Abstract Algebra and Famous Impossibilities : Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations /

This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical ques...

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Bibliographic Details
Main Authors:	Morris, Sidney A. (Author), Jones, Arthur (Author), Pearson, Kenneth R. (Author)
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	Cham : Springer International Publishing : Imprint: Springer, 2022.
Edition:	2nd ed. 2022.
Series:	Readings in Mathematics,
Subjects:	Algebraic fields. Polynomials. Mathematics. History. Field Theory and Polynomials. History of Mathematical Sciences. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

1. Algebraic Preliminaries
2. Algebraic Numbers and Their Polynomials
3. Extending Fields
4. Irreducible Polynomials
5. Straightedge and Compass Constructions
6. Proofs of the Geometric Impossibilities
7. Zeros of Polynomials of Degrees 2, 3, and 4
8. Quintic Equations 1: Symmetric Polynomials
9. Quintic Equations II: The Abel-Ruffini Theorem
10. Transcendence of e and π
11. An Algebraic Postscript
12. Other Impossibilities: Regular Polygons and Integration in Finite Terms
References
Index.