Constructive Aspects Of The Fundamental Theorem Of Algebra
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Constructive Aspects Of The Fundamental Theorem Of Algebra
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Author : Bruno Dejon
language : en
Publisher: John Wiley & Sons
Release Date : 1969
Constructive Aspects Of The Fundamental Theorem Of Algebra written by Bruno Dejon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
Constructive Aspects Of The Fundamental Theorem Of Algebra
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Author : Bruno Dejon
language : en
Publisher:
Release Date : 1969
Constructive Aspects Of The Fundamental Theorem Of Algebra written by Bruno Dejon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
The Fundamental Theorem Of Algebra
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Author : Benjamin Fine
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Fundamental Theorem Of Algebra written by Benjamin Fine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.
Constructive Aspects Of The Fundamental Theorem Of Algebra
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Author : IBM Research Laboratory
language : en
Publisher:
Release Date : 1969
Constructive Aspects Of The Fundamental Theorem Of Algebra written by IBM Research Laboratory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
Collected Papers Of Stephen Smale The In 3 Volumes Volume 3
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Author : Roderick S C Wong
language : en
Publisher: World Scientific
Release Date : 2000-06-30
Collected Papers Of Stephen Smale The In 3 Volumes Volume 3 written by Roderick S C Wong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-30 with Mathematics categories.
This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.
Wittgenstein Finitism And The Foundations Of Mathematics
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Author : Mathieu Marion
language : en
Publisher: Oxford University Press
Release Date : 1998
Wittgenstein Finitism And The Foundations Of Mathematics written by Mathieu Marion and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and by philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations. Marion shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy; and he also demonstrates that it has much to contribute to current debates about the foundations of mathematics.
The Mathematical Heritage Of Henri Poincare
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Author : Felix E. Browder
language : en
Publisher: American Mathematical Soc.
Release Date : 1983-12-31
The Mathematical Heritage Of Henri Poincare written by Felix E. Browder and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-12-31 with Mathematics categories.
On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This volume presents the written versions of all but three of the invited talks presented at this Symposium (those by W. Browder, A. Jaffe, and J. Mather were not written up for publication). In addition, it contains two papers by invited speakers who were not able to attend, S. S. Chern and L. Nirenberg. If one traces the influence of Poincari through the major mathematical figures of the early and midtwentieth century, it is through American mathematicians as well as French that this influence flows, through G. D. Birkhoff, Solomon Lefschetz, and Marston Morse. This continuing tradition represents one of the major strands of American as well as world mathematics, and it is as a testimony to this tradition as an opening to the future creativity of mathematics that this volume is dedicated. This part contains sections on topological methods in nonlinear problems, mechanics and dynamical systems, ergodic theory and recurrence, and historical material.
The Collected Papers Of Stephen Smale
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Author : Stephen Smale
language : en
Publisher: World Scientific
Release Date : 2000
The Collected Papers Of Stephen Smale written by Stephen Smale and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.
A Concrete Introduction To Higher Algebra
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Author : Lindsay Childs
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Concrete Introduction To Higher Algebra written by Lindsay Childs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is written as an introduction to higher algebra for students with a background of a year of calculus. The book developed out of a set of notes for a sophomore-junior level course at the State University of New York at Albany entitled Classical Algebra. In the 1950s and before, it was customary for the first course in algebra to be a course in the theory of equations, consisting of a study of polynomials over the complex, real, and rational numbers, and, to a lesser extent, linear algebra from the point of view of systems of equations. Abstract algebra, that is, the study of groups, rings, and fields, usually followed such a course. In recent years the theory of equations course has disappeared. Without it, students entering abstract algebra courses tend to lack the experience in the algebraic theory of the basic classical examples of the integers and polynomials necessary for understanding, and more importantly, for ap preciating the formalism. To meet this problem, several texts have recently appeared introducing algebra through number theory.
A Concrete Introduction To Higher Algebra
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Author : Lindsay N. Childs
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-04
A Concrete Introduction To Higher Algebra written by Lindsay N. Childs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-04 with Mathematics categories.
An informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated in a well-motivated fashion and made relevant by many applications -- to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.