Telephone: (903)886-5157 (Binnion) [(903)886-5175 (Dean's suite)]
FAX:       (903)886-5945 (Binnion) [(903)886-5199 (Dean's suite)]

E-mail: kremin@boisdarc.tamu-commerce.edu
This web page is located at http://www.tamu-commerce.edu/math/FACULTY/KREMIN/kremin.html

SB (Biology), MIT, 1981; MA, Maryland, 1990; PhD, Maryland (Interdisciplinary Applied Mathematics), 1994; JD, Dedman School of Law, Southern Methodist University, 2008. PhD dissertation title: Graded manifolds with spin-conformal structure; my advisor was Dr. Paul Green.

Besides the topics listed above, I am interested in implementing computational and graphics algorithms in Mathematica, whether in number theory, combinatorics and probability and statistics, Lie groups (rotation groups in both Euclidean space Rⁿ and Minkowski spacetime R^n-1,1), wavelets, dynamical systems, etc. I wish I had more time to spend trying to learn twistor theory in algebraic geometry (see link below), as well as level-set methods in differential geometry, including writing Mathematica code. And hopefully someday I will be able to find out what string theorists have been doing for the past 10 years.

• The Mathematician of the Day site at St. Andrews has much information about the history of mathematics.
• The on-line version of Neil Sloane's Encylopedia of integer sequences has well over 100000 sequences for lookup, either by values or by author.
• Three very useful sites that are quite encylopedic: Steve Finch's favorite mathematical constants, Mathworld by Eric Weisstein, and the relatively new PlanetMath by, well, lots of people. (The related Treasure Trove site by Eric Weisstein is also quite good. Another source, an all-purpose encyclopedia, is Wikipedia.)
• Free online mathematical reviews are available through Zentralblatt. Similarly, the archives at UCDavis house many preprints.
• The homepage of the campus chapter of Sigma Xi     The Scientific Research Society can be accessed here, for general information as well as schedules of upcoming events. There are links to organizations and other sites of interest to the scientific community (not just math).
• Mathematica-generated graphics, depicting a non-standard visualization of the Hopf fibration S³->S²->S¹, via the fibration RP³->S²->S¹, are available here. A link to a .dvi file of a paper on this topic is available there too. (Unfortunately, the .dvi file doesn't have any of the graphics in it.) Links to some Java applets based on some of the figures are also given there.
• (Old, pre-2002) information about the Texas Twistors, an informal offshoot of the North Texas Relativity Seminar dealing with issues related to twistor theory, is available here. Meetings have always been held sporadically, varying from several times a month to once every couple months, in the Dallas metroplex. Limited summaries of past meetings, and dates and times of future meetings, are available at the web site.
• IF your browser supports Java 1.0, go here to view a map on the torus that requires seven colors to be a legitimate coloring. (Note there that every one of the seven countries shares some boundary with each of the other six countries. Equivalently, the coloring indicates that one can embed a K₇ on the torus.) Go here to view a 3D-graphic illustrating what went wrong with a pseudo-random number generator, "RANDU", that was popular in the early 1970s. [But if that applet does not load properly, a temporary file is available here.] Go here to practice composing rotations, i.e. for practice in trying to guess the product of two or more rotations. Go here to view a 3D-graphic illustrating a possibly new approach to graphing surfaces in R³. And go here to view a 3D-graphic illustrating the 60-element group known as A₅ (the alternating group on 5 symbols). [Another graphic, illustrating S₄ (the symmetric group on 4 symbols) is available here.]

• For those using Netscape as their browser, here is a quite rudimentary javascript self-scoring math/general info quiz.
• Other, unrelated, Mathematica-generated graphics: If the network is fast enough, go here to view some fractal trees from a summer 2000 course offering, and here (December 2001) and here (December 2002) [or maybe here (December 2002)] for recent seasonal variations (with a different fractal seasonal greeting, December 2003, here, another fractal greeting, December 2004, here, and another greeting, December 2005, here). And go here for a math logo. These graphics may be slow to load, but if you hit reload probably will load much more quickly. (They are animated, but that might be browswer - version - number - dependent!) More Mathematica-generated graphics: The first one (...depicting the motion of a point on a "wheel", which in turn is moving on a "wheel" of different radius and different rotational frequency, and which in turn is moving on yet another "wheel" with still a different radius and rotational frequency...) is housed here. The next two show some 'fractiles' (fractal tilings of the plane), here and here. Another seasonal rendering, this one of a fractal shamrock, is available here. And last (for now), two distinct initial condition implementations of John Conway's Game of Life are visible here and here.
• The Mathematica notebook for the shortcourse I presented at the Texas Section of the MAA meeting in Houston on March 29, 2001 is available here. When you activate the link to it, presumably you can save the notebook to your harddrive (especially if using Internet Explorer, although Netscape should be fine too, depending on your browser version). A not-so-great web rendition of the notebook is available for those who don't have Mathematica or who just want to see what's in the notebook.
• The birthday paradox seems to surprise everyone when they first learn about it; some data are available here. For instance, the probability is over 85% that in a room of 50 randomly chosen people, on at least two days, there are least two people with the same birth date. (And over a 97% chance that in that same room, there's at least one day with at least two people with the same birthdate.) Similarly, partitioning problems (applied to money) also seem to surprise people; data are available here.For instance, there are 252 (213, respectively) ways to come up with $.99, if you are allowed to use a half-dollar coin (respectively, just the usual penny, nickel, dime, and quarter coins). Finally, there are numerous instances in mathematics of things that initially seem paradoxical; we are collecting such examples, ranging from elementary to somewhat deeper levels, in a site we tentatively call Strange... but true.
• Five-year-old-page: The tragic, dramatic loss of life on 11 September 2001 is depicted in a rudimentary web page that, hopefully sometime in the future, will more generally depict 'vital statistics' in real time. The page as it now stands can be accessed here.