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

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