Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Applications of mathematics in research
Name: rick a cazzato
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995


Question:
As a mathematics teacher, one of the most common questions students ask is; When will I ever use this? I can usually give them a adequate response. However, I would like to hear your response to this question. I know that the question is broad, but possible explain your research and how you are using mathematics for real world applications. I guess what I am asking is for you to describe your research and how mathematics is related or used that.


Replies:
Author: rtopper Well, I am a theoretical/computational chemist. I use mathematics every day in my work, directly. . . mostly calculus, trigonometry, and statistics. Chemists use trigonometry, together with spectroscopic devices that they either invent or buy, to determine the structure of molecules. Without trigonometry, we would understand very little about chemistry! Trigonometry is also at the heart of a method used to analyze spectral signals coming from molecules. This method is called "Fourier analysis." Fourier analysis is ESSENTIAL for all kinds of spectroscopy and many of the new medical imaging techniques (such as MRI).

We use statistics mostly to analyze the results of experiments, although I also use them for numerical fitting of calculated numbers. I use calculus to solve the Schrodinger equation, which is the equation describing the motions of atoms, electrons, and nuclei in molecules. So, in the end, mathematics is at the very heart of chemistry!

rtopper


Well I guess there are different forms of Schrodinger's equation. (smile) As a mathematician we "start" with an initial-boundary value problem and use a combination of pde, linear algebra, numerical analysis and harmonic analysis to determine an efficient solution. That these methods can be "refined" keeps us in business as well as forcing us to sharpen our skills!

billrob


I should tell you that "we" (theoretical chemists) use any form of quantum mechanics necessary to solve the problem at hand, ranging from HY = EY through Feynman path integrals through Lie algebras, Fourier analysis and all the tricks you mentioned.

Whatever it takes to get at molecular properties (including many Cray hours!) is how we tend to tackle things.

rtopper


As a theoretical physicist (now masquerading as a theoretical chemist) almost everything topper mentioned in his list is on my list too. The most important thing to understand however, is that for us trying to solve real problems, the techniques we use can be drawn from just about any area of mathematics, and so understanding of a broad range of mathematics is really quite necessary. There is a certain sense in which what is known in mathematics is "absolute truth", and can be relied on to help you just about anywhere. It is not just physics and chemistry in fact - a lot of new PhD's are now getting jobs on Wall Street using a wide range of mathematics applied to the very complex problems of economic and financial prediction. Mathematics provides a huge toolbox, and you need to practice with the tools and familiarize yourself with them for a long time before you are really qualified to apply them to the real world, but the applications are immense once you have acquired that proficiency.

asmith



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory