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Sprache: Englisch
Verlag: Kluwer Boston Incorporated, 2003
ISBN 10: 1402014384 ISBN 13: 9781402014383
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - It is by no means clear what comprises the 'heart' or 'core' of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on 'our heart' might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter 'Groups' to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in 'their' chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the 'big' Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.
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Taschenbuch. Zustand: Neu. Differential and Difference Dimension Polynomials | Alexander V. Mikhalev (u. a.) | Taschenbuch | xiii | Englisch | 2010 | Springer | EAN 9789048151417 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E. Kolchin in 1964 [KoI64]' but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. Actually, one can say that the differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. The first attempts of such description were made at the end of 19th century by Jacobi [Ja890] who estimated the number of algebraically independent constants in the general solution of a system of linear ordinary differential equations. Later on, Jacobi's results were extended to some cases of nonlinear systems, but in general case the problem of such estimation (that is known as the problem of Jacobi's bound) remains open. There are some generalization of the problem of Jacobi's bound to the partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differen tial equations were actively developed by F. Riquier [RiqlO] and M.
Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E. Kolchin in 1964 [KoI64]' but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. Actually, one can say that the differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. The first attempts of such description were made at the end of 19th century by Jacobi [Ja890] who estimated the number of algebraically independent constants in the general solution of a system of linear ordinary differential equations. Later on, Jacobi's results were extended to some cases of nonlinear systems, but in general case the problem of such estimation (that is known as the problem of Jacobi's bound) remains open. There are some generalization of the problem of Jacobi's bound to the partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differen tial equations were actively developed by F. Riquier [RiqlO] and M.
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Sprache: Englisch
Verlag: Walter de Gruyter, Incorporated, 1992
ISBN 10: 3110129744 ISBN 13: 9783110129748
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Zustand: Sehr gut. Zustand: Sehr gut | Seiten: 480 | Sprache: Englisch | Produktart: Bücher | This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff¿s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff¿s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff¿s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz ¿ Radon ¿ Frechet problem of characterization of Radon integrals as linear functionals.