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NMSU professor to create program to better explain higher math

As a professor of mathematics, Josefina Alvarez understands that students often have difficulty grasping the ideas behind a complex, abstract subject.



Josefina Alvarez is the first recipient of the Manasse Professorship at New Mexico State University. (NMSU photo)

As the first recipient of the S. P. Manasse and Margaret Manasse Professorship in New Mexico State University's College of Arts and Sciences, Alvarez will spend part of the next two years redesigning her department's "Introduction to Analysis" course to make the subject both vivid and accessible to new students.

Analysis is a branch of mathematics as old as Pythagoras, whose followers in ancient Greece studied the makeup of musical tones. Its concepts are in use today when the microprocessor in a synthesizer is used to recreate the sound of a trumpet. Even artists use the concepts of analysis when they lay a grid across a painting and ask, "What could I delete here and still have this picture?" Alvarez said.

Analysis involves the creation of mathematical models of physical objects or systems. One of the branches of higher mathematics, it is a required subject for math majors and secondary math education majors.

But Alvarez said both math majors and secondary education majors would benefit if the introductory course were reorganized to show analysis's historical development. She plans to use part of the money that goes with the Manasse chair to buy equipment for collecting data on temperature, light intensity, voltage and motion to demonstrate in the classroom the physics and math problems that led to the formation of its theories.

"It's my experience students are more receptive to mathematical concepts when they see them presented in the context of applications," she said.

Alvarez will also use part of the money provided by the Manasse chair to further her own research. She said she plans to invite two colleagues from Mexico -- Salvador Perez-Esteva, from the Instituto de Matematica in Cuernavaca, and Martha Guzman- Partida, from the Universidad de Sonora -- to Las Cruces to continue work on problems in harmonic and functional analysis.

The Manasse Professorship was made possible by an endowment from the estate of Solle P. and Margaret Manasse. The bequest specified that the money should be used to create a professorship in NMSU's College of Arts and Sciences. As a result, each year a faculty member in Arts and Sciences will receive a $12,000 research award that may be used over a two-year period, said Rene Casillas, dean of the college.

The College of Arts and Sciences will hold a ceremony awarding the chair to Alvarez on Thursday, Nov. 30, in NMSU's Science Hall. The ceremony will be preceded by a reception at 3:30 p.m. in the lobby area outside Room 102. The formal ceremony will begin in Room 102 at 4 p.m. and will include a presentation by Alvarez titled "The Sound of Mathematics."

While mathematics has repeatedly shown itself to be a superb tool for solving real world problems, its practical applicability is actually as far removed from its formative, abstract, ideas as thunder is from the flash of lightning, Alvarez explained.

"It is easy to lose contact with these ideas, while missing the fact that the technological thundering that we hear everywhere is indeed the sound of mathematics," she said.

Photo is available at http://kiernan.nmsu.edu/newsphoto/Alvarez_Josefina.jpg.
For a print, call (505) 646-3221.
CUTLINE: Josefina Alvarez is the first recipient of the Manasse Professorship at New Mexico State University. (NMSU photo)

Jack King
Nov. 16, 2000