eBook.de : Ihr Online Shop für eBooks, Reader, Downloads und Bücher
Connect 01/2015 eBook-Shops: Testsieger im epub Angebot, Testurteil: gut Die Welt: Kundenorientierte Internetseiten Prädikat GOLD
+49 (0)40 4223 6096
€ 0,00
Zur Kasse
PORTO-
FREI

Polynomials

Originaltitel: Mnogochleny. 'Algorithms and Computation i…
Sofort lieferbar Pünktlich zum Fest*
Buch (gebunden)
17% Rabatt

Schöner schenken:
17% Rabatt¹ sichern!
Ihr Gutscheincode: SANTA17
Buch € 85,49* inkl. MwSt.
Portofrei*
Dieses Buch ist auch verfügbar als:

Produktdetails

Titel: Polynomials
Autor/en: Victor V. Prasolov

ISBN: 3540407146
EAN: 9783540407140
Originaltitel: Mnogochleny.
'Algorithms and Computation in Mathematics'.
2004. 2004.
8 schwarz-weiße Abbildungen, Bibliographie.
Book.
Sprache: Englisch.
Übersetzt von D. Leites
Springer-Verlag GmbH

9. Juli 2004 - gebunden - XIII

The theory of polynomials constitutes an essential part of university of algebra and calculus. Nevertheless, there are very few books entirely devoted to this theory.Thisbook provides an exposition of the main results in the theory of polynomials, both classical and modern. Many of the modern results have only been published in journals so far.Considerable attention is given to Hilbert's 17th problem on the representation of non-negative polynomials by the sums of squares of rational functions and its generalizations. Galois theory is discussed primarily from the point of view of the theory of polynomials, not from that of the general theory of fields and their extensions.
Foreword
Notational conventions
Chapter 1. Roots of polynomials
1. Inequalities for roots
2. The roots of a polynomial and of its derivative
3. The resultant and the discriminant
4. Separation of roots
5. Lagrange's series and estimates of the roots of a polynomial
6. Problems to Chapter 1
7. Solutions of selected problems
Chapter 2. Irreducible polynomials
1. Main properties of irreducible polynomials
2. Irreducibility criteria
3. Irreducibility of trinomials and fournomials
4. Hilbert's irreducibility theorem
5. Algorithms for factorization into irreducible factors
6. Problems to Chapter 2
7. Solutions of selected problems
Chapter 3. Polynomials of a particular form
1. Symmetric polynomials
2. Integer-valued polynomials
3. Cyclotomic polynomials
4. Chebyshev polynomials
5. Bernoulli's polynomials
6. Problems to Chapter 3
7. Solutions of selected problems
Chapter 4. Certain properties of polynomials
1. Polynomials with prescribed values
2. The height of a polynomial and other norms
3. Equations for polynomials
4. Transformations of polynomials
5. Algebraic numbers
6. Problems to Chapter 4
Chapter 5. Galois theory
1. Lagrange's theorem and the Galois resolvent
2. Basic Galois theory
3. How to solve equations by radicals
4. Calculations of the Galois groups
Chapter 6. Ideals in polynomial rings
1. Hilbert's basis theorem and Hilbert's theorem on zeros
2. Gröbner bases
Chapter 7. Hilbert's seventeenth problem
1. The sums of squares: introduction
2. Artin's theory
3. Pfister's theory
Chapter 8. Appendix
1. The Lenstra-Lenstra-Lovasz algorithm
Bibliography
From the reviews:
"Problems concerning polynomials have impulsed resp. accompanied the development of algebra from its very beginning until today and over the centuries a lot of mathematical gems have been brought to light. This book presents a few of them, some being classical, but partly probably unknown even to expers, some being quite recently discovered. [...] Many historical comments and a clear style make the book very readable, so it can be recommended warmly to non-experts already at an undergraduate level and, because of its contents, to experts as well."
G.Kowol, Monatshefte für Mathematik 146, Issue 4, 2005
"... Despite the appearance of this book in a series titled Algorithms and Computation of Mathematics, computation occupies only a small part of the monograph. It is best described as a useful reference for one's personal collection and a text for a full-year course given to graduate or even senior undergraduate students. [.....] the book under review is worth purchasing for the library and possibly even for one's own collection. The author's interest in the history and development of this area is evident, and we have pleasant glimpses of progress over the last three centuries. He exercises nice judgement in selection of arguments, with respect to both representativeness of approaches and elegance, so that the reader gains a synopsis of and guide to the literature, in which more detail can be found. ..."
Edward Barbeau, SIAM Review, Sept. 2005, Vol. 47, No. 3
"... the volume is packed with results and proofs that are well organised thematically into chapters and sections. What is unusual is to have a text that embraces and intermingles both analytic and algebraic aspects of the theory. Although the subject is about such basic objects, many tough results of considerable generality are incorporated and it is striking that refinements, both in theorems and proofs continued thoughout the latter part of the Twentieth Century. [...] There is a plentiful of problems, some of which might be challenging even for polynomial people; solutions to selected problems are also included."
S.D.Cohen, MathSciNet, MR 2082772, 2005
 "Polynome bilden einen grundlegenden Baustein der Algebra gleichwie der Analysis. Nichtsdestotrotz werden sie in der herkömmlichen Literatur of als bloßes Mittel zum Zweck betrachtet, und es gibt nach wie vor wenige Bücher, die sich ausschließlich der Theorie der Polynome widmen. Das vorliegende Buch bildet einen wohltuenden Kontrast dazu. Es versteht sich als Sammlung der wichtigsten Resultate der Theorie der Polynome, klassischer ebenso wie moderner. [......] Als Einführung in die faszinierende Welt der Polynome ist es zweifellos jedem Interessierten wärmstens zu empfehlen."
O.Pfeiffer (Kapfenberg), IMN - Internationale Mathematische Nachrichten, 59, Issue 198, 2005
"This comprehensive book covers both long-standing results in the theory of polynomials and recent developments which have until now only been available in the research literature. After initial chapters on the location and separation of roots and on irreducibility criteria, the book covers more specialised polynomials ... . Finally there is a detailed discussion of Hilbert's 17th problem ... ."
Bulletin Bibliographique, Vol. 51 (1-2), 2005
"This is an exposition of polynomial theory and results, both classical and modern. ... the volume is packed with results and proofs that are well organised thematically into chapters and sections. What is unusual is to have a text that embraces and intermingles both analytic and algebraic aspects of the theory. ... it is all fascinating and relevant to a series devoted to 'algorithms and computations'. There is a plentiful supply of problems, some of which might be challenging even for polynomial people ... ."
S. D. Cohen, Mathematical Reviews, 2005f
"This volume is an excellent introduction to the main topics on polynomials. The author presents both classical and modern subjects. ... Each chapter contains a list of selected problems and their solutions. The book includes a rich bibliography and an useful index. It will be useful for undergraduate and graduate students in mathematics."
Doru Stefanescu, Zentralblatt MATH, Vol. 1063, 2005
"The theory of polynomials is a very important and interesting part of mathematics. ... We note that at the end of chapters 1-4 some interesting problems and their solutions can be found. This is an excellent book written about polynomials. We can recommend this book to all who are interested in the theory of polynomials." (Miklós Dormán, Acta Scientiarum Mathematicarum, Vol. 72, 2006)
"This is an interesting, useful, well-organized, and well-written compendium of theorems and techniques about polynomials. ... The present volume is a translation of the 2001 Russian second edition. ... This is primarily a reference work ... it does include a set of interesting problems (with some solutions) at the end if each chapter." (Allen Stenger, The Mathematical Association of America, August, 2011)
Kundenbewertungen zu Victor V. Prasolov „Polynomials“
Noch keine Bewertungen vorhanden
Zur Rangliste der Rezensenten
Veröffentlichen Sie Ihre Kundenbewertung:
Kundenbewertung schreiben
Unsere Leistungen auf einen Klick
Unser Service für Sie
Zahlungsmethoden
Bequem, einfach und sicher mit eBook.de. mehr Infos akzeptierte Zahlungsarten: Überweisung, offene Rechnung,
Visa, Master Card, American Express, Paypal mehr Infos
Geprüfte Qualität
  • Schnelle Downloads
  • Datenschutz
  • Sichere Zahlung
  • SSL-Verschlüsselung
Servicehotline
+49 (0)40 4223 6096
Mo. - Fr. 8.00 - 20.00 Uhr
Sa. 10.00 - 18.00 Uhr
Chat
Ihre E-Mail-Adresse eintragen und kostenlos informiert werden:
* Alle Preise verstehen sich inkl. der gesetzlichen MwSt. Informationen über den Versand und anfallende Versandkosten finden Sie hier.
Artikel mit dem Hinweis "Pünktlich zum Fest" werden an Lieferadressen innerhalb Deutschlands rechtzeitig zum 24.12.2018 geliefert.
Bei als portofrei markierten Produkten bezieht sich dies nur auf den Versand innerhalb Deutschlands.

** Deutschsprachige eBooks und Bücher dürfen aufgrund der in Deutschland geltenden Buchpreisbindung und/oder Vorgaben von Verlagen nicht rabattiert werden. Soweit von uns deutschsprachige eBooks und Bücher günstiger angezeigt werden, wurde bei diesen kürzlich von den Verlagen der Preis gesenkt oder die Buchpreisbindung wurde für diese Titel inzwischen aufgehoben. Angaben zu Preisnachlässen beziehen sich auf den dargestellten Vergleichspreis.
eBook.de - Meine Bücher immer dabei
eBook.de ist eine Marke der Hugendubel Digital GmbH & Co. KG
Folgen Sie uns unter: