Lectures on Mathematics - Couverture rigide

Klein, Felix

Couverture rigide

ISBN 10 : 0821827332 ISBN 13 : 9780821827338

Editeur : American Mathematical Society, 2001

Synopsis

In the late summer of 1893, following the Congress of Mathematicians held in Chicago, Felix Klein gave two weeks of lectures on the current state of mathematics. Rather than offering a universal perspective, Klein presented his personal view of the most important topics of the time. It is remarkable how most of the topics continue to be important today. Originally published in 1893 and reissued by the AMS in 1911, we are pleased to bring this work into print once more with this new edition. Klein begins by highlighting the works of Clebsch and of Lie. In particular, he discusses Clebsch's work on Abelian functions and compares his approach to the theory with Riemann's more geometrical point of view. Klein devotes two lectures to Sophus Lie, focussing on his contributions to geometry, including sphere geometry and contact geometry.Klein's ability to connect different mathematical disciplines clearly comes through in his lectures on mathematical developments. For instance, he discusses recent progress in non-Euclidean geometry by emphasizing the connections to projective geometry and the role of transformation groups. In his descriptions of analytic function theory and of recent work in hyperelliptic and Abelian functions, Klein is guided by Riemann's geometric point of view. He discusses Galois theory and solutions of algebraic equations of degree five or higher by reducing them to normal forms that might be solved by non-algebraic means. Thus, as discovered by Hermite and Kronecker, the quintic can be solved 'by elliptic functions'.This also leads to Klein's well-known work connecting the quintic to the group of the icosahedron. Klein expounds on the roles of intuition and logical thinking in mathematics. He reflects on the influence of physics and the physical world on mathematics and, conversely, on the influence of mathematics on physics and the other natural sciences. The discussion is strikingly similar to today's discussions about 'physical mathematics'. There are a few other topics covered in the lectures which are somewhat removed from Klein's own work. For example, he discusses Hilbert's proof of the transcendence of certain types of numbers (including $\pi$ and $e$), which Klein finds much simpler than the methods used by Lindemann to show the transcendence of $\pi$.Also, Klein uses the example of quadratic forms (and forms of higher degree) to explain the need for a theory of ideals as developed by Kummer. Klein's look at mathematics at the end of the 19th Century remains compelling today, both as history and as mathematics. It is delightful and fascinating to observe from a one-hundred year retrospect, the musings of one of the masters of an earlier era.

A propos du livre

Présentation de l'éditeur

Oliver, A.M., professor of mathematics, Cornell University. A. M. Sawin, Sc.M., Evanston. W. E. Story, Ph.D., professor of mathematics, Clark University. E. Study, Ph.D., professor of mathematics, University of Marburg. H. Taber, Ph.D., assistant professor of mathematics, Clark University. H. W. Tyler, Ph.D., professor of mathematics, Massachusetts Institute ofT echnology. J. M. Van Vleck, A.M., LL.D., professor of mathematics and astronomy, Wesleyan University. E. B. Van Vleck, Ph.D., instructor in mathematics, University of Wisconsin. C. A. Waldo, A.M., professor of mathematics, De Pauw University. H. S. White, Ph.D., associate professor of mathematics. Northwestern University. M. F. Winston, A.B., honorary fellow in mathematics, University of Chicago. A. ZiWET, assistant professor of mathematics. University of Michigan. The meetings lasted from August 28th tillS eptember 9th ;and in the course of these two weeks Professor Klein gave a daily lecture, besides devoting a large portion of his time to personal intercourse and conferences with those attending the meetings. The lectures were delivered freely, in theE nglish language, substantially in the form in which they are here given to the public. The only change made consists in obliterating the conversational form of the frequent questions and discussions by means of which Professor Klein understands so well to enliven his discourse. My notes, after being written out each day, were carefully revised by Professor Klein himself, both in manuscript and in the proofs. As an appendix it has been thought proper to give a translation of the interesting historical sketch contributed by Professor Klein to the work Die deutschen Universitdten. The translation was prepared by Professor H. W. Tyler, of theM assachusetts Institute ofT
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This book was originally published prior to 1923, and represents a reproduction of an important historical work, maintaining the same format as the original work. While some publishers have opted to apply OCR (optical character recognition) technology to the process, we believe this leads to sub-optimal results (frequent typographical errors, strange characters and confusing formatting) and does not adequately preserve the historical character of the original artifact. We believe this work is culturally important in its original archival form. While we strive to adequately clean and digitally enhance the original work, there are occasionally instances where imperfections such as blurred or missing pages, poor pictures or errant marks may have been introduced due to either the quality of the original work or the scanning process itself. Despite these occasional imperfections, we have brought it back into print as part of our ongoing global book preservation commitment, providing customers with access to the best possible historical reprints. We appreciate your understanding of these occasional imperfections, and sincerely hope you enjoy seeing the book in a format as close as possible to that intended by the original publisher.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2001
• Langue: anglais
• ISBN 10: 0821827332
• ISBN 13: 9780821827338
• Reliure: Relié
• Coordonnées du fabricant: non disponible