Can I read Graduate Texts In Mathematics 220:smooth Manifolds And Observables on EtoBox?

Graduate Texts In Mathematics 220:smooth Manifolds And Observables by Jet Nestruev is a nonfiction available to read on EtoBox.

What is Graduate Texts In Mathematics 220:smooth Manifolds And Observables about?

This text serves as an introduction to the theory of smooth manifolds, but it's quite unlike any other text on the subject. The classic approach to manifold theory is heavy on the (point-set) topology and analysis; this one is heavy on the algebra. In this book, the author shows that a manifold (in the traditional sense) is completely characterized by its ring of smooth functions. The question then becomes: which rings can be constructed in this way? The author answers this question and, in the process, ends up building a completely algebraic theory of manifolds--it's totally awesome. What's more, he uses the idea of physical observables to motivate the construction. This is a delightful surprise, since algebraists don't tend to focus much on applications of a theory. Indeed, the concept of physical observation is brought up in the first chapter and used to justify many of the algebraic constructions throughout the book. A traditional manifold book would probably leave the entire discussion of mechanics (and more generally, symplectic structures)until the end (if it's included at all). Though the technical prerequisites are modest, I suggest you study some other texts first (or c

Who reads Graduate Texts In Mathematics 220:smooth Manifolds And Observables?

Author

Jet Nestruev

Publisher

Springer-Verlag New York, Incorporated

Published

2003

Language

EN

ISBN

9781441930477

Category

nonfiction

Subjects

Science, Mathematics, Physics