Department of
Mathematics Newsletter

This is our second issue. 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

Alan Sharples Retires!

For 32 years, students at New
Mexico Tech have been learning Complex Analysis in the “Zed” plane. For 32 years, Applied Analysis tests have
been “set”, and office hours “sheduled”.
For 32 years, students have been enjoying the accent, and fearing the
exams, of Dr. Sharples. This summer,
however, was the last semester of full time teaching for Alan. He retired, effective August 4^{th}.

But wait! Who is that Englishman teaching Math 435 this fall? Why, it’s Alan Sharples, who decided that teaching one class gave him an excuse to stay in sunny Socorro, and avoid the infamous Cornish winters. He also says that as an emeritus professor, he feels free to speak his mind, although no one seems to have noticed any hesitancy on this score, before.

Dr. Sharples arrived in the fall of 1968 as the 6^{th}
member of the department. He taught
applied analysis from the beginning, and worked with several members of the
Physics department, the Bureau of Mines, and Engineering. Alan served as Chair of the department from
1974-1985, Chair of the Institute Presidential Search Committee in 1983, and
Chair of the Institute Senate.

An accomplished campanologist, enthusiastic camper and hiker, and dedicated gardener, Alan is most easily recognized by his mania for wearing shorts in all weathers. Some of the very few days we saw him wearing long pants were the days he returned from his twice-yearly trips back to England. These were important days, however, as Alan had usually managed a stop at the duty-free shop for a liter of “the malt”.

Alan is also now an emeritus member of the Applied Math group. He will, of course, be spending more time exercising his fingers on the piano and organ, but we expect he will continue to enliven our meetings (at the local pub) and defend his dart championship!

It is our sad duty to report that Professor
Emeritus Allan Gutjahr passed away January 3^{rd}, 2000. Allan joined the Math department in 1971,
and served the Institute as Professor of Mathematics, Chair of the Department,
Chair of the Institute Senate, Associate VP for Academic Affairs, VP for
Research, and other ways too numerous to mention. He was one of the first workers in the field of Stochastic Hydrology,
and was recently made a fellow of the AGU to honor him for his
contributions. We know his many
friends, students, and colleagues will miss him.

Contributions may be made to the Allan Gutjahr Endowed Scholarship Fund. New Mexico Tech is matching all contributions. Checks should be made payable to New Mexico Tech and sent to: Advancement Office, New Mexico Tech, 801 Leroy Place, Socorro, NM 87801. Please note that the check is for the Allan Gutjahr Scholarship Fund.

Jay Aden is our visiting Statistician this year, teaching Introduction to Applied Statistics, Probability, and Stochastic Processes. Jay is ABD at UNM, specializing in Probability. In addition, Jay and his wife Jenni are the proud parents of a new boy, Jack. Jay says,” I really enjoy the campus and the students here, and I look forward to hopefully a long relationship with all the students and faculty here at New Mexico Tech. To all the guys at the 1pm basketball gym game, I'll see you on the court.”

Art is covering a wide range of classes for us, from Trigonometry to Calculus to Vector Analysis. Art, a Professor Emeritus from the University of Alaska Anchorage, brings lots of experience and a love for teaching. Besides teaching his classes, Art is helping out by supervising the Trig course. The Bukowskis (Art and Marcia and their two living-at-home daughters Leah and Lacey ) love the Southwest, and we’re glad to have them here in Socorro. In more family news, the Bukowskis have a new grandson, Joseph.

Chris Cotter and Mark Claussen are also teaching for us again this year.

Math
Department Moves to Cramer

The Math Department
will be living in temporary quarters on the 2^{nd} floor or Cramer in
anticipation of the remodel of Weir Hall. The remodel should be finished
by Summer 2002. The new remodel of Weir Hall includes adding two
stairwells to meet fire codes, smaller classrooms, and of course our new home
which includes support areas such as a help room, computer room, conference
room and offices for the entire faculty and grad students. The plans for
Weir Hall are going through the final revisions and may be seen at http://www.vhga.net/prcss.html.

The Physical Plant gutted the 2nd Floor of Cramer and created a maze of
offices which now house the Math Department, Graduate Office, some of
Mechanical Engineering and Vannetta Perry's multi-function office of MST,
Science Olympiad, and Science Fair. The move was interesting since the
Math department had been firmly planted in Weir Hall for over 30 years. This
move prompted the need to clean house and do away with many antiquities that
had gathered in every nook and cranny for a few decades. Our move
occurred one week before classes started and four days prior to the math
placement exam for the semester, which prompted 4 days of intensely long days
and a very tired crew.

The departmental office is located in Cramer Hall room 206. Our contact
information remains the same for all faculty. Drop by and see our new
home in Cramer or visit the old Weir Hall before it closes for remodeling.

Dr. Curt Barefoot, professor of Mathematics, is now also teaching in the Computer Science department. He is teaching their Introduction to CS class, and a Cryptography course. We miss having Curt full-time in the department, but we welcome some closer ties to the CS department.

A team of New Mexico Tech students performed well in the 60th annual William Lowell Putnam Mathematical Competition. The competition was held on December 4, 1999. A total of 2,900 students from 431 colleges and universities in the US and Canada participated in the competition. 346 institutions fielded three member teams. Six NMT students participated, and three of these students (Kirk Blazek, Michael Eydenberg, and Kyle Campbell) ranked among the top 500 individual scorers. As a team, NMT ranked 28th out of 346 teams.

The William Lowell Putnam Mathematical Competition is an
annual mathematics contest for undergraduate students in the US and
Canada. Students sit for two sessions of three hours each. In each
session the students are challenged by six extremely difficult problems.

A sample problem from the 59th Putnam:

A right circular cone has base of radius 1 and height 3. A cube is
inscribed

in the cone so that one face of the cube is contained in the base of the
cone.

What is the side-length of the cube?

Calculus, Differential
Equations, Basic Concepts, these can all be tough courses. But if you were to ask which class gives
students the most trouble, you might well find it to be College Algebra! This course, a critical preparation for
Calculus, is a stumbling block for many.
To help students succeed in this course, and go on to be successful in
Calculus, the department has started a new program of Supplemental Instruction
(SI).

In SI, upperclassmen are hired as SI leaders. These leaders sit in on the course, acting
as ‘model students’. Then they offer
two-hour study sessions outside of class to groups of 4 – 6 students

At Tech, we are trying this out with 2 SI leaders per
section, each of whom offer 3 of the two-hour sessions. Every student in the course signs up for a
study session, although attendance is not required. At these sessions the students get back their graded homework,
and the SI leader can go over any problems that those particular 4 or 5
students had. If they have any questions
about the new material, the SI leader can go over it with them, then they can
get started on their next homework assignment.

We are trying this out as a three-year pilot
program. We hope to improve students’
success in College Algebra, and have them well enough prepared for Calculus
that their success in Calc I will be pretty much the same as the success of
students who place directly into Calc I.
The administration has funded the first year of the pilot, and we expect
they will be willing to keep the program going at least long enough to see if
it works.

The department tried something new this year, the first “New Mexico Tech Applied Math Problems Workshop”. This was a two-day event in which people from outside the department brought problems to be solved. The problems were presented in a seminar Friday afternoon, then we broke into groups and attacked the problem. The workshop concluded with a wrap-up and presentation of solutions (or progress) Saturday afternoon.

The first presenter was Eric Small from Tech’s Hydrology program. He presented a problem concerning the nonlinear nature of the flow of soil on hill-slopes. Basically, he wanted to determine a field measurable way to check the linear vs. the nonlinear model.

Next, Ron Thomas from Tech’s Electrical Engineering department presented a problem of arcing events in lightning bolts. Power measurements from different stations did not agree, and it was thought that anisotropies in the electric fields might be behind the variation.

During the workshop, we were able to solve Eric’s problem. A write-up of the solution can be found on the department’s web page at

http://www.nmt.edu/~math/events/events.html

The group working on Ron’s problem wasn’t quite as successful, but they were able to give some useful direction to the experimentalists. Anisotropies didn’t seem to explain the variations, so some new experiments, with known sources, are planned.

We had 21 participants, from 9 different departments. A couple of people said they would be interested in presenting a problem at the next workshop. We were pleased with our first “Problems Workshop” and plan to have another this spring.

New
Department Chair

As of July 1^{st}, Dr. Brian Borchers has taken
over as Chair of the department. Curt
Barefoot served his three year term and is back to full time teaching now,
although Curt is now half time in the Computer Science Department (see article
above).

**Brian Borchers**, with Roseanna Neupauer, has A MATLAB Implementation of the
Minimum Relative Entropy Method for Linear Inverse Problems, to appear in *Computers
& Geosciences.** He is also working in using
inverse methods to detect land mines with *Jan M. H. Hendrickx,
Bhabani S. Das, and Sung-Ho Hong.

**Ivan Avramidi** has a book out this year, ** Heat Kernel and Quantum Gravity,** in the Springer

**Bert
Kerr** has a paper
with G. Melrose
and J. Tweed to appear this year in the *International
Journal of Fracture, * "Stress
Intensification Due To An Edge Crack In An Anisotropic Elastic Solid”. He is also continuing his mini-permeameter
work with John Wilson of the Hydrology program.

**Anwar
Hossain** is
continuing his research with William Zimmer of UNM, and had a couple of papers
with him this past year: “Comparisons of Methods of Parameter Estimation for a
Pareto Distribution of the First Kind” in Communications in Statistics, and”
Least Squares Type Estimators for the General Three Parameter Pareto Distribution”, in. Journal of Statistical
Research.

**Steve Schaffer** is continuing his work on
semicoarsening multigrid methods for elliptic partial differential equations
with widely varying coefficients. He is also starting to work on the
parallel implementation of the 2- and 3-dimensional algorithm with Sue Goudy, a
PhD student in the computer science department. He has just returned from
a year long sabbatical in Norway where he worked on developing a discrete
particle code for modeling cemented granular materials. He is continuing
this research with several colleagues in Norway. He is also planning to
work in the hopefully not-too-distant future with Dr. Matt Heizler in the
Bureau of Mines on modeling aspects in geochronology

**Bill Stone **continues
working with
Fred Phillips of the Earth & Environmental Science Department on low-energy
cosmic-ray neutron fluxes near the land/atmosphere interface. He is also working with Jan Hendrickx, of
Hydrology, on unsaturated water flow, and is starting some work with Dave
Raymond, of Physics, on nonlinear balance equations and vorticity potentials.

Graduate Students

August 1999

David Kebler, “Solutions of the Diffusion Equation with One or More Sinks Using the Method of Multiple Scales”. David is now working on his Ph.D. in Math at the University of Utah

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

May 2000

Timothy Hannan, “Elliptic Curve Public Key Cryptosystems”. Tim is now working on his Ph.D. in Math at
New Mexico State.

August 2000

Julie Luna, “Predicting Student Retention and Academic Success at New Mexico Tech”.

**Contact Information**

** **

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