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Galois Theory for Beginners A Historical Perspective 2nd Edition by Jörg Bewersdorff 1470466589 9781470466589

Name: Galois Theory for Beginners A Historical Perspective 2nd Edition by Jörg Bewersdorff 1470466589 9781470466589
SKU: EB-38645098
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Galois Theory for Beginners A Historical Perspective Second Ed 2nd Edition Jörg Bewersdorff Digital Instant Download

Author(s): Jörg Bewersdorff

ISBN(s): 9781470466589, 1470466589

Edition: 2

File Details: PDF, 34.87 MB

Year: 2021

Language: English

Sell by: Logan Foster

SKU: EB-38645098 Category: Mathematics - Algebra Tag: Jörg Bewersdorff

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Galois Theory for Beginners: A Historical Perspective 2nd Edition by Jorg Bewersdorff – Ebook PDF Instant Download/Delivery: 1470466589, 9781470466589

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ISBN 10: 1470466589
ISBN 13: 9781470466589
Author: Jorg Bewersdorff

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.

Galois Theory for Beginners 2nd Table of contents:

Chapter 1. Cubic Equations
Literature on Quadratic and Cubic Equations
Exercises
Chapter 2. Casus Irreducibilis: The Birth of the Complex Numbers
Literature on the History of Complex Numbers
Exercises
Chapter 3. Biquadratic Equations
Literature on Biquadratic Equations
Exercises
Chapter 4. Equations of Degree n and Their Properties
The Fundamental Theorem of Algebra: Plausibility and Proof
Literature on Equations of Degree 𝑛
Exercises
Chapter 5. The Search for Additional Solution Formulas
Permutations
The Fundamental Theorem on Symmetric Polynomials
Ruffini and the General Equation of Fifth Degree
Exercises
Chapter 6. Equations That Can Be Reduced in Degree
The Decomposition of Integer Polynomials
Eisenstein’s Irreducibility Criterion
Exercises
Chapter 7. The Construction of Regular Polygons
Constructions with Straightedge and Compass
The Classical Construction Problems
Exercises
Chapter 8. The Solution of Equations of the Fifth Degree
The Transformations of Tschirnhaus and of Bring and Jerrard
Literature on Equations of the Fifth Degree
Exercises
Chapter 9. The Galois Group of an Equation
Computing the Galois Group
A Quick Course in Calculating with Polynomials
Literature on Galois Groups and Their History
Exercises
Chapter 10. Algebraic Structures and Galois Theory
Groups and Fields
The Fundamental Theorem of Galois Theory: An Example
The Unsolvability of the Classical Construction Problems
Literature on Galois Theory and Algebraic Structures
Exercises
Chapter 11. Galois Theory According to Artin
Literature on Galois Theory from the Viewpoint of Linear Algebra