Background
Kline, Morris was born on May 1, 1908 in Brooklyn. Son of Bernard and Sarah (Spatt) Kline.
(El objetivo de esta obra del historiador y matemático MOR...)
El objetivo de esta obra del historiador y matemático MORRIS KLINE es el de analizar con rigor la génesis y evolución de las ideas verdaderamente centrales del pensamiento matemático, haciendo hincapié en aquellas que más han contribuido al progreso de la ciencia. El autor no se limita al estudio del desarrollo histórico de
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( "Kline is a first-class teacher and an able writer. . ....)
"Kline is a first-class teacher and an able writer. . . . This is an enlarging and a brilliant book." ― Scientific American "Dr. Morris Kline has succeeded brilliantly in explaining the nature of much that is basic in math, and how it is used in science." ― San Francisco Chronicle Since the major branches of mathematics grew and expanded in conjunction with science, the most effective way to appreciate and understand mathematics is in terms of the study of nature. Unfortunately, the relationship of mathematics to the study of nature is neglected in dry, technique-oriented textbooks, and it has remained for Professor Morris Kline to describe the simultaneous growth of mathematics and the physical sciences in this remarkable book. In a manner that reflects both erudition and enthusiasm, the author provides a stimulating account of the development of basic mathematics from arithmetic, algebra, geometry, and trigonometry, to calculus, differential equations, and the non-Euclidean geometries. At the same time, Dr. Kline shows how mathematics is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other phenomena. Historical and biographical materials are also included, while mathematical notation has been kept to a minimum. This is an excellent presentation of mathematical ideas from the time of the Greeks to the modern era. It will be of great interest to the mathematically inclined high school and college student, as well as to any reader who wants to understand ― perhaps for the first time ― the true greatness of mathematical achievements.
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(This comprehensive history traces the development of math...)
This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.
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(It may seem unnecessary at this late date to discuss the ...)
It may seem unnecessary at this late date to discuss the relationship of electromagnetic theory to geometrical optics. The content of both fields is well known and everyone knows also that geometrical optics is the limit for vanishing wave length of electromagnetic theory. Moreover, since Maxwell's theory supersedes the older geometrical optics, presumably, then, geometrical optics could be discarded. The optical industry continues to use it but perhaps that is because it is behind the times. There are, however, at least three major reasons for pursuing and clarifying the relationship in question. The first is the purely theoretical or academic problem of building a mathematical bridge between the two domains, electromagnetic theory and geometrical optics. The older bases for asserting that geometrical optics is a limiting case of electromagnetic theory are vague and from a mathematical standpoint highly unsatisfactory. The second major reason for the investigation is a practical one. To solve problems of electromagnetic theory, whether in the range of radio frequencies or visible light frequencies, one should solve Maxwell's equations with the appropriate initial and boundary conditions. However, as is well known, Maxwell's equations can be solved exactly in only a few problems. Hence physicists and engineers, especially those concerned with ultra-high frequency problems, have resorted to the simpler methods of geometrical optics. Although these methods have proved remarkably efficacious in the optical domain, they are intrinsically limited; they do not furnish information about some of the most important phenomena such as diffraction, polarization, and interference, to say nothing about the numerical accuracy of what geometrical optics does yield. Hence the practical question becomes whether the establishment of a better link between Maxwell's theory and geometrical optics will provide more accurate approximate methods of solving electromagnetic problems. Insofar as ultra-high frequency problems are concerned, the answer, based on work of the last ten years, can already be given affirmatively. Tags: optics geometrical theory wave equations equation electromagnetic light field time asymptotic waves differential media solution rays solutions discontinuities space mathematical Category: Science - Quantum Mechanics Visit Forgotten Books at: http://www.forgottenbooks.org
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(The major creations and developments in mathematics from ...)
The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.
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(This comprehensive history traces the development of math...)
This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.
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(This comprehensive history traces the development of math...)
This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Originally published in 1972, it is now available as a three volume paperback edition. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.
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( This work has been selected by scholars as being cultur...)
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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consultant mathematician author
Kline, Morris was born on May 1, 1908 in Brooklyn. Son of Bernard and Sarah (Spatt) Kline.
Bachelor, New York University, 1930. Doctor of Philosophy, New York University, 1936.
Instructor, New York University, New York City, 1930-1936;
fellow, Institute for Advanced Study, Princeton, New Jersey, 1936-1938;
director division electromagnetic research, Courant Institute, New York University, 1946-1966;
professor, Courant Institute, New York University, 1952-1975;
Fulbright lecturer, Guggenheim fellow, Technology Hochschule Aachen, 1958-1959. Visiting professor Brooklyn College, 1974-1976. Consultant Americana & Britannica Encys.
Lecturer in field of mathematics education.
(El objetivo de esta obra del historiador y matemático MOR...)
(The major creations and developments in mathematics from ...)
(Excerpt from Electromagnetic Theory and Geometrical Optic...)
( This work has been selected by scholars as being cultur...)
(This comprehensive history traces the development of math...)
(Reveals the important contributions of mathematics to the...)
(This three-volume paperback edition traces the developmen...)
(This comprehensive history traces the development of math...)
(This comprehensive history traces the development of math...)
(It may seem unnecessary at this late date to discuss the ...)
( "Kline is a first-class teacher and an able writer. . ....)
(Hard Cover/Textbook. 577 Pages; Index; 1967 Addison-Wesle...)
Civilian employee United States Army, World World War World War II.
Married Helen Mann, September 4, 1939. Children: Elizabeth, Judith, Douglas.