Editorial Reviews. Review. From the reviews: “An introduction to the formalism of differential and integral calculus on smooth manifolds. Many prospective. Loring W. Tu. An Introduction to Manifolds. Second Edition. May 19, Springer. Berlin Heidelberg NewYork. HongKong London. Loring W. Tu Tu’s An Introduction to Manifolds is accordingly offered as the first of a quartet of works that should make for a fine education in.

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Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology.

Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems.

This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in ihtroduction. Read more Read less. Discover Prime Book Box for Kids. Kindle Cloud Reader Read instantly in your browser.

Customers who bought this item also bought. Page 1 introdduction 1 Start over Page 1 of 1. Tensor Calculus Made Simple. Principles of Tensor Calculus. Third Edition Dover Books on Mathematics. Editorial Reviews Review From the reviews: Indeed, I propose to use it myself, given that I am one introduuction the non-experts …. The book is divided into seven parts, plus four appendices. The higher dimensional analogues of smooth curves and surfaces are called manifolds. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology.

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An Introduction to Manifolds (Universitext) 2, Loring W. Tu –

There was a problem filtering reviews right now. Please try again later. I borrowed this book from a library to learn differential geometry. So I cannot comment about Amazon’s deliverance.

An Introduction to Manifolds : Loring W. Tu :

As a Physics PhD student I should say that this book can be very helpful as long as one is aware that the purpose of the author is to teach differential geometry on a fast track. This means that some of the details of the each topic have not been covered.

For instance the details kanifolds some of the proofs have been left as the exercises of chapter. This was exactly my purpose from reading this book which is completely satisfied and that’s why I am giving it 5 stars. However if you have more time and are loriny to learn all the details, the book by John Lee “Introduction to Smooth Manifolds”would serve you better because he covers almost the same material well, there are three chapters which have not been mentioned here at all but in over pages.

Jeffrey Lee’s book, “Manifolds and Differential Geometry” is also a nice book esp someone wants to learn Riemannian geometry too.

About the prerequisites, while I had some background in point set topology from Munkres, but it was not really necessary because there is a short appendix at the end which has reviewed the required concepts of topology. A solid background in Algebra and Analysis would be necessary though.

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Overall, reading this book is relatively easily and is very well suited for self-study. The exercises of each chapter are relatively easy and sometimes introduce some new concepts. We used John Lee’s Introduction to Smooth Manifolds and the terse encyclopedic nature of the book didn’t really help me understand what the professor was saying. Luckily, I found Loring Tu’s book which gives a gentler introduction to the subject.

Loring Tu’s book has many computational examples and easy to medium level exercises, which are essential because of the onslaught of notation one encounters in manifold theory. I’ve been able to compare this book with John Lee’s Introduction to Smooth Manifolds, which seems to be one of the standard texts for an introductory geometry course.

My guess is that when Mr. Tu was writing his book, he started with John Lee’s book and got rid of all of the obscure and difficult examples. He then expanded out the important essential ones in more manifoldx so that a student who has never seen manifold theory would have a better chance of understanding.

When I first began reading the text, I had a difficult time understanding the concepts, but the presentation of the material really laid bare all of the esoteric topics that I hadn’t encountered formally before. He labels every problem, so a student doesn’t wade through pages of text needlessly trying to inrroduction which part of the text will be most useful, but this method allows the student to hone in on the material which is exactly pertinent to that problem.


I am by far not the best and brightest student, but I have been able to read the text and given a few tk for each section, introoduction all exercises throughout the reading and at the end of the section. With many hints and solutions at the end of the textbook, I can be sure I’m not only learning the material, I’m learning it correctly!

I would agree with some of the other reviewers that this should be a text every graduate student in mathematics should read. It is a complete book! One person found this helpful. This is an excellent book for what it is.

A gentle yet rigorous introduction to the subject. I like the careful handling of various notion of orientation, the introduction to category theory which is unusual for a book of this ttu. An as others have pointed out, it is a nanifolds book for Bott and Tu’s book on differential forms which is horrible in terms of introducing basic concepts.

Some complain that the book is dry. It is somewhat dry, yes but that makes the book concise; think of it as learning the alphabet before you being to poetry.

It is one of the best books in its category. Exact and closed definitions. It’s a very nice text. Exact and closed definitions, clear derivations of propositions and theorems. This work may be used as a textbook anybody who are interesting in different aspect of topology, abstract algebra and manifold.

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