To go to my new index page, click here .
For students at Georgetown University; other information at my fabled home(ly) page.
If you are coming to campus and you need directions, see the directions page .
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Last updated May 30, 2007
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Office location: St. Mary's, 3rd floor, D315; telephone 687-2703 -
Here are the two new class web pages created by my students in
Topics in Topological Graph Theory
for the Spring Semester 2007.
Schedule, Spring 2007 (all times PM)
If you need to see me at some other time, send me e-mail: kainen at georgetown.edu However, rather than posing lengthy mathematical questions by e-mail, come in and talk to me - it's faster and more efficient.
If you ever find yourself too sick to attend class, be sure to read ``Under the weather?'' which spells out the steps you can take to get caught up and when to take them. If you are concerned about how you are doing in a class, read what to do to improve . While I'm on the subject, here is good procedure to follow when writing things up for homework, quizzes, and tests.
*** new announcement 1/26/07 ***
Here is an opportunity for those who are so inclined. There is a conference on complex computer models aimed at undergrads. It's in North Carolina on Fri.--Sat. March 2--3 with a deadline for applicatons of Feb. 14. If the topics sound of interest, then you can fill out an application form online. I don't know if they will pay for your airfare (registration costs didn't seem to be included when I glanced through briefly). I'm not recommending this - just drawing it to your attention.
There are actually many such events (even for this group SAMSI as you will see if you look around on their website). In fact, there are Summer internships and other research-oriented programs that aim for undergraduates, and you can do some looking around online for feasible locations - some may even pay you something for the summer.
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Two general suggestions for elementary courses which may be useful. _Don't_ buy a calculator and don't buy the ``ancillary materials'' which publishers put out as add-ons to their already voluminous (and over-priced) textbooks. BTW, one can often buy the text online for less - in case you don't know that.
If you have some ideas about improving campus ambience , let some administrators know how you feel!
If you are interested in either the application of mathematical ideas to visual perception or to the use of graphical displays to convey mathematical concepts, check out the new web page for the Laboratory for Visual Mathematics . Also, there is a propectus (as a word .doc file) for the Psychophysics Club is now starting up; see the lab's webpage for more information.
For Spring 06, I taught Abstract Algebra (Math 203) , MWF 1:15 to 2:05 Reiss 284 and Probability and Statistics (Math 040-05) , 2:15 to 3:05 M (STM G40), TW (REI 283), F(REI 262).
Also, tutorial on expander graphs and number theory
For Fall 2005: I taught Graph Theory (math 224) and Calculus I (math 035-08).
Spring 2005: I taught Short Course (math 003-01) and Probability and Statistics (math 040-04). Also, I gave a module for the interdisciplinary program in cognitive science on Lissajous figure perception .
Some new material on topological graph theory .
I also taught a module (as part of the cognitive science program). I am a member of the Center for the Brain Basis of Cognition CBBC .
See the cog sci web page Cognitive Science for info on this interesting interdisciplinary program, in which I often teach a module during the Spring semester. I also occasionally give a course on neural networks or related topics which is cross-listed as a cognitive science course.
Last conference organized: Topology in BIology and Chemistry Nov. 12--13, 2004, part of Knots in Washington XIX. There may be another in the series next fall or spring - in honor of Nicholas Cozzarelli (1938--2006) - who was a speaker at our first conference and an inspiring intellect in the field.
During Fall 2003, I taught Math 264, Mathematical Models in Biology, See the math 264 page for an outline of the syllabus and related material. Also, see the Cognitive Science web site for the current modules and courses.
The antidote to negative thinking is poetry; or, under the heading of ``if you can't lick them, join them'', you might try dystopian fiction .
I have also taught courses in combinatorics and number theory, as well as tutorials in topology and neural networks. Pointers to suitable pages one of these days; for instance Number Theory (Math 211).
Here's a story based on mathematics (topology in this case) which some of you may enjoy. A subway named Mobius - see his home page for lots more (or use google.com to find the The Mathematical Fiction Homepage.
The Fall 2002 topology reading course was interesting; see the new topology page for this course.
For information on the previous reading course on topology (Math 302), please see the previous course page and for info on topology itself, take a look at my topology page. (There is a proof of the extreme value and intermediate value theorems from calculus ;-)
See picture , and another picture from Topics in Discrete Math, Fall 2001.
An interesting article by the famous physicist Eugene Wigner: The unreasonable effectiveness of mathematics in the natural sciences.
I've put together a booklist for a reading group on dystopian (i.e., negative utopia) novels.
This semester, there will be a psychophysics club. Psychophysics is related to neuroscience, psychology, neural networks, art (!), and, of course, mathematics. If you are interested in such topics (e.g., visual and auditory perception including illusions), here is an opportunity to show some initiative!
See the following page for a demonstration of how one can detect colors even when some of the color information has been discarded. One sees full color (better than in the computer demo below) when a black-and-white image is combined with a shades-of-red image. Check it out! Land's retinex theory was developed by the guy who invented the polaroid process. When I saw it demonstrated at a Gordon Research Conference in the late 1970s, one could hear the jaws dropping!
I gave a module on math modeling and psychophysics for the Interdisciplinary Program in Cognitive Science in Spring 2001. See cognitive science for general information on the program and the various modules.
You can see the mathematical psychophysics page for information on the module I taught. The vision page has some related material.
Both of the above pages reflect my interest in mathematical applications in biology. For connections to medicine, please see my page containing ideas on how to fight the potentially crippling syndrome PFFD
My brother is an expert in lighting (homes, restaurants and museums), and he has also done work related to three-dimensional visual display. See his website .
The Math Club meets on most Wed. evenings at 7:30 in Reiss 256. See Prof. Vogt for further information.
