Background
Edwards, Harold Mortimer was born on August 6, 1936 in Champaign, Illinois, United States. Son of Harold Mortimer and Marian Bell (Scarlett) Edwards.
( Contents and treatment are fresh and very different fro...)
Contents and treatment are fresh and very different from the standard treatments Presents a fully constructive version of what it means to do algebra The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader
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( Modern conceptual treatment of multivariable calculus, ...)
Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.
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(Although number theorists have sometimes shunned and even...)
Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory. Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990), Linear Algebra (1995), and Essays in Constructive Mathematics (2005). For his masterly mathematical exposition he was awarded a Steele Prize as well as a Whiteman Prize by the American Mathematical Society.
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( In a book written for mathematicians, teachers of mathe...)
In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes’ theorem. The result is genuine mathematics, both in spirit and content, and an exciting choice for an honors or graduate course or indeed for any mathematician in need of a refreshingly informal and flexible reintroduction to the subject. For all these potential readers, the author has made the approach work in the best tradition of creative mathematics. This affordable softcover reprint of the 1994 edition presents the diverse set of topics from which advanced calculus courses are created in beautiful unifying generalization. The author emphasizes the use of differential forms in linear algebra, implicit differentiation in higher dimensions using the calculus of differential forms, and the method of Lagrange multipliers in a general but easy-to-use formulation. There are copious exercises to help guide the reader in testing understanding. The chapters can be read in almost any order, including beginning with the final chapter that contains some of the more traditional topics of advanced calculus courses. In addition, it is ideal for a course on vector analysis from the differential forms point of view. The professional mathematician will find here a delightful example of mathematical literature; the student fortunate enough to have gone through this book will have a firm grasp of the nature of modern mathematics and a solid framework to continue to more advanced studies. The most important feature…is that it is fun―it is fun to read the exercises, it is fun to read the comments printed in the margins, it is fun simply to pick a random spot in the book and begin reading. This is the way mathematics should be presented, with an excitement and liveliness that show why we are interested in the subject. ―The American Mathematical Monthly (First Review) An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically rigorous, entertaining but serious. Remarkable diverse applications, physical and mathematical. ―The American Mathematical Monthly (1994) Based on the Second Edition
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(Man sollte weniger danach streben, die Grenzen der mathe-...)
Man sollte weniger danach streben, die Grenzen der mathe- matischen Wissenschaften zu erweitern, als vielmehr danach, den bereits vorhandenen Stoff aus umfassenderen Gesichts- punkten zu betrachten - E. Study Today most mathematicians who know about Kronecker's theory of divisors know about it from having read Hermann Weyl's lectures on algebraic number theory We, and regard it, as Weyl did, as an alternative to Dedekind's theory of ideals. Weyl's axiomatization of what he calls "Kronecker's" theory is built-as Dedekind's theory was built-around unique factor- ization. However, in presenting the theory in this way, Weyl overlooks one of Kronecker's most valuable ideas, namely, the idea that the objective of the theory is to define greatest com- mon divisors, not to achieve factorization into primes. The reason Kronecker gave greatest common divisors the primary role is simple: they are independent of the ambient field while factorization into primes is not. The very notion of primality depends on the field under consideration-a prime in one field may factor in a larger field-so if the theory is founded on factorization into primes, extension of the field entails a completely new theory. Greatest common divisors, on the other hand, can be defined in a manner that does not change at all when the field is extended (see 1.16). Only after he has laid the foundation of the theory of divisors does Kronecker consider factorization of divisors into divisors prime in some specified field.
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( This is an introduction to Galois Theory along the line...)
This is an introduction to Galois Theory along the lines of Galois’s Memoir on the Conditions for Solvability of Equations by Radicals. It puts Galois’s ideas into historical perspective by tracing their antecedents in the works of Gauss, Lagrange, Newton, and even the ancient Babylonians. It also explains the modern formulation of the theory. It includes many exercises, with their answers, and an English translation of Galois’s memoir.
http://www.amazon.com/gp/product/038790980X/?tag=2022091-20
Edwards, Harold Mortimer was born on August 6, 1936 in Champaign, Illinois, United States. Son of Harold Mortimer and Marian Bell (Scarlett) Edwards.
Bachelor, University of Wisconsin, 1956; Master of Arts, Columbia University, 1957; Doctor of Philosophy, Harvard University, 1961.
Instructor, Harvard University, 1961-1962; research associate, Columbia University, 1962-1963; assistant professor, Columbia University, 1963-1966; assistant professor, New York University, New York City, 1966-1969; associate professor, New York University, 1969-1979; professor mathematics, New York University, since 1979; visiting senior lecturer, Australian National U., 1971.
( Contents and treatment are fresh and very different fro...)
(Although number theorists have sometimes shunned and even...)
(Man sollte weniger danach streben, die Grenzen der mathe-...)
(Man sollte weniger danach streben, die Grenzen der mathe ...)
( In a book written for mathematicians, teachers of mathe...)
( Modern conceptual treatment of multivariable calculus, ...)
( This is an introduction to Galois Theory along the line...)
(New book, minor wear from shelf storage, back cover bevel...)
Member American Mathematics Society (Steele prize 1980, Albert Leon Whiteman Memorial prize 2005), Mathematics Association America.
Married Betty Rollin, January 21, 1979.