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Integers, Polynomials, and Rings: A Course in Algebra
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Ronald S Irving
Mathematics is often regarded as the study of calculation, but in fact, mathematics is much more. It combines creativity and logic in order to arrive at abstract truths. This book is intended to illustrate how calculation, creativity, and logic can be combined to solve a range of problems in algebra. Originally conceived as a text for a course for ...
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Fourier series and orthogonal polynomials
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Dunham Jackson
This text illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Begins with a definition and explanation of the elements of Fourier series, and examines Legendre polynomials and Bessel functions. Also includes Pearson frequency functions and chapters on orthogonal, Jacobi, ...
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Field Theory
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Steven Roman, PH.D.
Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. ...
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The Real Fatou Conjecture. (Am-144)
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Jacek Graczyk, Grzegorz Swiatek
In 1920, Pierre Fatou expressed the conjecture that - except for special cases - all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set ...
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Polynomial Operator Equations in Abstract Spaces and Applications
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Ioannis Argyros, Aoannis K Argyros
Polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of ...
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Polynomials
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Edward J Barbeau
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 ...
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Global Bifurcation Theory and Hilbert's Sixteenth Problem
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Valery A Gaiko
This volume is devoted to the qualitative investigation of two-dimensional polynomial dynamical systems, and is aimed at solving Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles. The author presents a global bifurcation theory of such systems and suggests a new global approach to the study of limit cycle ...
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Structured Matrices and Polynomials
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Victor Pan
Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. ...
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Combinatorial Methods: Free Groups, Polynomials, and Free Algebras
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Vladimir Shpilrain, Alexander Mikhalev, Jie-Tai Yu
The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology at the beginning of the 20th Century. This book is divided into ...
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Elliptic Polynomials
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John S Lomont, John Brillhart
A remarkable interplay exists between the fields of elliptic functions and orthogonal polynomials. In the first monograph to explore their connections, Elliptic Polynomials combines these two areas of study, leading to an interesting development of some basic aspects of each. It presents new material about various classes of polynomials and about ...
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Orthogonal Polynomials of Several Variables
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Charles F Dunkl, Yuan Xu, G -C Rota (Editor)
This is the first modern book on orthogonal polynomials of several variables, which are interesting both as objects of study and as tools used in multivariate analysis, including approximations and numerical integration. The book, which is intended both as an introduction to the subject and as a reference, presents the theory in elegant form and ...
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Problems and Theorems in Analysis II: Theory of Functions, Zeros, Polynomials, Determinants, Number Theory, Geometry
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George Polya, George Pbolya, Gabor Szego
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Walsh Equiconvergence of Complex Interpolating Polynomials
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Amnon Jakimovski, Ambikeshwar Sharma, Jszsef Szabados
This book is a collection of the various old and new results, centered around the following simple and beautiful observation of J. L. Walsh - If a function is analytic in a finite disc, and not in a larger disc, then the difference between the Lagrange interpolant of the function, at the roots of unity, and the partial sums of the Taylor series, ...
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Heights of Polynomials and Entropy in Algebraic Dynamics
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Graham Everest, Thomas Ward
The main theme of the book is the theory of heights as they appear in various guises. This includes a large body of results on Mahler's measure of the height of a polynomial of which topic there is no book available. The genesis of the measure in a paper by Lehmer is looked at, which is extremely well-timed due to the revival of interest following ...
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Polynomial Convexity
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Edgar Lee Stout
This comprehensive monograph is devoted to the study of polynomially convex sets, which play an important role in the theory of functions of several complex variables. "Polynomial Convexity" presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. It motivates the ...
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Approximation and Computation: A Festschrift in Honor of Walter Gautschi
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R. V. M. Zahar (Editor)
In recognition of Walter Gautschi's many contributions to mathematics and computer science, and to celebrate his 65th birthday, an international conference was held in his honour at Purdue University in December 1993. These papers are taken from that conference. This book provides a survey of current topics in the fields of approximation, ...
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From Polynomials to Sums of Squares
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by
Terence H Jackson
"From Polynomials to Sums of Squares" describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is ...
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Knots & Physics
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by
Louis H. Kauffman
This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical framework, create a context that naturally includes a wide range of interrelated topics in topology and mathematical physics. The author takes ...
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Effective Polynomial Computation
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by
Zippel
Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are ...
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Double Affine Hecke Algebras
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Ivan Cherednik
This is a unique, essentially self-contained, monograph in a new field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications. Chapter 1 is ...
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Orthogonal polynomials and their applications proceedings of the international congress
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Vinuesa
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Handbook of Computational Methods for Integration
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Michael R Schaferkotter, Prem K Kythe
During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open ...
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Orthogonal Polynomials and Special Functions
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by
Walter Van Assche (Editor), Francisco Marcelln (Editor), Walter Van Assche (Editor)
Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference ...
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Polynomials and Pollen: Parables, Proverbs, Paradigms and Praise for Lois
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Jay Wright
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Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy
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by
Teo Mora, G -C Rota (Editor), B Doran (Editor)
Polynomial equations have been long studied, both theoretically and with a view to solving them. Until recently, manual computation was the only solution method and the theory was developed to accommodate it. With the advent of computers, the situation changed dramatically. Many classical results can be more usefully recast within a different ...
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