A History Of Abstract Algebra
DOWNLOAD
Download A History Of Abstract Algebra PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A History Of Abstract Algebra book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
A History Of Abstract Algebra
DOWNLOAD
Author : Israel Kleiner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-20
A History Of Abstract Algebra written by Israel Kleiner 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 2007-09-20 with Mathematics categories.
This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.
A History Of Abstract Algebra
DOWNLOAD
Author : Jeremy Gray
language : en
Publisher: Springer
Release Date : 2018-08-07
A History Of Abstract Algebra written by Jeremy Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-07 with Mathematics categories.
This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
A Book Of Abstract Algebra
DOWNLOAD
Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2010-01-14
A Book Of Abstract Algebra written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
The Genesis Of The Abstract Group Concept
DOWNLOAD
Author : Hans Wussing
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
The Genesis Of The Abstract Group Concept written by Hans Wussing and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
"It is a pleasure to turn to Wussing's book, a sound presentation of history," declared the Bulletin of the American Mathematical Society. The author, Director of the Institute for the History of Medicine and Science at Leipzig University, traces the axiomatic formulation of the abstract notion of group. 1984 edition.
Abstract Algebra
DOWNLOAD
Author : Thomas Judson
language : en
Publisher: Orthogonal Publishing L3c
Release Date : 2023-08-11
Abstract Algebra written by Thomas Judson and has been published by Orthogonal Publishing L3c this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-11 with categories.
Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
Abstract Algebra And Famous Impossibilities
DOWNLOAD
Author : Sidney A. Morris
language : en
Publisher: Springer Nature
Release Date : 2022-11-26
Abstract Algebra And Famous Impossibilities written by Sidney A. Morris and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-26 with Mathematics categories.
This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction. Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel’s original approach. Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus.
Fundamental Concepts Of Abstract Algebra
DOWNLOAD
Author : Gertrude Ehrlich
language : en
Publisher: Courier Corporation
Release Date : 2013-05-13
Fundamental Concepts Of Abstract Algebra written by Gertrude Ehrlich and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-13 with Mathematics categories.
This undergraduate text presents extensive coverage of set theory, groups, rings, modules, vector spaces, and fields. It offers numerous examples, definitions, theorems, proofs, and practice exercises. 1991 edition.
A First Course In Abstract Algebra
DOWNLOAD
Author : John B. Fraleigh
language : en
Publisher: Addison Wesley Longman
Release Date : 2003
A First Course In Abstract Algebra written by John B. Fraleigh and has been published by Addison Wesley Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Algebra, Abstract categories.
Considered a classic by many, A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.
Introductory Modern Algebra
DOWNLOAD
Author : Saul Stahl
language : en
Publisher: Wiley
Release Date : 2013-08-19
Introductory Modern Algebra written by Saul Stahl and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-19 with Mathematics categories.
Praise for the First Edition "Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra." —CHOICE Introductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the Second Edition uniquely facilitates the understanding of pivotal algebraic ideas. The author provides a clear, precise, and accessible introduction to modern algebra and also helps to develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can inform us about such diverse items as multivariate functions and the 15-puzzle. Featuring new sections on topics such as group homomorphisms, the RSA algorithm, complex conjugation, the factorization of real polynomials, and the fundamental theorem of algebra, the Second Edition also includes: An in-depth explanation of the principles and practices of modern algebra in terms of the historical development from the Renaissance solution of the cubic equation to Dedekind's ideals Historical discussions integrated with the development of modern and abstract algebra in addition to many new explicit statements of theorems, definitions, and terminology A new appendix on logic and proofs, sets, functions, and equivalence relations Over 1,000 new examples and multi-level exercises at the end of each section and chapter as well as updated chapter summaries Introductory Modern Algebra: A Historical Approach, Second Edition is an excellent textbook for upper-undergraduate courses in modern and abstract algebra.
Unknown Quantity
DOWNLOAD
Author : John Derbyshire
language : en
Publisher: National Academies Press
Release Date : 2006-05-02
Unknown Quantity written by John Derbyshire and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-02 with Science categories.
Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages-and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics-it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.