| Title | : | Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts |
| Author | : | |
| Rating | : | |
| ISBN | : | - |
| Format Type | : | Kindle , Hardcover , Paperback , Audiobook & More |
| Number of Pages | : | - |
Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry . Using 235 hand drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner.
Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2 forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2 forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book.
Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts Reviews
-
Avoid the hardcover because the quality is very poor. It is a print on demand version of the book which sadly is nevertheless superb. But for than one hundred bucks a feel betrayed!
-
One’s review is supposed to be of the contents, not the print quality. “ "When a wise man points at the moon the imbecile examines the finger"
-
I am very pleased with this book. The figures are black and white but extremely innovative. I think this masterpiece will become the modern MTW (Misner, Thorne, and Wheeler) of differential geometry. In other words: epic, legendary, enthusiastic without the MTW backdrop of taking the (presumably male) reader on any distasteful romantic conquests.
Back to the book at hand: very clever and insightful. I’ve looked at a few complex analysis and differential geometry books and have some familiarity with differential forms. I am definitely learning new things from this text.
The author’s genuine enthusiasm clearly shines through. Reading this book is unexpectedly delightful: like attending an impeccably planned opera while simultaneously listening to a professor spend an entire afternoon joyfully answering a question after a lecture.
Oh, and the index is very thorough! If what you are looking for is in the book, you will find a listing with every possible combination of ideas. I recommend reading the index to experience a thoughtful grouping of ideas in a new light. This is a 5 act book, but I’d call the index Act 6.
I have read the whole book at this point, and I will continue to browse for fun. I could also envision returning to pages with literal fruits and vegetables in figures: this book could serve as a kitchen laboratory manual for leisurely fruit peel curvature explorations. In addition, student led math/science clubs could use the book as a starting point for developing public outreach demonstrations suitable for anyone old enough to chew fruit. -
The moon will be there. And may be seen with or without a finger pointing. But if that finger has an obvious wound or hideous blemish, which might be cancerous, you do want to call for attention to that.
-
This book is very physical. Full of intuitions and motivations. The introduction of the Riemann tensor, Jacobi equation leading to the Einstein field equation is the best I have read. The starting point is also low, only requiring some basic calculus and linear algebra background. It was a real joy to read.
The only downside is that the book binding is really bad. Multiple pages are loose and off with very light use. -
Beautifully illustrated, topics lucidly explained. Absolutely recommend to all interested in differential geometry.
-
Great illustrations, Excellent explanations
-
I just received this paperback and started reading. The explanations are very clear with beautiful pictures as his "Visual Complex Analysis" book published in 1990s was. It is very pleasurable to read this book. I actually took his math class long time ago at University of San Francisco. His math class with visualization changed my entire perspective toward mathematics.
-
The material in the book is fine, although the small font detracts from my reading experience. However, the problem is really with the quality of the printing. The copy I received looked as if the printer was running out of toner, so all the illustrations appear very faintly, with extremely poor contrast. I have a PDF of the book and the difference between the electronic figures and the printed version is enormous. So much so that I am actually returning my print copy.
-
Received this yesterday (yes, the day of publication). Can't stop picking it up and browsing. REAL mathematics. My first university destroyed my interest in maths with a purist course axioms, theorems, proofs ground through painfully.
There is a chasm in differential geometry between the curves and surfaces level, then the differential forms level, which I have struggled to get over, even with Loring Tu's fine book on manifolds. Needham's text has masses of real examples which I believe will bridge this gap. I did not know I did not know so much!
Looks even better than Visual Complex Analysis. -
This book will become a classic in no time. Tristan Needham’s approach to the subject is fresh and, indeed, extremely visual. His practical examples regarding transport on surfaces are incredibly clear. Jacobi fields become very intuitive objects. It is a great companion to any good text in differential geometry.
