The Shape of Space (Textbooks in Mathematics) 2nd Edition by Jeffrey R. Weeks (PDF)

Description

Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

User’s Reviews

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

⭐I can’t give him five stars as good as Jeffery Weeks is, because the book doesn’t even mentions Bianchi’s manifold types. I also missed a discussion of his own manifold classification scheme and his program Snap Pea.I bought the book so I could understand his low volume M003[3,-1] Weeks space. It ,too, isn’t mentioned. He did give some coverage to the dodecahedron type of hyperbolic manifold.He probably should have left cosmology out as he seems to have very little idea of particle formation during the early universe?There is no doubt that Jeffery Weeks is a brilliant geometer, he just seems to have limited his background not to include fractal/ scaling theory, gravitational physics or Lie algebras?What makes this book so good is his coverage of orientability in Manifolds. The only real physical evidence that nature may have orientablity incorporated is the parity of the electron, some asymmetry in mesons and times arrow in thermodynamics. His ideas and the dialog in the text about the expansion of space and what there was before the big bang is sophistry ( that is the bad teaching before philosophy)and not science or mathematics. That he presents it is a shame on his thesis adviser who was supposed to have made sure he knew what meta-mathematics and metaphysics were?I think it is a well written book and should be read bythose wishing to understand modern manifold theory,it just isn’t complete and he just assumes he knows muchmore than is actually known.

⭐I have a bachelors degree in Math.As Feynman said, what we really mean by math is careful reasoning. This book brings you the joy of careful reasoning, guided by an expert.Perhaps what turns some people off math in school is that the supreme example of careful reasoning is the mathematical PROOF. (Or perhaps it’s just that most math teachers are so poor.) A proof tends to look dull and ponderous on the outside, and a student can easily miss the beauty of the underlying ideas. On the other hand, for your own amusement you can figure something out to your own satisfaction, without necessarily constructing a watertight proof. This book helps you do just that.Many newspapers contain Sudoku problems, often with the reassuring claim that no math is required! People who hated math in school can be seen working happily on Sudoku puzzles, for the sheer joy of exercising their ability to reason carefully. The same ability would bring them far more joy while reading this book and answering the puzzles/exercises sprinkled throughout.

⭐I was hoping for a more dumb-downed book. This is a textbook. If you don’t do the homework, you will get lost. It reminds me of reading Godel, Escher, Bach: “This makes sense”, “I get that”, “OK”, then suddenly “WTF are you talking about?!?” I recommend it, but it’s heavy going. Four stars is not entirely fair because it is excellent for what it is; it’s just not what I was expecting. OK, just changed my rating to five stars.

⭐This book is my favorite introductory exploration of geometry and topology without the mathematical details.

⭐The book is great, but Amazon sold it to me as a new book and it was crunched at one corner of the spine, like it had been dropped. I suggest buying it elsewhere.

⭐Amazing book for grad students and high schoolers alike. I was hoping for a lighter version of Thurston’s book to have better intuition of 3 manifolds, and this book delivered.

⭐I’ve wanted this book for years. But I’m a math/geometry grad.

⭐Appealing to both mathematicians and non-mathematicians. Well written with fun applications such as tic-tac toe on a Klein bottle. I highly recommend this book.

⭐I love this book. Unfortunately I did not get to keep the copy I bought, I had to give it to the library as I lost their copy. The book is just fantastic. The writing style is great, it really lays the concepts out for you neatly, and with a few good chuckles.You definitely do not need a strong background in mathematics to really enjoy this book, nor will a maths background make it feel too slow (unless you have done topology or metric spaces).If you have any interest in the subject, read this book. The writing is just great. Interesting and informing, and definitely funny at parts.

⭐Out of the ordinary book

⭐Fairly large print, easy to read with lots of illustrations and excercises

⭐Dies Buch macht Topologie auf einfühlsame Weise greifbar. Der Inhalt sollte auch für Oberschüler gut verständlich sein, die bereit sind das Abenteuer einzugehen, und sich von Jeffrey Weeks durch die spannende Welt der Topologie führen lassen. Es enthält viele Bilder, die die Begriffe der Topologie erst begreifbar machen. Dies Buch ist eher als eine Einführung zu einführenden Büchern der Topologie zu verstehen. J. Weeks benutzt dazu alle Elemente, vom Tic-Tac-Toc-Spiel auf dem Torus, bis zum Schachspiel auf höheren Manigfaltigkeiten. Er benutzt ähnlich wie in Abbott’s buch “Flächenland” Flächenbewohner als Forscher ihrer Umwelt, um die Merkwürdigkeiten einer Welt auf einem Torus oder Möbiusbandes begreifbar zu machen. Das ganze hat zum Ziel, die mögliche Form unseres Unversums zu beschreiben. Er bleibt aber nicht an diesem Punkt stehen, sondern führt den Leser sogar in die verschiedenen Geometrien des 3-dimensionalen raums ein. Mit diesem Buch macht Mathe wirklich Spaß. Ich würde mir wünschen, das dieses Buch mal ins Deutsche übersetzt wird, um ein größeres Publikum zu erreichen.Some information was somewhat difficult to follow and comprehend.

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