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Geometric Measure Theory, Fourth Edition: A Beginner's Guide, by Frank Morgan
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Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Measure Theory: A Beginner's Guide is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject.
New to the 4th edition:
* Abundant illustrations, examples, exercises, and solutions.
* The latest results on soap bubble clusters,
including a new chapter on "Double Bubbles in
Spheres, Gauss Space, and Tori."
* A new chapter on "Manifolds with Density and
Perelman's Proof of the Poincar� Conjecture."
* Contributions by undergraduates.
- Sales Rank: #2247070 in Books
- Published on: 2008-09-23
- Original language: English
- Dimensions: 9.00" h x 6.00" w x .75" l, 1.35 pounds
- Binding: Hardcover
- 264 pages
Review
“The text is simply unique. It doesn't compare to any other because its goals are different. It cannot be used as the only source of information for learning GMT, yet learning this subject without owning a copy of this book would be ridiculous since it gives a fast and efficient insight in many aspects of the theory.”
-Thierry De Pauw, niversite catholique de Louvain, Belgium
“The book is unique in its format and exposition. Without it, it would be difficult to get in touch with the subject. It paves the way to more advanced books. All other books on the market about this subject are rather technical and difficult to read for an inexperienced student.”
-Stefan Wenger, Courant Institute of Math, New York University
About the Author
Frank Morgan is the Dennis Meenan '54 Third Century Professor of Mathematics at Williams College. He obtained his B.S. from MIT and his M.S. and Ph.D. from Princeton University. His research interest lies in minimal surfaces, studying the behavior and structure of minimizers in various settings. He has also written Riemannian Geometry: A Beginner's Guide, Calculus Lite, and most recently The Math Chat Book, based on his television program and column on the Mathematical Association of America Web site.
Most helpful customer reviews
8 of 8 people found the following review helpful.
Intended as a standalone text?
By Johan Nystrom
This brief comment (rather than a proper review) really refers to the third edition.
The prospective purchaser should know that the book contains very little hardcore mathematics. Yes, the book is ABOUT mathematics, but it contains very little of the gory details that actually constitute the real mathematics, like definitions, theorems and proofs (and the intuition behind it all for that matter). You could say that it is about mathematics written elsewhere. Elsewhere here means "Geometric Measure Theory" by Herbert Federer. This is also stated (in other words) in the preface of the third edition.
Perhaps this fourth edition is better than the third in this respect, but otherwise it comes at a very hefty price for a number of illustrations and solved problems. Get a real math book first, and only then this one if you can afford it. Federer's book is the real thing, but it might be too much of the real thing. It is not an easy read. The target audience is the mature mathematician and the "able student". It is a rare "advanced undergraduate" student that would master it. Thus a book like Morgans book that makes Federer's text a little more accessible is welcome. What brings the rating down is the price tag and the fact that it isn't obvious to the purchaser that this book REQUIRES a companion book. I actually felt fooled when I first got this book for $100+.
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