Electronic ISBN:  9781470421465 
Product Code:  STML/35.E 
180 pp 
List Price:  $38.00 
Individual Price:  $30.40 

Book DetailsStudent Mathematical LibraryVolume: 35; 2006MSC: Primary 12;
Now available in Second Edition: STML/95
Galois theory is the culmination of a centurieslong 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.ReadershipUndergraduates 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


Additional Material

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 wellwritten and pleasant to read.
Bill Satzer for MAA Reviews


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Now available in Second Edition: STML/95
Galois theory is the culmination of a centurieslong 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.
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 wellwritten and pleasant to read.
Bill Satzer for MAA Reviews