Euclidean-Geometry Books

I am no expert in this field, but I do not understand why this great book has not gotten wider exposure. The author gives a wonderful intro to the "geometry of compact Riemann surfaces based on hyperbolic geometry and on cutting and pasting." (Quoting from the preface.)

Perhaps Amazon has not helped his cause by miss-listing the author as J. Buser instead of Peter Buser, and compounding the problem by not returning this book on a search by author for Peter Buser.

All in all, this (fairly) advanced amateur gives Peter Buser's book on Riemann Surfaces five stars.

very good book for learning algebra or mat 191.

This is one of the best mathematics books I own. Chatters writting is clear and intuitive.

One cannot say that Lewis Carroll would be pleased, since he helps with the narration of this account of some additional travels of his darling Alice. Many of the other original Wonderland characters also help Dr. What If and him explain and illustrate a wide variety of geometric problems.
Although the author does an excellent job in presenting difficult concepts, this is not a textbook, Think of it as an excursion into the wonderland of advanced geometry. Experts will frolic, amateurs with grin and eventually understand and beginners will smile right up to the point (pun intended), where they get lost.
Problems are given at the end of each chapter and detailed solutions appear in the back of the book. A partial list of the topics covered includes inversions, reflections, a hyperbolic T-party, hyperbolic geometry, and projections. Verse with a decidedly Carrollean flavor appears throughout the text.
A joy to read and even better the second time through, it is a fitting sequel to the original adventures.

Published in Journal of Recreational Mathematics, reprinted with permission.

Although the book has a flavor towards continuum mechanics, the necessary concepts of linearity needed for the working physicist are presented in an elegant manner. The problems contribute a major understanding and expansion of the topics presented in the chapter. This book in conjuction with Finite-dimensional vector spaces by Halmos will present the reader the view from the top necessary to continue with topics such as Hilbert Spaces and Quantum Mechanics. I highly recommend this book.

This is an absolutely amazing book on linear algebra with
many cool topics related to eigenvalues, many hard to find
inequalities, variational principles, matrix equations, spectral
dichotomy, Hausdorff sets, spectral analysis, cool inequalities
using complex analysis, etc. A great reference book.

Popular mathematics can be done at a level that is also suitable for "advanced" survey courses in mathematics. This book is an existence proof of that. Davis does a superb job of tracing the development of five major areas of mathematics, some of which are more historical than others.
The areas are:

*) Greek mathematics of irrational numbers, Euclidean geometry, conic sections and Kepler's discovery of the motion of the planets.
*) The development of non-Euclidean geometry, and examples of non-Euclidean geometries such as hyperbolic and spherical geometries. This includes a brief discussion of Einstein's theories of relativity.
*) Number theory, factorization, prime numbers, the Euclidean algorithm, congruence arithmetic, and the work of Pierre de Fermat.
*) Cryptography, in particular that number theory is the theoretical foundation of modern cryptographic methods.
*) Fractal geometry and how iteration is used to construct the Mandelbrot and Julia sets.

Davis does an excellent job in explaining how the math was developed and is used and makes no attempt to "spoil the reader by sparing the equation", although equations are not multiplied beyond their necessity. A large number of exercises are included at the end of each section, which makes it possible to use it as a textbook.

This book hosts almost all there is to know and is known, about the worlds favorite transcendental constant. ALso many proofs of the nature on pi. e.g. the one by Hilbert and Lindemann. As well as the proof of the irrationality of zeta(3).

Definitely worth the money, and this book should be famous but it isnt!

Mostly for the advanced math person though, but lots of articles for the layman!

Enjoy!

This is the only book I've ever seen that makes the hyperbolic plane seem so natural and accessible. It takes ordinary Euclidean plane geometry as its basis, which allows the book to cover a lot of material in a very satisfying manner, without requiring advanced background like group theory or differential geometry. (In fact, the only background required is basically exposure to proofs, and occasionally a little calculus or linear algebra.) It's also extremely well-written, and the problems are well thought out. A great text for college juniors or seniors (or even advanced sophomores), and also great for self-study.

I bought the book on the strength of the pretty pictures scattered throughout the book (much much more interesting than the front cover). The text of the book is as impressive.

"Quasicrystals and Geometry" is a bit between an overview and a cookbook. Sections of the book are historical, parts are practical. Explicit and easy to follow instructions for generation of penrose tilings (and many other really cool tilings) are included.

Despite what the introduction says, this book is not written for a lay audience. A quarter or two of college level math seems to be assumed.