SoftcoverISBN:  9781470465001 
Product Code:  STML/95 
List Price:  $59.00 
Individual Price:  $47.20 
AMS Member Price:  $47.20 
eBookISBN:  9781470466589 
Product Code:  STML/95.E 
List Price:  $59.00 
Individual Price:  $47.20 
AMS Member Price:  $47.20 
SoftcoverISBN:  9781470465001 
eBookISBN:  9781470466589 
Product Code:  STML/95.B 
List Price:  $118.00$88.50 
AMS Member Price:  $94.40$70.80 
Softcover ISBN:  9781470465001 
Product Code:  STML/95 
List Price:  $59.00 
Individual Price:  $47.20 
AMS Member Price:  $47.20 
eBook ISBN:  9781470466589 
Product Code:  STML/95.E 
List Price:  $59.00 
Individual Price:  $47.20 
AMS Member Price:  $47.20 
Softcover ISBN:  9781470465001 
eBookISBN:  9781470466589 
Product Code:  STML/95.B 
List Price:  $118.00$88.50 
AMS Member Price:  $94.40$70.80 

Book DetailsStudent Mathematical LibraryVolume: 95; 2021; 217 ppMSC: Primary 12; Secondary 01;
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 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.ReadershipUndergraduate 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


Additional Material

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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 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.
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