex, you can find it all online, in different places. Just use google.
Finally, you can always ask me questions about Latex.

The problem of the fortnight: The Mathematics Department in San Diego posts a new fun problem periodically. If you'd like to submit a solution, give it or e-mail it to me, so that I can fax them all together to San Diego. Winners receive prizes.

Exam solutions:

First hourly exam pdf
Second hourly exam pdf
Third hourly exam pdf

Educational links:

A serious paper on teaching/learning at the university level by Prof. Steven Zucker
A more light-hearted, but very true guide on how to be on good terms with your professor (who assigns your grade) by Prof. Doug Andrews at Wittenberg University

Math links: The links below lead to sites with encyclopedias of math terms. You can use them to find definitions, examples, and some theorems.

Some scholarship opportunities for prospective teachers: