Smooth Manifolds 1st Edition by Rajnikant Sinha (PDF)

Description

This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard’s theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate students of mathematics, the book will also prove useful for researchers. The prerequisites for this text have intentionally been kept to a minimum so that undergraduate students can also benefit from it. It is a cherished conviction that “mathematical proofs are the core of all mathematical joy,” a standpoint this book vividly reflects.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The previous reviewer is correct — all the detailed calculations are provided in excruciating detail. But let me play devil’s advocate. Anyone who is going to master manifold theory and/or Riemannian geometry has to do these calculations at least once to grok the subject properly. Most of the grad texts elide over the detailed calculations — which can be perplexing for the mathematically immature. This book *does* serve a purpose — if only as a reference text for the detail, should one get stumped for some reason. It cannot, however, serve as a primary text. I too prefer authors like Tu, Jost, Boothby, and Lee (and all these can serve as primary texts). That doesn’t mean this book is devoid of merit.

⭐This book attempts to present differentiable manifolds to mathematical beginners – an admirable goal. Some readers may find the style – showing all the details of involved calculations, for example – admirable, and helpful in learning the subject. I am not a beginner and having two pages of equations that I can easily do myself is distracting. One can view this as the other side of the spectrum from one of Lang’s books on the subject (almost all the details are left out). There are books in between, for example Warner, Boothby, Bishop and Crittenden, Lee to name a few that are more to my taste.

⭐no puedo opinar, me censuran los censores de amazon.esExcellent ouvrage ! Pédagogie assumée car tous les concepts sont présentés à partir d’un niveau minimum requis.! Outil efficace pour plonger dans ces notions et poursuivre ! Une référence en ce domaine ! Service sur Marketplace très satisfaisant !

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