POLYNOMIALS AND POLYNOMIAL INEQUALITIES GRADUATE TEXTS IN MATHEMATICS

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Polynomials And Polynomial Inequalities

Author : Peter Borwein
ISBN : 9781461207931
Genre : Mathematics
File Size : 26.67 MB
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After an introduction to the geometry of polynomials and a discussion of refinements of the Fundamental Theorem of Algebra, the book turns to a consideration of various special polynomials. Chebyshev and Descartes systems are then introduced, and Müntz systems and rational systems are examined in detail. Subsequent chapters discuss denseness questions and the inequalities satisfied by polynomials and rational functions. Appendices on algorithms and computational concerns, on the interpolation theorem, and on orthogonality and irrationality round off the text. The book is self-contained and assumes at most a senior-undergraduate familiarity with real and complex analysis.
Category: Mathematics

Polynomials

Author : Victor V. Prasolov
ISBN : 9783642039805
Genre : Mathematics
File Size : 61.5 MB
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Covers its topic in greater depth than the typical standard books on polynomial algebra
Category: Mathematics

Advances In Applied Mathematics And Approximation Theory

Author : George A. Anastassiou
ISBN : 9781461463931
Genre : Mathematics
File Size : 47.60 MB
Format : PDF, Kindle
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Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the best articles presented at “Applied Mathematics and Approximation Theory 2012,” an international conference held in Ankara, Turkey, May 17-20, 2012. This volume brings together key work from authors in the field covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators, statistical approximation, fuzzy approximation, fractional analysis, semigroups, inequalities, special functions and summability. The collection will be a useful resource for researchers in applied mathematics, engineering and statistics.​
Category: Mathematics

Number Theory And Polynomials

Author : Chris Smyth
ISBN : 9780521714679
Genre : Mathematics
File Size : 56.52 MB
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Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Category: Mathematics

Polynomials

Author :
ISBN : 9783642040122
Genre : Polynomials
File Size : 89.24 MB
Format : PDF, ePub, Mobi
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Category: Polynomials

Polynomials

Author : Victor V. Prasolov
ISBN : 9783642039805
Genre : Mathematics
File Size : 58.51 MB
Format : PDF, ePub
Download : 929
Read : 791

Covers its topic in greater depth than the typical standard books on polynomial algebra
Category: Mathematics

Irresistible Integrals

Author : George Boros
ISBN : 0521796369
Genre : Mathematics
File Size : 60.63 MB
Format : PDF, Kindle
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The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in nineteenth century analysis and it has now been revived with the appearance of symbolic languages. The authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting-rather than the shortest-path to the results. They illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This is a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.
Category: Mathematics

Matrix Analysis

Author : Rajendra Bhatia
ISBN : 9781461206538
Genre : Mathematics
File Size : 41.9 MB
Format : PDF
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This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.
Category: Mathematics

Positive Polynomials And Sums Of Squares

Author : Murray Marshall
ISBN : 9780821844021
Genre : Mathematics
File Size : 42.89 MB
Format : PDF, Kindle
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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.
Category: Mathematics

Equations And Inequalities

Author : Jiri Herman
ISBN : 9781461212706
Genre : Mathematics
File Size : 90.35 MB
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A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.
Category: Mathematics