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Galois Theory for Beginners: A Historical Perspective
 

Translated by David Kramer

Galois Theory for Beginners
Now available in new edition: STML/95
eBook ISBN:  978-1-4704-2146-5
Product Code:  STML/35.E
List Price: $49.00
Individual Price: $39.20
Galois Theory for Beginners
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Galois Theory for Beginners: A Historical Perspective

Translated by David Kramer

Now available in new edition: STML/95
eBook ISBN:  978-1-4704-2146-5
Product Code:  STML/35.E
List Price: $49.00
Individual Price: $39.20
  • Book Details
     
     
    Student Mathematical Library
    Volume: 352006; 180 pp
    MSC: Primary 12;

    Now available in Second Edition: STML/95

    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 an angle, and the construction of regular \(n\)-gons are also presented.

    This book is suitable for undergraduates and beginning graduate students.

    Readership

    Undergraduates and graduate students interested in Galois Theory.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Cubic equations
    • Chapter 2. Casus irreducibilis: The birth of the complex numbers
    • Chapter 3. Biquadratic equations
    • Chapter 4. Equations of degree $n$ and their properties
    • Chapter 5. The search for additional solution formulas
    • Chapter 6. Equations that can be reduced in degree
    • Chapter 7. The construction of regular polygons
    • Chapter 8. The solution of equations of the fifth degree
    • Chapter 9. The Galois group of an equation
    • Chapter 10. Algebraic structures and Galois theory
  • Reviews
     
     
    • For those with minimal exposure to undergraduate mathematics, the book would make for some formidable reading. ... it provides excellent historical and mathematical context.

      S. J. Colley, Oberlin College for CHOICE Reviews
    • ...the author has produced both a lovely invitation and a profound first introduction to the realm of Galois theory for everyone.

      Zentralblatt MATH
    • ...the book is well-written and pleasant to read.

      Bill Satzer for MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 352006; 180 pp
MSC: Primary 12;

Now available in Second Edition: STML/95

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 an angle, and the construction of regular \(n\)-gons are also presented.

This book is suitable for undergraduates and beginning graduate students.

Readership

Undergraduates and graduate students interested in Galois Theory.

  • Chapters
  • Chapter 1. Cubic equations
  • Chapter 2. Casus irreducibilis: The birth of the complex numbers
  • Chapter 3. Biquadratic equations
  • Chapter 4. Equations of degree $n$ and their properties
  • Chapter 5. The search for additional solution formulas
  • Chapter 6. Equations that can be reduced in degree
  • Chapter 7. The construction of regular polygons
  • Chapter 8. The solution of equations of the fifth degree
  • Chapter 9. The Galois group of an equation
  • Chapter 10. Algebraic structures and Galois theory
  • For those with minimal exposure to undergraduate mathematics, the book would make for some formidable reading. ... it provides excellent historical and mathematical context.

    S. J. Colley, Oberlin College for CHOICE Reviews
  • ...the author has produced both a lovely invitation and a profound first introduction to the realm of Galois theory for everyone.

    Zentralblatt MATH
  • ...the book is well-written and pleasant to read.

    Bill Satzer for MAA Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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