Über die Theorie des Kreisels (Classic Reprint)

Science & Math

Felix, Klein

Physics

Forgotten Books

Famous Problems of Elementary Geometry: The Duplication of the Cube; The Trisection of an Angle; The Quadrature of the Circle; An Authorized ... Ausgearbeitet Von F. Tägert

Franklin Classics Trade Press

The Mathematical Theory of the Top: Lectures Delivered on the Occasion of the Sesquicentennial Celebration of Princeton University

History

On Riemann's Theory of Algebraic Functions and Their Integrals: A Supplement to the Usual Treatises (Classic Reprint)

Excerpt from On Riemann's Theory of Algebraic Functions and Their Integrals: A Supplement to the Usual TreatisesTheory of Functions treated geometrically. Part I, Winter-semester 1880 81, Part II, Summer-semester 1881.I denote thus the contents of the investigations with which Riemann was concerned in the first part of his Theory of the Abelian Functions. The theory of the O-functions, as developed in the second part of the same treatise, is in the first place, as we know, of an essentially different character, and is excluded from the following presentation as it was from my course of lectures.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Mathematics

"Nothing comparable to it." — Mathematics Teacher. This comprehensive three-part treatment begins with a consideration of the simplest geometric manifolds: line-segment, area, and volume as relative magnitudes; the Grassmann determinant principle for the plane and the Grassmann principle for space; classification of the elementary configurations of space according to their behavior under transformation of rectangular coordinates; and derivative manifolds. The second section, on geometric transformations, examines affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. The text concludes with a systematic discussion of geometry and its foundations. 1939 edition. 141 figures.

Elementary Mathematics from an Advanced Standpoint: Geometry

Dover Publications

Four volumes in one: Famous Problems of Elementary Geometry, by Klein. A fascinating, simple, easily understandable account of the famous problems of Geometry--The Duplication of the Cube, Trisection of the Angle, Squaring of the Circle--and the proofs that these cannot be solved by ruler and compass. Suitably presented to undergraduates, with no calculus required. Also, the work includes problems about transcendental numbers, the existence of such numbers, and proofs of the transcendence of $e$. From Determinant to Tensor, by Sheppard. A novel and simple introduction to tensors. ``An excellent little book, the aim of which is to familiarize the student with tensors and to give an idea of their applications. We wish to recommend the book heartily ... The beginner will find the book a valuable introduction and the expert an interesting review with a refreshing novelty of presentation.'' --Bulletin of the AMS Chapter headings: 1: Origin of Determinants; 2: Properties of Determinants; 3: Solution of Simultaneous Equations; 4: Properties; 5: Tensor Notation; 6: Sets; 7: Cogredience, etc. 8: Examples from Statistics; 9: Tensors in Theory of Relativity. Introduction to Combinatory Analysis, by MacMahon. An introduction to the author's two-volume work. Three Lectures on Fermat's Last Theorem, by Mordell. This famous problem is so easy that a high-school student might not unreasonably hope to solve it: it is so difficult that as of the 1962 publication date of this book, tens of thousands of amateur and professional mathematicians, Euler and Gauss among them, failed to find a complete solution. Mordell himself had a solution (as he said he did). This work is one of the masterpieces of mathematical exposition.

Famous Problems and Other Monographs

American Mathematical Society

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.

Lectures on Mathematics

In the land of the strenuous life

Books For Libraries Press

Text: English, German (translation)

Development of Mathematics in the 19th Century (Lie Groups) (English and German Edition)

Math Science Pr

Ueber Riemann's Theorie der Algebraischen Functionen und ihrer Integrale. Eine Ergänzung der Gewöhnl (German Edition)

Europe

BiblioLife

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Books by Felix, Klein