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Galois Theory for Beginners: A Historical Perspective

Translated by David Kramer
Now available in new edition: STML/95
Available Formats:
Electronic ISBN: 978-1-4704-2146-5
Product Code: STML/35.E
List Price: $38.00 Individual Price:$30.40
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Galois Theory for Beginners: A Historical Perspective
Translated by David Kramer
Now available in new edition: STML/95
Available Formats:
 Electronic ISBN: 978-1-4704-2146-5 Product Code: STML/35.E
 List Price: $38.00 Individual Price:$30.40
• 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.

• Chapters
• Chapter 1. Cubic equations
• Chapter 2. Casus irreducibilis: The birth of the complex numbers
• 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 reviewers who would like to review an AMS book
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.

• Chapters
• Chapter 1. Cubic equations
• Chapter 2. Casus irreducibilis: The birth of the complex numbers
• 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 reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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