Volume: 95; 2021; 217 pp; Softcover
MSC: Primary 12; Secondary 01
Print ISBN: 978-1-4704-6500-1
Product Code: STML/95
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Electronic ISBN: 978-1-4704-6658-9
Product Code: STML/95.E
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Supplemental Materials
Galois Theory for Beginners: A Historical Perspective, Second Edition
Share this pageJörg 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 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
Table of Contents
Galois Theory for Beginners: A Historical Perspective, Second Edition
- Cover Cover11
- Title page iii5
- Copyright iv6
- Contents v7
- Preface to the English Edition vii9
- Prefaces to the German Editions ix11
- Chapter 1. Cubic Equations 123
- Chapter 2. Casus Irreducibilis: The Birth of the Complex Numbers 2749
- Chapter 3. Biquadratic Equations 4163
- Chapter 4. Equations of Degree n and Their Properties 4769
- Chapter 5. The Search for Additional Solution Formulas 5779
- Chapter 6. Equations That Can Be Reduced in Degree 7799
- Chapter 7. The Construction of Regular Polygons 85107
- Chapter 8. The Solution of Equations of the Fifth Degree 105127
- Chapter 9. The Galois Group of an Equation 117139
- Chapter 10. Algebraic Structures and Galois Theory 147169
- Chapter 11. Galois Theory According to Artin 183205
- Epilogue 199221
- Index 211233
- Back Cover Back Cover1242