Classical Algebra: Its Nature, Origins, and Uses 1st Edition by Roger L. Cooke (PDF)

Description

This insightful book combines the history, pedagogy, and popularization of algebra to present a unified discussion of the subject. Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors.This book successfully ties together the disconnect between classical and modern algebraand provides readers with answers to many fascinating questions that typically go unexamined, including:What is algebra about?How did it arise?What uses does it have?How did it develop?What problems and issues have occurred in its history?How were these problems and issues resolved?The author answers these questions and more, shedding light on a rich history of the subject—from ancient and medieval times to the present. Structured as eleven “lessons” that are intended to give the reader further insight on classical algebra, each chapter contains thought-provoking problems and stimulating questions, for which complete answers are provided in an appendix.Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, Classical Algebra: Its Nature, Origins, and Uses is an excellent book for mathematics courses at the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics.

User’s Reviews

Editorial Reviews: Review Winner of the 2008 CHOICE Outstanding Academic Title Award “The book is written in an utmost lucid and cultured style, basically accessible to anyone with a general interest in mathematics, and a valuable contribution to the overall popularization of algebra into the bargain.” (Zentralblatt Math, 2008)”Cooke does a superb job of beginning to bridge the gulf between quadratic equations and group theory.” (CHOICE, September 2008)”Classical Algebra deserves a large audience, and should be in every undergraduate library.” (MAA Reviews, June 2, 2008) From the Inside Flap This insightful book combines the history, pedagogy, and popularization of algebra topresent a unified discussion of the subjectClassical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors.This book successfully ties together the disconnect between classical and modern algebraand provides readers with answers to many fascinating questions that typically go unexamined, including:What is algebra about?How did it arise?What uses does it have?How did it develop?What problems and issues have occurred in its history?How were these problems and issues resolved?The author answers these questions and more, shedding light on a rich history of the subject—from ancient and medieval times to the present. Structured as eleven “lessons” that are intended to give the reader further insight on classical algebra, each chapter contains thought-provoking problems and stimulating questions, for which complete answers are provided in an appendix.Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, Classical Algebra: Its Nature, Origins, and Uses is an excellent book for mathematics courses at the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics. From the Back Cover This insightful book combines the history, pedagogy, and popularization of algebra topresent a unified discussion of the subjectClassical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors.This book successfully ties together the disconnect between classical and modern algebraand provides readers with answers to many fascinating questions that typically go unexamined, including:What is algebra about?How did it arise?What uses does it have?How did it develop?What problems and issues have occurred in its history?How were these problems and issues resolved?The author answers these questions and more, shedding light on a rich history of the subject—from ancient and medieval times to the present. Structured as eleven “lessons” that are intended to give the reader further insight on classical algebra, each chapter contains thought-provoking problems and stimulating questions, for which complete answers are provided in an appendix.Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, Classical Algebra: Its Nature, Origins, and Uses is an excellent book for mathematics courses at the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics. About the Author Roger Cooke, PhD, is Emeritus Professor of Mathematics in the Department of Mathematics and Statistics at the University of Vermont. Dr. Cooke has over forty years of academic experience, and his areas of research interest include the history of mathematics, almost-periodic functions, uniqueness of trigonometric series representations, and Fourier analysis. He is also the author of The History of Mathematics: A Brief Course, Second Edition (Wiley). Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Over the decades, I have read many many books on algebra and have always wondered what Galois Theory is good for. The proof that the general quintic cannot be solved by radicals since its Galois Group is not solvable is fine. But it always seemed to me that all the fancy theory about field extensions and its automorphisms was a lot of excessive firepower brought to bear on a relativity simple problem of whether you can invert the relation between the coefficients and solutions using radicals. Like hunting rabbits using a tank. Unless you could use Galois Theory for something more, like figure out which quintic could be solved by radicals and actually solving them, it seemed like a lot of investment for very little return. And none of the books on Galois Theory ever told you how to make use of it for such practical purposes, until now: finally, a book that tells you the truth about Galois Theory. This books clearly explains what I had suspected all along: to calculate the Galois Group of a given equation, you effectively need to know what the solutions are beforehand. So from a practical point of view, Galois Theory is more or less useless. It is refreshing to find a book which honestly tells you the limitation of the theory as well as its strengths. This clarification alone is well worth the price of the book.

⭐

Keywords

Free Download Classical Algebra: Its Nature, Origins, and Uses 1st Edition in PDF format
Classical Algebra: Its Nature, Origins, and Uses 1st Edition PDF Free Download
Download Classical Algebra: Its Nature, Origins, and Uses 1st Edition 2008 PDF Free
Classical Algebra: Its Nature, Origins, and Uses 1st Edition 2008 PDF Free Download
Download Classical Algebra: Its Nature, Origins, and Uses 1st Edition PDF
Free Download Ebook Classical Algebra: Its Nature, Origins, and Uses 1st Edition