Doing Mathematics: Convention, Subject, Calculation, Analogy (2nd Edition)

by Martin H. Krieger

Book Overview

Doing Mathematics discusses some ways mathematicians and mathematical physicists do their work and the subject matters they uncover and fashion. The conventions they adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies they discover and employ, all depend on the mathematics -- what will work out and what won't. The cases studied include the central limit theorem of statistics, the sound...

• Format: Hardcover
• Language: English
• ISBN: 9814571830
• ISBN13: 9789814571838
• Release Date: March 2015
• Publisher: World Scientific Publishing Company
• Length: 492 Pages
• Weight: 1.85 lbs.
• Dimensions: 1.2" x 6.1" x 9.0"

Customer Reviews

What do mathematicians really do-- From the Author

I am the author of this book, and I thought it would be useful to say a bit more about the book. First of all, it is a a sequel to another book of mine, Constitutions of Matter (1996) published by Chicago, a study of the models mathematical physicists employ. And that is a sequel to Doing Physics (1992) published by Indiana, a description of some of the models physicists have in their toolkit.Second, the book can be read at various levels, and that may be why it was chosen as a Library of Science selection. I have a friend who is a Hollywood director (originally trained as an attorney), and he understood it exactly, even though he knows little technical physics or mathematics. He read across that material and got the point. On the other hand, if you have an advanced degree in mathematics, as did another readers or two, you can read it for the technical details as well as the more general features. I have chosen movie stars of mathematics (C. Fefferman, R. Langlands) for much of the work. I also include a rather wonderful letter of Andre Weil (the mathematician) written to his sister (Simone Weil) about how he does mathematics. It appears in French in his collected papers, and it is here translated into English. I suspect that someone like Gian-Carlo Rota would have found congenial what I done here, although he would say that I have been insufficiently phenomenological.My goal is to say something that mathematicians would find unexpectionable, for they might say--sure, this is what we do. But it is said in such a way that others gain access to that, and to that in terms of classy examples.Third, I have deliberately not gotten into philosophy of mathematics arguments. I suspect that my materials would be useful for such, but those arguments do not much affect what I say in my descriptions.Finally, I want to provide a way into what mathematicians do that suggests that it is not so strange compared to what other thinkers do--albeit it is mathematics, not poetry, not rhetoric, not sociology. It is mathematics.Martin Krieger