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Smooth Manifolds and Observables by Jet Nestruev is a nonfiction available to read on EtoBox.

What is Smooth Manifolds and Observables about?

"This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances. Motivating this synthesis is the mathematical formalization of the process of observation from classical physics. A broad audience will appreciate this unique approach for the insight it gives into the underlying connections between geometry, physics, and commutative algebra. The main objective of this book is to explain how differential calculus is a natural part of commutative algebra. This is achieved by studying the corresponding algebras of smooth functions that result in a general construction of the differential calculus on various categories of modules over the given commutative algebra. It is shown in detail that the ordinary differential calculus and differential geometry on smooth manifolds turns out to be precisely the particular case that corresponds to the category of geometric modules over smooth algebras. This approach opens the way to numerous applications, ranging from delicate questions of algebraic geometry to the theory of elementary particles. Smooth Manifolds an

Who reads Smooth Manifolds and Observables?

Author

Jet Nestruev

Publisher

Springer International Publishing, Imprint Springer

Published

2020

Language

EN

ISBN

9783030456504

Category

nonfiction

Subjects

Mathematics, Science, Physics