I got my Ph.D. at the University of Buenos Aires under Alberto P. Calderón. It is an honor to have studied with one of the great mathematicians of the twentieth century. My general area of research is harmonic analysis, and very often I find myself using a lot of functional analysis. What do these names mean anyway? They actually mean a lot of good mathematics. Harmonic analysis had its beginnings in the interest the Pythagoreans took in understanding the inns and outs of music. Many centuries later, harmonic analysis still tries to pull things apart, to analyze the smaller components and to being able to put things back together. It is the same as looking at the mechanism of a watch and wondering which of the pieces are really essential to put the watch back together. Well, sort of. How about functional analysis? It started much, much later, when people realized that instead of looking at one thing at the time, one could look at families of things and try to understand their common properties. Now, if we put both harmonic and functional analysis together, we can wonder what are the essential pieces that compose all the watches of a given kind. Got it?
If you want to see some of my research, click here.
I am a tenured Professor of Mathematics in the Department of Mathematical Sciences at New Mexico State University. I will not bore you with a recitation of awards, visiting positions, presentations, publications, work with students, conferences organized, and the sort. You can check all that in my vitae.
Perhaps it is time to talk about teaching. I can hardly believe it was August of 1969 when I first walked in a classroom with a fresh master's degree under my arm. I think I have come a long way since then, distancewise and otherwise. I teach at all levels, from introductory to Ph.D. and regardless of the level, I can recognize a few principles that I apply to any course I teach. Here they are, in no particular order:
- Do justice to mathematics. It is the most spectacular and entertaining subject you can teach.
- Place mathematical concepts within a historical context.
- Emphasize recurrent patterns, in particular, emphasize the role of mathematics as a modeling tool.
- Place mathematical ideas in the context of students' interests.
- Place mathematical skills in the context of the need for the skills.
- Concentrate on a few important concepts.
- Emphasize writing and group work.
- Use technology to enhance the understanding of concepts.
- Find real life occurrences of mathematics in newspapers, magazines, the Internet, etc.
- Grade promptly and carefully all the work students are required to turn in.
- Have fun.
In 1995, something very important happened in my teaching career: I taught for the first time a course on mathematics appreciation for non-science majors. This was a tremendous eye opening experience. The majority of the students I encountered were fed-up with mathematics, afraid of mathematics, and suspicious of anyone trying to sell them mathematics as a cool thing. But they had tons of non-technical knowledge. So, my challenge was to convincingly show them that there is mathematics in music, in art, in philosophy, in politics, and ultimately, that beautiful mathematical ideas stand at the center of civilization and permeate everybody's lives. The positive feedback I got from many students and the awards I have won, indicate that I have been pretty successful. In return, out of my interaction with hundreds of very diverse students, I have gained a deeper and richer appreciation of mathematics and I have improved considerably my skills in communicating this appreciation to others. Want to check out some of my writing on this matter? Click here, here, here or here.
That's all? Not quite. My professional duties are spelled out as teaching, research and service. I have already showed you some of my research and my teaching. I definitely do not skimp on service either, as you can see here.
Thank you for taking the time to check out my website. You can send me comments to jalvarez@nmsu.edu. Hasta la vista!