Articles liés à The Fundamental Theorem of Algebra

9780387946573: The Fundamental Theorem of Algebra
Couverture rigide
ISBN 10 : 0387946578 ISBN 13 : 9780387946573
Editeur : Springer-Verlag New York Inc., 1997

Synopsis

The purpose of this book is to examine three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. It is ideal for a "capstone" course in mathematics for junior/senior level undergraduate mathematics students or first year graduate students. It could also be used as an alternative approach to an undergraduate abstract algebra course.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer-Verlag New York Inc.
Date d'édition
1997
Langue
anglais
ISBN 10 
0387946578
ISBN 13 
9780387946573
Reliure
Relié
Nombre de pages
221
Coordonnées du fabricant
non disponible
Personne responsable
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