Abstract Algebra and Famous Impossibilities

Abstract Algebra and Famous Impossibilities

AngličtinaMěkká vazbaTisk na objednávku
Morris Sidney A.
Springer, Berlin
EAN: 9783031057007
Tisk na objednávku
Předpokládané dodání v pondělí, 3. února 2025
1 580 Kč
Běžná cena: 1 755 Kč
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Podrobné informace

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 questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction.

Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel’s original approach.

Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus.

EAN 9783031057007
ISBN 3031057007
Typ produktu Měkká vazba
Vydavatel Springer, Berlin
Datum vydání 28. listopadu 2023
Stránky 218
Jazyk English
Rozměry 235 x 155
Země Switzerland
Autoři Jones, Arthur; Morris Sidney A.; Pearson Kenneth R.
Edice 2nd ed. 2022
Série Undergraduate Texts in Mathematics