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Galois Theory for Beginners: A Historical Perspective, Second Edition
 

Translated by David Kramer

Softcover ISBN:  978-1-4704-6500-1
Product Code:  STML/95
List Price: $59.00
Individual Price: $47.20
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-6658-9
Product Code:  STML/95.E
List Price: $59.00
Individual Price: $47.20
AMS Member Price: $47.20
Softcover ISBN:  978-1-4704-6500-1
eBook: ISBN:  978-1-4704-6658-9
Product Code:  STML/95.B
List Price: $118.00 $88.50
AMS Member Price: $94.40 $70.80
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Galois Theory for Beginners: A Historical Perspective, Second Edition

Translated by David Kramer

Softcover ISBN:  978-1-4704-6500-1
Product Code:  STML/95
List Price: $59.00
Individual Price: $47.20
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-6658-9
Product Code:  STML/95.E
List Price: $59.00
Individual Price: $47.20
AMS Member Price: $47.20
Softcover ISBN:  978-1-4704-6500-1
eBook ISBN:  978-1-4704-6658-9
Product Code:  STML/95.B
List Price: $118.00 $88.50
AMS Member Price: $94.40 $70.80
  • Book Details
     
     
    Student Mathematical Library
    Volume: 952021; 217 pp
    MSC: Primary 12; Secondary 01;

    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.

    Readership

    Undergraduate and graduate students interested in Galois theory.

  • Table of Contents
     
     
    • Chapters
    • Cubic equations
    • Casus irreducibilis: The birth of the complex numbers
    • Biquadratic equations
    • Equations of degree $n$ and their properties
    • The search for additional solution formulas
    • Equation that can be reduced in degree
    • The construction of regular polygons
    • The solution of equations of the fifth degree
    • The Galois group of an equation
    • Algebraic structures and Galois theory
    • Galois theory according to Artin
    • Epilogue
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 952021; 217 pp
MSC: Primary 12; Secondary 01;

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.

Readership

Undergraduate and graduate students interested in Galois theory.

  • Chapters
  • Cubic equations
  • Casus irreducibilis: The birth of the complex numbers
  • Biquadratic equations
  • Equations of degree $n$ and their properties
  • The search for additional solution formulas
  • Equation that can be reduced in degree
  • The construction of regular polygons
  • The solution of equations of the fifth degree
  • The Galois group of an equation
  • Algebraic structures and Galois theory
  • Galois theory according to Artin
  • Epilogue
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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