Polynomials

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Polynomials

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Author : E.J. Barbeau
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-09

Polynomials written by E.J. Barbeau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-09 with Mathematics categories.

The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 "explorations" invite the reader to investigate research problems and related topics.

Positive Polynomials And Sums Of Squares

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Author : Murray Marshall
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Positive Polynomials And Sums Of Squares written by Murray Marshall and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

The study of positive polynomials brings together algebra, geometry and analysis. The subject is of fundamental importance in real algebraic geometry when studying the properties of objects defined by polynomial inequalities. Hilbert's 17th problem and its solution in the first half of the 20th century were landmarks in the early days of the subject. More recently, new connections to the moment problem and to polynomial optimization have been discovered. The moment problem relates linear maps on the multidimensional polynomial ring to positive Borel measures. This book provides an elementary introduction to positive polynomials and sums of squares, the relationship to the moment problem, and the application to polynomial optimization. The focus is on the exciting new developments that have taken place in the last 15 years, arising out of Schmudgen's solution to the moment problem in the compact case in 1991. The book is accessible to a well-motivated student at the beginning graduate level. The objects being dealt with are concrete and down-to-earth, namely polynomials in $n$ variables with real coefficients, and many examples are included. Proofs are presented as clearly and as simply as possible. Various new, simpler proofs appear in the book for the first time. Abstraction is employed only when it serves a useful purpose, but, at the same time, enough abstraction is included to allow the reader easy access to the literature. The book should be essential reading for any beginning student in the area.

The Theory Of Equations General Properties Of Polynomials

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Author : William Snow Burnside
language : en
Publisher:
Release Date : 1899

The Theory Of Equations General Properties Of Polynomials written by William Snow Burnside and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1899 with Determinants categories.

Analytic Theory Of Polynomials

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Author : Qazi Ibadur Rahman
language : en
Publisher: Oxford University Press
Release Date : 2002

Analytic Theory Of Polynomials written by Qazi Ibadur Rahman and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Language Arts & Disciplines categories.

Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications

Polynomials And Equations

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Author : K.T. Leung
language : en
Publisher: Hong Kong University Press
Release Date : 1992-12-01

Polynomials And Equations written by K.T. Leung and has been published by Hong Kong University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-01 with Mathematics categories.

Primarily a textbook to prepare Sixth Form students for public examinations in Hong Kong, this book is also useful as a reference for undergraduate students since it contains some advanced theory of equations beyond the sixth form level.

Classical And Quantum Orthogonal Polynomials In One Variable

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Author : Mourad Ismail
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-21

Classical And Quantum Orthogonal Polynomials In One Variable written by Mourad Ismail and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-21 with Mathematics categories.

The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.

Polynomial Methods In Combinatorics

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Author : Larry Guth
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-10

Polynomial Methods In Combinatorics written by Larry Guth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-10 with Mathematics categories.

This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.

Chebyshev Polynomials

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Author : J.C. Mason
language : en
Publisher: CRC Press
Release Date : 2002-09-17

Chebyshev Polynomials written by J.C. Mason and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-17 with Mathematics categories.

Chebyshev polynomials crop up in virtually every area of numerical analysis, and they hold particular importance in recent advances in subjects such as orthogonal polynomials, polynomial approximation, numerical integration, and spectral methods. Yet no book dedicated to Chebyshev polynomials has been published since 1990, and even that work focuse

Small Fractional Parts Of Polynomials

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Author : Wolfgang M. Schmidt
language : en
Publisher: American Mathematical Soc.
Release Date : 1977

Small Fractional Parts Of Polynomials written by Wolfgang M. Schmidt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.

Knowledge about fractional parts of linear polynomials is fairly satisfactory. Knowledge about fractional parts of nonlinear polynomials is not so satisfactory. In these notes the author starts out with Heilbronn's Theorem on quadratic polynomials and branches out in three directions. In Sections 7-12 he deals with arbitrary polynomials with constant term zero. In Sections 13-19 he takes up simultaneous approximation of quadratic polynomials. In Sections 20-21 he discusses special quadratic polynomials in several variables. There are many open questions: in fact, most of the results obtained in these notes ar almost certainly not best possible. Since the theory is not in its final form including the most general situation, i.e. simultaneous fractional parts of polynomials in several variables of arbitary degree. On the other hand, he has given all proofs in full detail and at a leisurely pace. For the first half of this work, only the standard notions of an undergraduate number theory course are required. For the second half, some knowledge of the geometry of numbers is helpful.

Geometry Of Polynomials

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Author : Morris Marden
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Geometry Of Polynomials written by Morris Marden and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history, beginning with the contributions of Cauchy and Gauss. Thus, the number of entries in the bibliography of this edition had to be increased from about 300 to about 600 and the book enlarged by one third. It now includes a more extensive treatment of Hurwitz polynomials and other topics. The new material on infrapolynomials, abstract polynomials, and matrix methods is of particular interest.