Since much of what we will see is directly linked to seeing the power of axiomatized mathematics to unambiguously communicate (certain) ideas, we will piggy-back on the visit of Keith Devlin (NPR's "Science Guy") in April. One of Devlin's research areaa concerns ``what it is to think, to reason, and to engage in conversation.'' We will meet with him in late March or early April to discuss his book Goodbye Descartes (The End of Logic and the Search for a New Cosmology of the Mind.
Euclidean and Non-Euclidean Geometries , Third Edition, Marvin Jay Greenberg, W.H. Freeman and Company, 1993.
Monday: | 9:00-9:50 AM | 1:00-1:50 PM | ||
Wednesday: | 3:00-3:50 PM | 7:00-8:30 PM | ||
Friday: | 1:00-1:50 PM |
I am also available for meetings at other times. In particular I will frequently be available on Thursday during class hour. If you have trouble meeting during office hours please make an appointment for a better time.
On Tuesday we will discuss Devlin's book and other non-geometry issues and questions.
On Wednesday we will brainstorm on the homework problems.
On Friday students will present solutions of homework
problems on the board. Any problem we agree to accept
will receive a perfect grade. Problems that are not
presented or that we do not accept will be due in written
form the next Monday.
Weeks 8-15
On Monday I will lecture on new material and collect homework.
On Tuesday I will lecture or we will discuss problems.
On Wednesday we will brainstorm on homework problems.
On Friday we will alternate between lecture and presenting homework on the board.
Examination One | Tuesday February 8 |
Examination Two | Tuesday March 8 |
Examination Three | Tuesday April 12 |
You are not to work with anyone when doing these assignments with two exceptions.
As long as you cite it, feel free to use (or not) any technology that you like (e.g., CABRI, Geometers Sketchpad, calculators, Mathematica, MATLAB, etc.).
The primary goal of this course is for you to learn the basics of `mathematical reasoning' or `mathematical ways of knowing'. You will learn how mathematics addresses the related concepts of proof, communication, meaning, and truth. To provide contrast with mathematical methodology, your paper will examine either how some other discipline (your major, minor or some other field of interest) approaches these same fundamental concepts or you will further develop some concept presented in Devlin's book. You can find examples of papers addressing the first of these themes at
math.ups.edu/~bryans/Current/HTML/journalhome.html.
Clearly this material begs for entire books rather than a paper written in 2-4 weeks, so keep your topic focussed. The primary goal of the paper is for you to begin to explore such philosophical fundamentals as: proof, communication, or truth.
Due March 11: Last day to have a topic accepted. You should meet with me before this to discuss possible topics since merely turning in a topic on this date does not guarantee it will be accepted. Don't wait until the last minute.
Due April 8: Turn in 3 copies of a draft of the paper (please print on both sides to save paper). I will distribute 2 of those copies to your referees. (This means each of you will referee two papers.) The referees will read the paper for accuracy, clarity of exposition and appropriateness for the Journal of Undergraduate Mathematics at Puget Sound as outlined in the Journal Guidelines for Authors (see the class web page for details).
Due April 15 Referees give their reports to authors.
Due April 22: Turn in the final version of the paper along with all referee comments. If the paper receives a passing grade, it will be published in the journal.
The author will receive a grade for the paper itself and the referees will receive grades for the quality of their comments.
To have your information posted you need to print your name, the class (MATH 300), and a code on a sheet of paper. Then sign the paper and physically hand it to me. The code is to be a sequence of up to 23 symbols I can type on a keyboard.
Homework | 55% |
Paper | 10% |
Referee Reports | 3% |
Examinations | 24% |
Final Examination | 8% |
and locate the Journal of Undergraduate Mathematics at Puget Sound ``Guidelines for Authors'' page. Then send an e-mail message to me at bryans@ups.edu indicating that you have an account, understand how to access the World Wide Web, and are aware of how to avoid mistakenly sending e-mail to Beverly Smith that is meant for Bryan Smith.
Points | Logic and Mathematics |
5 | Arguments are correct, complete and without extraneous or misleading material. |
4 | Arguments have only one of: a few minor errors, omissions or inappropriate material. |
2 | Arguments have at least two of: minor errors, omissions and inappropriate material. |
0 | Arguments are more seriously flawed. |
Points | Use of Terminology and Notation |
2 | All technical terms, concepts and notation are used correctly. |
1 | There are minor problems with terminology and or concepts. |
0 | There are major problems with terminology or concepts. |
Points | Written Presentation |
3 | Follows citation requirements and all other writing guidelines. |
2 | Follows almost all of the guidelines with only one or two minor lapses. |
1 | Has more than one or two minor lapses on following the guidelines. |
0 | Has a major lapse in followingthe guidelines. |
It is best to think of these formal homeworks as officially assigned papers in which you completely explain and justify your analyses of the problems. I expect your problem solving and your papers to be