Abstract Algebra and Famous Impossibilities

Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations

Inbunden, Engelska, 2022

AvSidney A. Morris,Arthur Jones,Kenneth R. Pearson,Sidney a. Morris

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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.

Produktinformation

Utgivningsdatum2022-11-28
Mått155 x 235 x 18 mm
Vikt554 g
FormatInbunden
SpråkEngelska
SerieUndergraduate Texts in Mathematics
Antal sidor218
Upplaga2
FörlagSpringer International Publishing AG
ISBN9783031056970

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Sidney A. Morris is Emeritus Professor at the Federation University, Australia (formerly University of Ballarat) and Adjunct Professor at La Trobe University, Australia. His primary research is in topological groups, topology, and transcendental number theory, with broader interests including early detection of muscle wasting diseases, health informatics, and predicting the Australian stock exchange. He is the author of several books.Arthur Jones [1934–2006] and Kenneth R. Pearson [1943–2015] were Professors in Mathematics at La Trobe University, Australia. Each had a great passion for teaching and for mathematics.

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.