We hope you enjoy this first issue of our newsletter. We hope to continue to send these out on a somewhat regular (quasi-periodic?) basis. We'd like to include alumni news, but you will have to help us by letting us know what's up.

We could also use a better name for this publication. Any suggestions? Send them to us at math@nmt.edu

After 32 years of Number Theory, Calculus, and ‘Weird Math", Clyde Dubbs is riding his bicycle into the sunset, starting at the end of the Spring 1999 semester.

Clyde arrived at New Mexico Tech in 1967. Since then he has taught a wide variety of classes in the Math department, from his specialty of number theory to differential equations, probability, and linear algebra. And, of course, many years' worth of math and CS majors have suffered enjoyed Basic Concepts, better known as "weird math" with Mr. Dubbs. Now he will have more time for his garden, long bike rides, and enjoying life with Susan, his wife of one year. Clyde isn't retiring completely, though. He hopes to continue helping out Tech's Master's of Science Teaching program, teaching a class this spring at the Albuquerque Academy, as part of New Mexico Tech's service to the teachers in that city to the North.

Allan Gutjahr, Professor of Mathematics, and former Vice President for Research and Economic Development, has retired from New Mexico Tech as of August 1, 1999.

Allan arrived at Tech in 1971 as the first statistician in the Math department. He soon started doing joint work with the Hydrology group, and continued to work in stochastic processes related to groundwater problems. This year, in recognition of his fundamental work in the application of statistical methods to groundwater hydrology, Allan was named a Fellow of the American Geophysical Union.

In 1992 Allan began a six year stint as Vice President for Research, but eventually returned to the teaching he loved. He experienced some health problems in 1998-99, and decided that it was time to slow down a bit. Of course, as an emeritus professor, we still expect to see Dr. Gutjahr here at the office!

Ivan is joining the department this Fall semester, 1999. Originally from Russia, Ivan has been at the University of Iowa for the past two years. His interests are in Mathematical Physics, Heat Kernel Asymptotics and applications of mathematics. He has also been involved with undergraduate math contests such as the Putnam Exam, and in undergraduate research projects. Ivan, along with his wife Valentina, and son Grigori, has just moved to town.

Chris received his Ph.D. from University of California at Santa Cruz and taught for awhile at the University of Northern Colorado. Recently, he has been free-lancing as a computer consultant. He'll be helping us out this year, while Steve Schaffer is on sabbatical and we look for a permanent replacement for Allan Gutjahr.

Mark Claussen is an Astrophysicist with the NRAO who will be teaching a calculus class for us. With his interests in planet and star formation, Mark should be able to bring an exciting perspective to Calc II!

In the final years of the last decade of the last century in the millenium, the much-loved first course in ordinary differential equations, Math 335, has at last entered the 20^th century, with the addition of an optional computer lab.

Over the past several years, it has been apparent that there has been a shift, in the standard first course in differential equations, away from the formal solution of a relatively small collection of standard differential equations to a more qualitative, geometric and computer-based approach. The applied math group has recognized this change with the addition of the lab. It is growing in popularity with about 45% of those students registered for the class now attending. Modeling is now more the order of the day. Differential equations, seemingly impossible to solve previously by analytic means, succumb with relative ease using slope fields. Initial displacements and velocities can be changed at will with the touch of a key. Students can now discover the optimal speed at which to drive their almost undamped cars or pickup trucks over a typical New Mexico washboarded road in order to achieve maximal amplitude of oscillation. The mysteries of the Heaviside function and the shifting theorems have now fallen to the power of MAPLE over the Laplace transform. No longer do students dread the case when the indicial equation has equal roots in the Frobenius solution of a differential equation about a regular singular point. Provided that one is content with a finite, albeit large, number of terms in the series, the solution is accomplished painlessly with a little programming.

In the longer term, when we have developed a sufficiently large number of projects, we hope to make the lab an integral part of the differential equations experience.

The department has started a new option to our master's program – an MS in Math with emphasis in Industrial Mathematics. This degree is designed to prepare students with skills in modeling and problem solving, knowledge of applications, communication skills, and the ability to work with others. The degree includes courses in modeling, core areas of mathematics, and an area of application, as well as a summer internship in industry. We will have more to say about this program as it develops. For now, you can check out the web page at <http://www.nmt.edu/~math/industrial/industrial.html>.

Ivan Avramidi is working in the areas of Heat kernel asymptotics and Gauge theories. Recent papers include "A new explicit expression for the Korteweg-De Vries hierarchy", with R. Schimming, to appear in Mathematische Nachrichten, "Covariant techniques for calculation of the heat kernel", to appear in Review in Mathematical Physics and "Heat kernel asymptotics of operators with non-Laplace principal part", with T. Branson, which has been submitted to Communications in Mathematical Physics.

Brian Borchers, with Jan Hendrickx and Bhabani Das of the Earth & Environmental Science Department, has a paper on "Modeling Distributions of Water and Dielectric Constants Around Landmines in Homogeneous Soils" appearing soon in Detection and Remediation Technologies for Mines and Minelike Targets IV. He is also working in the inversion of soil conductivity profiles from electromagnetic induction measurements, and the MAX-SAT problem, which is an HP-hard combinatorial optimization problem with lots of applications in Artificial Intelligence.

Bert Kerr is continuing to work with John Wilson from hydrology, studying (and occasionally solving) an assortment of 'mixed boundary value problems in potential theory', related to the hydrology department's work with gas permeameters. Their first collaboration: 'Determination of geometric factors for a permeameter, applied to a semi-infinite homogeneous isotropic sample', will be submitted for review sometime in the fall. Progress is also being made on a related project: 'Determination of geometric factors for a permeameter, applied to a semi-infinite layered sample'.

Bert also has a paper, titled 'The disturbance of a uniform heat flow by two line cracks in an infinite anisotropic solid', (co-authored with G. Melrose and J. Tweed), in the Aug. '99 issue of J. of Thermal Stresses.

Fred Phillips of the Earth & Environmental Science Department and Bill Stone, with June Fabryka-Martin of Los Alamos, have recently completed a paper on "An improved approach to calculating low-energy cosmic-ray neutron fluxes near the land/atmosphere interface". Low energy neutron flux is used in dating exposed surfaces, and this model more accurately describes how the flux is generated.

I am currently on sabbatical leave at the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway for the 99/00 school year. I am here with my wife, Kim, and my two children, Britany (age 11) and Willie (age 4). We arrived here in late July and spent a few weeks visiting some friends in Oslo, getting over the jet-lag and seeing some of the beautiful country before heading about 500 kilometers north to Trondheim. We are living in a nice housing community in the town of Tiller just outside of Trondheim. The neighborhood, consisting of about thirty 4-plex units, has virtually no traffic and is perfect for kids. Britany has already made several new friends and we've spent many evenings playing "deadball" (a cross between American baseball and cricket) with the neighborhood kids. She's been recruited to be on a girl's handball team, a very popular sport here which is a cross (hmm!) between basketball and field hockey and is played indoors. She is, no doubt, most excited about the horseback riding

lessons that she's taking. Willie loves to play in the little forest behind our house and has an impressive collection of stick guns that he keeps in his "fort". He seems to have really taken to soccer which nearly everyone plays here. He asked me the other day, "Do we have to go back to Socorro?", so I think he's adjusted quite well to his new surroundings.

Although almost everyone here speaks English, we've had our share of problems not knowing Norwegian. A few days after arriving, I was parking my car downtown and put several kroners (Norwegian currency) in a parking meter and was waiting for the receipt. I soon figured out that the parking meter was actually a toll booth (cars pay a toll to enter the city!) which explained why it was located in the middle of the street. I'm sure the

onlookers were wondering why a pedestrian was putting money in a toll booth. Oh well.

I was invited to give a talk at a Physics conference on rock mechanics, which was located in a beautiful resort in the southern most part of Norway near the town of Grimstad. My talk was on the current work that I have been doing in micro-mechanical modeling of granular materials for predicting the stress dependent rock and fluid flow properties in oil reservoirs. This is a new area for me and quite a departure from my main area of research in multigrid methods. The talk was well received by the audience of physicists who were very forgiving of my lack of knowledge in their field. My plans for this year are to continue my research in this area. I will be working with a group of physicists and engineers here in Trondheim and in Oslo on developing the micro-mechanical model and implementing it in a numerical code.

August 1998

Steven Rowswell, "Solving the Quasi-Linear Wave Equation Using Particle Splitting Methods in Smoothed Particle Hydrodynamics". Steve is now working for Trilogy Software in Austin, Texas.

December 1998

Jon Stinger, "Nonlinear Inversion of 834 Angstrom Airglow to Ionospheric O+ Number Density"

May 1999

Roseanna Neupauer, "A Comparison of Two Methods for Recovering the Release History of a Groundwater Contaminant Source". Roseanna is continuing on with a Ph.D. in Hydrology here at New Mexico Tech.

Pansy Stone-Chavez, "Public Key Cryptography: The RSA Cryptosystem". Pansy will be teaching at UNM's Valencia branch campus this fall.

August 1999

David Kebler, "Solutions of the Diffusion Equation with One or More Sinks Using the Method of Multiple Scales". David will be continuing for a Ph.D. in Math at Montana State.

Baokun Li, " Projection Dimension and Continuity". Li will be continuing on for a Ph.D. in Math at New Mexico State.

If you have questions, or story ideas for our next issue, or if you need to contact us for any reason, the Mathematics department can be reached at

Department of Mathematics

New Mexico Tech

801 Leroy Place

Socorro NM 87801

Telephone: (505) 835-5393

Fax: (505) 835-5366

e-mail: math@nmt.edu

URL: http://www.nmt.edu/~math/homepage.html