Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This Book Is In German. ... Read more

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This Book Is In French. ... Read more

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The two volumes collected here represent what were to be the first two parts of Klein's plan to write a complete history of the mathematics of the 19th Century. This remarkable book was written by Klein during the last years of his life, a time coinciding with exciting mathematical activity and also the first World War. It is his personal view of the significant developments in mathematics in the 1800s (and early 1900s), especially those connected with the German school. This period includes the time of Klein's greatest activity and influence as a mathematician. The selection of topics reflects Klein's own interests in mathematics. The topics in the first volume include: Gauss's work in pure and applied mathematics; mathematics in France during the early decades of the 19th Century; the contributions of Mobius, Plucker and Steiner to the development of algebraic geometry; mechanics and mathematical physics in England and Germany up to the 1880s; complex analysis according to Riemann and according to Weierstrass; automorphic functions and the interplay between group theory and function theory. The second volume focuses on invariants and their applications in mathematical physics, with particular emphasis on special relativity. Both volumes were published after Klein's death. The final draft for the first volume was prepared by Courant and Neugebauer. The second volume was prepared by Courant and Cohn-Vossen. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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Diese Vorlesungsausarbeitung wurde aus Notizen aus dem Nachlaß von Felix Klein erstellt. Die Darstellung ist so gewählt, daß sie weitgehend den Sprechweisen der heutigen Mathematiker angepaßt ist. ... Read more

Customer Reviews (1)

Introduction to Riemann surfaces
After a short introduction and quick looks at linear fractional transformations (chapter 3) and stereographic projection (chapter 4), the idea of Riemann surfaces is introduced very thoroughly with many examples and pictures in the case of rational functions (chapter 5). We then look at the Riemann surfaces of the elementary transcendental functions (chapter 6), where they elucidate the nature of singularities, for example. Then we turn to algebraic functions (chapters 7-12). This is where Riemann surfaces really shine. The genus of a Riemann surface is a simple yet penetrating concept. Integrals such a the lemniscatic integral (p. 183) or the general elliptic integral (p. 160) are immediately seen to be non-integrable by elementary functions since the integrands have genus 1; conversely, any integral of a genus 1 integrand is reducible to an elliptic integral (p. 177). This is also the proper setting for algebraic geometry since algebraic curves are ultimately Riemann surfaces; singularities are branch points of the Riemann surface (as determined by the Puiseux expansion), irreducibility means connectedness for the Riemann surface, etc., and all this paves the way for a function theoretic treatment of Plucker formulae etc. The function theoretic point of view is crucial for matters of classification (e.g. the elliptic integral result above is really a curve classification theorem) and again the genus is a key concept, being invariant under 1-1 equivalence mappings, typified by taking evolutes (p. 166) or polar reciprocation (p. 167), for example. Chapters 13-15 are introduced as follows: "And now we return to the original plan of our lectures. We wish to expose the essence of the functions used in analysis with the aid of geometry and visualisation. ... I will use the time until Easter to develop certain fundamental theorems. Then after Easter we can take up the actual Riemannian theory of Abelian integrals." (pp. 196-197). Now, our good friends at Teubner has decided to cut this printed edition before Easter, so all we get to see in these final chapters is a fairly elementary, although very pleasant, introduction to "infinitesimal calculus in the complex domain". I imagine Klein would not have been very happy with this arrangement since he made a point of not including this material earlier (the fact that the Riemann surface clarifies path integration is mentioned only in chapter 15), and included it now only as a stepping stone. Judging by the table of contents of the rest of the course (pp. 237-238), it seems that, as the editor says (p. 7), one can find much of this material in either Klein's book "On Riemann's Theory of Algebraic Functions and Their Integrals" or his 1891/92 Gottingen lectures on Riemann surfaces, but this is a poor defence, I think, especially since if anything should have been cut with reference to the 91/92 lectures then it should definitely have been the applications to algebraic geometry. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This well-known work covers the solution of quintics in terms of the rotations of a regular icosahedron around the axes of its symmetry. Its two-part presentation begins with discussions of the theory of the icosahedron itself; regular solids and theory of groups; introductions of (x + iy); a statement and examination of the fundamental problem, with a view of its algebraic character; and general theorems and a survey of the subject. The second part explores the theory of equations of the fifth degree and their historical development; introduces geometrical material; and covers canonical equations of the fifth degree, the problem of A's and Jacobian equations of the sixth degree, and the general equation of the fifth degree. Second revised edition with additional corrections.
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Customer Reviews (2)

Excellent but ...
... but it's a real pity this edition doesn't include any of the figures which used to be present in the German-language editions. They were actually useful to better grasp the concepts discussed.

Also, though far less important as it frequently happens with this kind of heavily theoretical topics, there's a lack of numerical examples.

Algebraic Geometry
This is a famous book first published in German in 1884. In a fairly elementary way Professor Klein finds algebraic equations for the tetrahedron, cube and icosahedron by means of their rotational and reflection symmetry.Unfortunately there are no Figures such as provided by Coxeter,Regular Complex Polytopes,Cambridge Univ. Press 1991, probably because the facilities were not available.
The tetrahedron,cube and icosahedron are all Platonic solids which the ancient Greeks recognised as basic to the construction of the physical universe and their finite symmetries are the basis of considerable study in particle physics today. Interestingly enough I plotted Klein's equation for the tetrahedron (using a computer program unavailable in 1884)and found a cube which is well-known to be isomorphic to the tetrahedron. ... Read more

Product Description
This book an EXACT reproduction of the original book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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Felix Klein, a great geometer of the nineteenth century, rediscovered an idea from Hindu mythology in mathematics: the heaven of Indra in which the whole Universe was mirrored in each pearl in a net of pearls. Practically impossible to represent by hand, this idea barely existed outside the imagination, until the 1980s when the authors embarked on the first computer investigation of Klein's vision.In this extraordinary book they explore the path from some basic mathematical ideas to the simple algorithms that create delicate fractal filigrees, most appearing in print for the first time.Step-by-step instructions for writing computer programs allow beginners to generate the images. ... Read more

Customer Reviews (4)

Great mathematics and graphics
The mathematician Felix Klein(1849-1925) made some great discoveries that can now be well understood by using computer graphics.Felix Klein is known for his work in non-euclidean geometry and for his work on the connections between geometry and group theory.

Some fairly simple mathematical ideas and algorithms reveal an endless universe of fractals. The book includes step-by-step instructions for writing computer programs allowing readers to perform further explorations.

How mathematics can be used to create physical beauty
As a long-time reviewer of mathematics books, there was a time when I grew very bored with books written for the general mathematical audience. For years, it seemed mandatory that all contain a section on basic fractals and the Mandelbrot and Julia sets. It was not that the topics were not interesting, I found them fascinating, it was just that the explanations were all so similar that it became tedious to read them. Therefore, when I looked at the coverage of this book, I felt a pang of negative nostalgia, thinking that what I would find would be a repeat of what I had read so many times.
Well, I am happy to report that my pang was unfounded. The first chapter covers the language of symmetry, and some of the enormous number of forms in which it appears, which sets the stage for the fractal operations. A large part of the book is devoted to the patterns that are simultaneously symmetrical under two Mobius maps, which makes the analysis of fractals in this book different from what I have seen in others. Indra's necklace is a limit set formed by a chain of tangent circles, and is quite beautiful.
Very high quality figures are heavily used throughout the book to demonstrate the results of the operations. They are also beautiful, and in my opinion, some are works of art. Other mathematical operations that are used in the generation of the results are: matrix operations, group theory, non-Euclidean geometry, continued fractions, formal language theory, tiling of surfaces and function theory. The incorporation of so many different areas of mathematics really spices up the book, and makes it more enjoyable for a wider audience of mathematicians. It cannot be said that it is written for a general audience, the level of mathematics is beyond the non-mathematician, and one probably has to have the skill set of a junior or senior undergraduate math major in order to understand the explanations.
Mathematical results are very beautiful in their internal consistency and the power of the ideas. In this book, you also see some of the physical beauty that can be created by applying mathematics in the appropriate way

Discrete groups made easy
[this review shall replace the already existing one]

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 thislatter 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.

Discontinuous Groups now made easy !
Indras pearls provides a very well-made introduction to the basics of the theory of discontinuous groups acting on the complex plane. The whole discussion about limit sets had been accomplished in such a hand-by-hand method.
That is, the reader starts from complex numbers and, after, he is taken into deepest concepts as Möbius trasformations and so to discontinuous groups (Schottky, Fuchsian, ...).
Limit sets of kleinian groups are related to another interesting topic in today maths: complex dynamics on the Riemann sphere (Julia sets, ...). The success of this latter topic helped to increase the interests for discontinuous groups too. Indra pearls also witnesses and resumes the last twenty years of efforts spent for studying the properties of the limit sets.
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, guarantees the easy-learning of the approach, achieved by the authors. In this direction, it could be evinced that authors were really enjoyed while writing.
The goal has been reached: finding an easy way to introduce the harsch theory of discontinuous groups.
Interested readers will be rewarded about their choice and also excited. ... Read more

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Chapters: John Horton Conway, Évariste Galois, Niels Henrik Abel, Felix Klein, Sophus Lie, Richard Borcherds, Arthur Cayley, John R. Stallings, James W. Cannon, Brian Bowditch, Karen Vogtmann, Zlil Sela, Mladen Bestvina, Rostislav Grigorchuk, Marcus Du Sautoy, Arthur Byron Coble, John G. Thompson, Ferdinand Georg Frobenius, Mikhail Gromov, Theodor Molien, Yozo Matsushima, Jacques Tits, Joseph Gallian, James Alexander Green, Guido Zappa, Max Dehn, Richard Brauer, Charles Leedham-Green, Irving Kaplansky, Issai Schur, Bertram Huppert, Camille Jordan, William Burnside, Stephen Arthur Jennings, Jonathan Lazare Alperin, Hanna Neumann, Robert Fricke, Joseph Bernstein, Geoff Smith, Marshall Hall, László Pyber, Michael Aschbacher, George Glauberman, Otto Hölder, Graham Higman, David Harbater, Philip Hall, Daniel Gorenstein, Friedrich Wilhelm Levi, Bernhard Neumann, Hellmuth Kneser, James Wiegold, Bhama Srinivasan, Cheryl Praeger, Walter Feit, Hermann Rothe, Michio Suzuki, Richard A. Parker, Roger Evans Howe, Brian Hartley, Gilbert Baumslag, Wilhelm Magnus, Charles Sims, Mark Ronan, Robert Arnott Wilson, Sergei Adian, Hans Julius Zassenhaus, Christine Hamill, Paul Gustav Heinrich Bachmann, Dan Segal, Alfred Young, Pyotr Novikov, Émile Léonard Mathieu, Käte Fenchel, Robert Steinberg, Peter Ludwig Mejdell Sylow, Giovanni Frattini, Walther Von Dyck, Dudley E. Littlewood, Simon P. Norton, John Mckay, Hans Fitting, Zvonimir Janko, Aleksandr Gennadievich Kurosh, Edna Grossman, Roger Carter, Donald G. Higman, John Britton, Panos Papasoglu, Otto Schreier, R. L. Griess, George Abram Miller. Source: Wikipedia. Pages: 317. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Arthur Cayley (16 August 1821 26 January 1895) was a British mathematician. He helped found the modern British school of pure mathematics. As ...More: http://booksllc.net/?id=311034 ... Read more

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The beginnings of American mathematical research
Without question, the United States was an extremely dynamic, energetic country in the 19th century. However, in the area of mathematics, there was a very little. If one desired a solid mathematical education, Europe was the only answer. However, there were a few far-sighted individuals who understood how important mathematics is in a modern society.
While not well-known among the general community, one man's vision served to change the face of educational institutions in America. That man was Johns Hopkins who, when he died, bequeathed his fortune, around $7,000,000, to establish an educational institution in Baltimore where graduate education and research was to be emphasized. To build the mathematics department, Johns Hopkins University imported a British mathematician by the name of James Joseph Sylvester.
The trials and tribulations of building a world-class department from scratch is a tale that is very interesting to read. Creating the prototype of the modern department conducting research, many of their problems have a very familiar ring to them. The subsequent rapid progress is truly a tribute to those pioneers. Johns Hopkins opened in 1876 with an import as a department head, by only sixteen years later, in 1893, there was an international mathematics conference in Chicago.
While today that may not seem significant, at the time it took significant effort for a European to make the additional trip from the east coast to the Midwest. This is a tribute to the high quality of work already being done at the newly created University of Chicago and the head of the mathematics department, Eliakim Hastings Moore.
In between there were many trials, tribulations, tiffs, and tumbles, the combination of which make this one of the best books in the history of mathematics. Thoroughly referenced, it will satisfy your academic and historical urges.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more

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This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more