Galois Theory for Beginners
eBook - PDF

Galois Theory for Beginners

A Historical Perspective, Second Edition

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Galois Theory for Beginners

A Historical Perspective, Second Edition

Book details
Table of contents
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About This Book

Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations.Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting the angle, and the construction of regular $n$-gons are also presented.This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.

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Yes, you can access Galois Theory for Beginners by Jörg Bewersdorff in PDF and/or ePUB format, as well as other popular books in Matematica & Matematica generale. We have over one million books available in our catalogue for you to explore.

Information

Publisher
American Mathematical Society
Year
2021
ISBN
9781470466589
Topic
Matematica
Subtopic
Matematica generale

Table of contents

  1. Cover
  2. Title page
  3. Copyright
  4. Contents
  5. Preface to the English Edition
  6. Prefaces to the German Editions
  7. Chapter 1. Cubic Equations
  8. Chapter 2. Casus Irreducibilis: The Birth of the Complex Numbers
  9. Chapter 3. Biquadratic Equations
  10. Chapter 4. Equations of Degree n and Their Properties
  11. Chapter 5. The Search for Additional Solution Formulas
  12. Chapter 6. Equations That Can Be Reduced in Degree
  13. Chapter 7. The Construction of Regular Polygons
  14. Chapter 8. The Solution of Equations of the Fifth Degree
  15. Chapter 9. The Galois Group of an Equation
  16. Chapter 10. Algebraic Structures and Galois Theory
  17. Chapter 11. Galois Theory According to Artin
  18. Epilogue
  19. Index
  20. Back Cover