Math 510

Math 510, Introduction to the Foundations of Geometry
(5:35-6:50 TuTh in LA-4)
Office hours during final exam week:

12-2 on Tue, 12/11
2-4 on Wed, 12/12
2:30-4:30 on Thu, 12/13
1-2 Fri, 12/14

Syllabus: Here is the syllabus.

Online resources:

I use Blackboard to post your grades periodically throughout the semester
Discovery notes: the latex source file and the compiled pdf.

Homework:

Assigned	Due date	Read	Exercises
9/6	9/13	pp. 1-23	pp. 43-44, 1.2-4 Turn in: 1.1 on p. 43
9/13	9/20	pp. 23-27	pp. 43-48, 1.5, 6, 14 (also try to prove your construction really does what it's supposed to) Turn in: 1.7 on p. 46
9/20		pp. 28-34	No new homework. Prepare for the upcoming exam on 9/27.
9/27	10/4	pp. 32-40	pp. 45-48, 1.9, 10, 15, 16 Turn in: 1.12 on p. 46
10/9	10/18	pp. 53-68	p. 46, 1.13 pp. 48-49, 1.1, 2, 4 Turn in: 1.5 on p. 49 Optional: turn in 1.12 if you would like me to average it with the rest of your HW. This is not an extra credit exercise. If you don't turn in this problem, it simply won't affect your HW score either way. If you do turn it in, I will average your score on it with all your other HW scores. This could move your average score up or down, depending on how well you did on 1.12. Simply put, it is in your interest to turn in 1.12 only if you did well on it.
10/18	10/25	pp. 69-81	pp. 91-92, 2.1-4 Turn in: 2.5 on p. 92
10/25	11/1	pp. 72-85	pp. 91-95, 2.6, 8, 9, 17, 19 Turn in: 2.7 on p. 92
11/1	11/8	pp.81-91	No new homework. Prepare for the upcoming exam on 11/6.
11/8	11/15	pp. 84-91	pp. 91-95, 2.12abd, 13-15 Turn in: 2.11 on p. 93
11/15	11/20		pp. 91-95, 2.10, show that 2.12c is actually false Turn in: 2.10b on p. 93
11/20	11/29		Turn in: proofs of Theorems 2 and 3bcd in the discovery notes.
11/27	12/4		Turn in: the proof of Theorem 4 in the discovery notes.
11/29	12/6		Turn in: the proofs of Theorems 5-8 in the discovery notes.
12/4	12/14		Turn in: the proofs of Theorems 12-15 in the discovery notes.
12/6	12/14		Turn in: the proofs of Theorems 17-19 in the discovery notes.

Exam solutions:

First hourly exam pdf
Second hourly exam pdf
Final exam pdf

The Putnam Competition: This is not strictly related to this course. The William Lowell Putnam Mathematical Competition will be held on Sat, Dec 1 this year. It is administered locally at the Calexico campus. The exercises primarily test your ability to construct rigorous mathematical arguments to solve (difficult) unfamiliar problems and not lexical knowledge. If you like proofs and enjoy the challenge of thinking about such problems, I encourage you to sign up for the competition by contacting me by Oct 7. Registration must reach the organizers by Oct 12. Here is an archive of past exercises and solutions.

Discovery notes: During part of this course, you compile your own notes from the work we do in class and the work 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 concerns 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, just keep reading.

You can get a start by looking at the source code of the beginning 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. I don't know much about Macs, but Latex should be readily available for them. If you have a Mac, you may want to look at the Tex for Mac OS X wiki.
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 a DOS window, which is so 1980s.
TeXnicCenter is another text editor that plays nice with MiKTeX with similar features to Texmaker.
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 produces 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 include figures in your latex document, you can use the graphicx package. It is already part of most current Latex distributions. To draw high quality figures, I recommend Winfig, which is a Windows port of the classic xfig program on Unix. You can also use other graphics programs, but the advantage of xfig/Winfig is that they produce scalable vector graphics, i.e. your figure won't look pixelated.
The Department of Engineering at the University of Cambridge has a nice site on Latex with all kinds of primers, manuals, and tutorials. Check out Latex: An introduction, or The LaTex Wikibook, or Detexify - LaTeX symbol classifier on this page.
Here is another online manual for Latex.
The American Mathematical Society's Short Math Guide for Latex is another good resource on typesetting math.
I like this Latex cheat sheet by Winston Chang.
To find a zillion other online tutorials for Latex, just google Latex tutorial.
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.

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: