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[epub pdf] Introduction to Smooth ManifoldsAuthor John M Lee –

This Book Is An Introductory Graduate Level Textbook On The Theory Of Smooth Manifolds Its Goal Is To Familiarize Students With The Tools They Will Need In Order To Use Manifolds In Mathematical Or Scientific Research Smooth Structures, Tangent Vectors And Covectors, Vector Bundles, Immersed And Embedded Submanifolds, Tensors, Differential Forms, De Rham Cohomology, Vector Fields, Flows, Foliations, Lie Derivatives, Lie Groups, Lie Algebras, And The Approach Is As Concrete As Possible, With Pictures And Intuitive Discussions Of How One Should Think Geometrically About The Abstract Concepts, While Making Full Use Of The Powerful Tools That Modern Mathematics Has To Offer This Second Edition Has Been Extensively Revised And Clarified, And The Topics Have Been Substantially Rearranged The Book Now Introduces The Two Most Important Analytic Tools, The Rank Theorem And The Fundamental Theorem On Flows, Much Earlier So That They Can Be Used Throughout The Book A Few New Topics Have Been Added, Notably Sard S Theorem And Transversality, A Proof That Infinitesimal Lie Group Actions Generate Global Group Actions, A Thorough Study Of First Order Partial Differential Equations, A Brief Treatment Of Degree Theory For Smooth Maps Between Compact Manifolds, And An Introduction To Contact Structures Prerequisites Include A Solid Acquaintance With General Topology, The Fundamental Group, And Covering Spaces, As Well As Basic Undergraduate Linear Algebra And Real AnalysisJohn M Lee Is Professor Of Mathematics At The University Of Washington In Seattle, Where He Regularly Teaches Graduate Courses On The Topology And Geometry Of Manifolds He Was The Recipient Of The American Mathematical Society S Centennial Research Fellowship And He Is The Author Of Four Previous Springer Books The First Edition Of Introduction To Smooth Manifolds, The First Edition And Second Edition Of Introduction To Topological Manifolds, And Riemannian Manifolds An Introduction To Curvature

6 thoughts on “Introduction to Smooth Manifolds

  1. says:

    Le livre tait neuf de chez neuf et c tait bien la derni re dition.En effet, ce point est tr s important pour les connaisseurs Les anciennes versions sont revendues parfois aux prix plein alors que la derni re est meilleure et plus compl te.

  2. says:

    There is not much to say about the quality of the text and the book As readers mentioned, this is a first class textbook, and is probably the best for self study on this subject Loring Tu s book is also great, but feels a bit shallow in terms of examples and exercises However, my copy already had to be glued back together, even after careful use This is a Springer problem, and I will not take any stars away Content wise, it is actually quite similar to Spivak s Comprehensive Intro to Differential Geometry, Vol 1 It s all about manifolds, without specializing on any particular structure However, it is definitely slower in pace and gentler Spivak definitely has a way of introducing details that are interesting but difficult and not necessary for a first timer to go through And with Spivak, there are still pages I ve had to read and re read just to understand the point, but Lee s text is gentle enough that I usually at least appreciate what he s trying to do, even if I miss the exact reasoning or details on first read I suppose it s in part because I am reading it after Spivak Nevertheless, Lee is the rare mathematician who really tries to make sure that students don t get lost Cynically, for the reason that the text hand holds too much, professional differential geometers are unlikely to rate it particularly highly mathematicians want texts to be sleek and laconic not a word than what is logically necessary but indifferent to the student seeing the topic for the first time like any of the three Rudin texts, for example It s great if a you have a great professor or b you happen to be extremely smart But for most people engaged in self study, it quickly leads them to give up.

  3. says:

    Differential Geometry is a tough subject I myself am not very interested in the subject and hence, do not wish to slave away trying to see the important ideas I want it stated cleary This book does this and with great clarity.The hardcover copy I have is nearly 2 inches thick and is densely packed with almost anything a student could want for Differential Geometry Yet, even though it is thick and dense, it is nothing like Algebra by Serge Lang In some cases, it is far better.The exposition is clear and the visuals allow for intuition to be built I have not gotten through the text and I cannot say I ever will, but I d be damned if I didn t say that I would use this book for future studies.So what are some problems with the book Well, it certainly is hard to say It is an introductory text, but can be read like a reference text The appendix allows for students who are coming back to quickly go through the pre requisite and learn what is needed The four appendices cover everything from Topology to Calculus to Algebra not the kiddy Calculus and Algebra With all this, it Lee makes it clear what is needed to be known to read beforehand No google searches looking for prerequisite requirments.Even then, if there are gaps in understanding, one can certainly look them up Even then, Lee has his own books that goes into those backgrounds like Introduction to Topological Manifolds.By no means are the problems easy Lee makes it clear that they are tough and brutal for the uninitiated Plus, they can take hours, days, or weeks to solve depending on the problem Hence, it does not hurt to go ask for help In fact, it is encouraged.Thus, Lee, good sir, has done us a great favor.

  4. says:

    This book is exceptionally clear which was all I really wanted after gaining insight from Spivak However it offered much with good writing, motivation, examples, and problems This has made the book my go to on the subject As an added bonus, the notation Lee uses is the most intuitive that I ve seen.

  5. says:

    It works well a textbook in a course on differential topology, even if the instructor does not assign it as the class textbook It is a very adaptable book with a lot of material The one thing that you should know to do is skip chapters as needed.

  6. says:

    This book has been indispensable for my Differential Geometry class The proofs and examples are excellent, and the exercises are appropriately difficult.