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Applications to the sciences

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Historically, it has been the needs of the physical sciences which have driven the development of many parts of mathematics, particularly analysis. The applications are sometimes difficult to classify mathematically, since tools from several areas of mathematics may be applied. We focus on these applications not by discussing the nature of their discipline but rather their interaction with mathematics.

Most of the areas in this group (the blue ones in the picture here) are collectively known as "mathematical physics". Somewhat more recently, increasingly sophisticated mathematical tools are used in the engineering, biology, and the social sciences (the violet areas in the picture).

Observe that the branches of mathematics most closely allied with the fields of mathematical physics are the parts of analysis, particularly those parts related to differential equations. The other sciences draw on these as well as Probability and Statistics and, increasingly, numerical methods.

In addition to the resources mentioned on the index pages for these individual disciplines, one might summarize here the many resources which apply to mathematical physics generally. For example, there is a newsgroup sci.physics.research (moderated) and unmoderated groups sci.physics and sci.physics.particle.

You might want to continue the tour with a trip through the remaining subject areas of mathematics.

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Last modified 1999/05/12 by Dave Rusin. Mail: feedback@math-atlas.org