**Student Mathematical Library**

Volume: 35;
2006;
180 pp;
Softcover

MSC: Primary 12;

Print ISBN: 978-0-8218-3817-4

Product Code: STML/35

List Price: $38.00

Individual Price: $30.40

**Electronic ISBN: 978-1-4704-2146-5
Product Code: STML/35.E**

List Price: $38.00

Individual Price: $30.40

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#### Supplemental Materials

# Galois Theory for Beginners: A Historical Perspective

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*Jörg Bewersdorff*

Translated by David Kramer

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.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Galois Theory for Beginners: A Historical Perspective

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface to the English Edition vii8 free
- Prefaces to the German Editions ix10 free
- Chapter 1. Cubic Equations 122 free
- Chapter 2. Casus Irreducibilis: The Birth of the Complex Numbers 930
- Chapter 3. Biquadratic Equations 2344
- Chapter 4. Equations of Degree n and Their Properties 2748
- Chapter 5. The Search for Additional Solution Formulas 3758
- Chapter 6. Equations That Can Be Reduced in Degree 5576
- Chapter 7. The Construction of Regular Polygons 6384
- Chapter 8. The Solution of Equations of the Fifth Degree 81102
- Chapter 9. The Galois Group of an Equation 93114
- Chapter 10. Algebraic Structures and Galois Theory 125146
- Epilogue 165186
- Index 177198
- Back Cover Back Cover1202