- Tapa dura: 418 páginas
- Editor: Cambridge University Press (25 de abril de 2002)
- Idioma: Inglés
- ISBN-10: 0521352533
- ISBN-13: 978-0521352536
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
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- n.° 1183 en Libros en idiomas extranjeros > Ciencias, tecnología y medicina > Matemáticas > Filosofía e historia de las matemáticas
- n.° 1846 en Libros en idiomas extranjeros > Ciencias, tecnología y medicina > Matemáticas > Geometría
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Indra's Pearls: The Vision of Felix Klein (Inglés) Tapa dura – 25 abr 2002
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Descripción del producto
'[This book is] richly illustrated with these wonderful and mysterious pictures and gives detailed instructions for recreating them, right down to the level of computer programs (written in pseudo-code, and easy to translate into any computer language) … the reader who attempts any substantial subset of [the projects] will gain enormously … Even those who are convinced they have no ability to visualize may change their minds … It is almost required reading for the experts in the field … I truly love this book.' John H. Hubbard, The American Mathematical Monthly
'It has been a great pleasure to read such a gracefully written, original book of mathematics … it is a flowing narrative, leavened with wit, whimsy, and lively cartoons by Larry Gonick. The three authors, with the support of Cambridge University Press, have produced a book that is as handsome in physical appearance as its content is stimulating and accessible. The book is an exemplar of its genre and a singular contribution to the contemporary mathematics literature.' Albert Marden, Notices (journal of the American Mathematical Society)
'The production of the book leaves nothing to be desired. It is splendid. Printed entirely on glossy paper, with practically all of the many figures in glorious color, the book has a number of admirable design features: large type and wide margins wherein references are given and occasional comments (often quite talky) are made. Cambridge University Press has done a beautiful job, and David Tranah of the Press deserves special commendation for his role in pulling out all the stops.' Philip J. Davis, SIAM News
'All of it is patiently explained … By the time you finish, you'll know your way around the complex plane.' Brian Hayes, American Scientist
'The book itself is a work of art … I am sure that [it] will have a major impact on the way we teach geometry and dynamics … a jewel that will more than repay the persistent reader's efforts.' Michael Field, Science
'I rarely feel a certain kind of euphoria by just looking at the cover of a mathematics book. But that happened with Indra's Pearls: The Vision of Felix Klein … [contains] fantastic illustrations together with apparently well-founded mathematical explanations … [it is] presented in an accessible way which dares to prioritize general comprehension above a strict theoretical approach … As far as I know, this book is one of the most beautiful examples of the illustration of the inherent aesthetic beauty (which exists) within mathematics … the images are of the highest quality obtainable at present for mathematical structures. Everyone, who ever tried to create something comparable, knows how difficult it is.' Jürgen Richter-Gebert, Technische Universität München
'This unique book can serve as a pedagogical and visual introduction to group theory for schoolchildren, and yet is just as suitable for professional mathematicians: I believe that both of them would read the book from the beginning to the end. Finally, it can be used as a book for popularising science, but is very different from most fashionable books on strings, black holes, etc: it gives you the joy of seeing, thinking and understanding.' European Mathematical Society
'This is a beautifully presented book, rich in mathematical gems.' The Mathematical Gazette
'One can browse through the numerous beautiful and fascinating pictures and marvel at them … Readers with widely different backgrounds will find something enjoyable in this unique book.' Acta Scientiarum Mathematicarum
Reseña del editor
Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries. For a century, these images barely existed outside the imagination of mathematicians. However, in the 1980s, the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.Ver Descripción del producto
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Central to the book is the concept of the group and particular subgroups. Fractals, chaos, and other concepts from dynamical systems emerge from this book in a beautiful way. There are also historical vignettes of the key figures in the development of the subject.
The pseudocode is well explained in words, then algorithm. I have only just started to play with this. On a second and subsequent readings I hope to work through the projects that the authors provide.
This seems to have been a long labour of love for the three authors and their collaborators. My first read was a pleasure and motivator to learn more.
My own approach using Iterated Function Systems isn't actually the same as
the Limit set approach, yet sometime the results come out very similar.
For comparison the graphics in :
The Arithmetic of Hyperbolic 3-Manifolds (Graduate Texts in Mathematics)
are very minimal and the presentation of the Mathematics makes no effort to be understandable
to ordinary people.
Another example is:
Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics)
which has some very awesome mathematics, but again has minimal graphics
and makes very little effort at really teaching the subject in an understandable manner.
Don't get me wrong, the Limit set Klein group approach in Indra's Pearl's
isn't easy, but for a very difficult subject the authors really try to
make the subject approachable to most anyone.
For me the Klein group approach to geometry has been an eye opener,
that put Teichmüller space into my mind alongside Reimannian conformal geometry
and the quantum mechanical groups of physics. I think future generations of students
will bless these authors for this representation.
Indras pearls provides a very well-made introduction to the basics of the theory of discrete groups acting on the complex plane. The whole discussion on the related limit sets had been accomplished in such a hand-by-hand method.
The reader starts from complex numbers and after he is led into the deepest concepts: Möbius trasformations, limit sets of discrete groups (Schottky, Fuchsian, ...).
These limit sets are related to another interesting topic in today maths: complex dynamics on the Riemann sphere (Julia sets, ...).
As known, computer experiments had been fundamental for supporting complex dynamics and the successive success of this latter topic helped to promote and increase the interests for discrete groups too: in fact this book evinces already strong interest in the visualization and in the study of the properties of such limit sets since '80s, due to the efforts of the same authors.
One of the major points of attraction in Indra pearls is that all the theory had been helped by displaying a lot of detailed and colorful pictures which, aside the historical biography of the mathematicians that contributed to this theory, set this book as one of the masterpieces in this topic, for his lucid
and fresh approach to basic concepts.
In addition, the presence of amusing comic-strips, explaining some topological concepts on manifolds (for example), guarantees the easy-learning for the reader and also the approach, as imaginaed and completely accomplished by the authors. In this direction, it is clear how passion had been squandered by authors.
The goal has been reached: finding an easy way to introduce the harsch theory of discrete groups.
Interested readers will be rewarded and also excited.
No doubts: this book strikes and it will be a corner-stone for present and future.