Books in Field theory and polynomials

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Numerical Methods for Roots of Polynomials - Part II

• 1st Edition
• Volume 16
• July 19, 2013
• J.M. McNamee + 1 more
• English
• eBook 978-0-08-093143-2

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Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic.

Numerical Methods for Roots of Polynomials - Part I

• 1st Edition
• Volume 14
• June 4, 2007
• J.M. McNamee
• English
• eBook 978-0-08-048947-6

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Numerical Methods for Roots of Polynomials - Part I (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton’s, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent’s method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled “A Handbook of Methods for Polynomial Root-finding”. This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic.

Topological Fields

• 1st Edition
• Volume 157
• June 1, 1989
• S. Warner
• English
• eBook 978-0-08-087268-1

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Aimed at those acquainted with basic point-set topology and algebra, this text goes up to the frontiers of current research in topological fields (more precisely, topological rings that algebraically are fields).The reader is given enough background to tackle the current literature without undue additional preparation. Many results not in the text (and many illustrations by example of theorems in the text) are included among the exercises. Sufficient hints for the solution of the exercises are offered so that solving them does not become a major research effort for the reader. A comprehensive bibliography completes the volume.

Topics in Field Theory

• 1st Edition
• Volume 155
• February 1, 1989
• G. Karpilovsky
• English
• eBook 978-0-08-087266-7

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This monograph gives a systematic account of certain important topics pertaining to field theory, including the central ideas, basic results and fundamental methods.Avoiding excessive technical detail, the book is intended for the student who has completed the equivalent of a standard first-year graduate algebra course. Thus it is assumed that the reader is familiar with basic ring-theoretic and group-theoretic concepts. A chapter on algebraic preliminaries is included, as well as a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.

Near-Rings and Near-Fields

• 1st Edition
• Volume 137
• April 1, 1987
• G. Betsch
• English
• eBook 978-0-08-087248-3

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Most topics in near-ring and near-field theory are treated here, along with an extensive introduction to the theory.There are two invited lectures: ``Non-Commutative Geometry, Near-Rings and Near-Fields'' which indicates the relevance of near-rings and near-fields for geometry, while ``Pseudo-Finite Near-Fields'' shows the impressive power of model theoretic methods. The remaining papers cover such topics as D.G. near-rings, radical theory, KT-near-fields, matrix near-rings, and applications to systems theory.