Complex Polynomials
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Complex Polynomials
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Author : T. Sheil-Small
language : en
Publisher: Cambridge University Press
Release Date : 2002-11-07
Complex Polynomials written by T. Sheil-Small 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 2002-11-07 with Mathematics categories.
This book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis.
Shape Preserving Approximation By Real And Complex Polynomials
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Author : Sorin G. Gal
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-09
Shape Preserving Approximation By Real And Complex Polynomials written by Sorin G. Gal 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 2010-06-09 with Mathematics categories.
First comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables Of interest to grad students and researchers in approximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineering Contains many open problems to spur future research Rich and updated bibliography
Polynomials Dynamics And Choice
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Author : Scott Crass
language : en
Publisher: CRC Press
Release Date : 2022-08-23
Polynomials Dynamics And Choice written by Scott Crass and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-23 with Mathematics categories.
Working out solutions to polynomial equations is a mathematical problem that dates from antiquity. Galois developed a theory in which the obstacle to solving a polynomial equation is an associated collection of symmetries. Obtaining a root requires "breaking" that symmetry. When the degree of an equation is at least five, Galois Theory established that there is no formula for the solutions like those found in lower degree cases. However, this negative result doesn't mean that the practice of equation-solving ends. In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry. Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes. The two algorithms in Part I provide frameworks that capture structural issues that can arise in deliberative settings. While decision-making has been approached in mathematical terms, the novelty here is in the use of equation-solving algorithms to illuminate such problems. Features Treats the topic—familiar to many—of solving polynomial equations in a way that’s dramatically different from what they saw in school Accessible to a general audience with limited mathematical background Abundant diagrams and graphics.
Polynomial Convexity
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Author : Edgar Lee Stout
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-28
Polynomial Convexity written by Edgar Lee Stout 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 2007-07-28 with Mathematics categories.
This comprehensive monograph details polynomially convex sets. It presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. Coverage examines in considerable detail questions of uniform approximation for the most part on compact sets but with some attention to questions of global approximation on noncompact sets. The book also discusses important applications and motivates the reader with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries.
Polynomials And Vanishing Cycles
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Author : Mihai Tibăr
language : en
Publisher: Cambridge University Press
Release Date : 2007-05-17
Polynomials And Vanishing Cycles written by Mihai Tibăr 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 2007-05-17 with Mathematics categories.
A systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations is proposed in this tract. Lefschetz theory, complex Morse theory and singularities of hypersurfaces are presented in detail leading to the latest research on topics such as the topology of singularities of meromorphic functions and non-generic Lefschetz pencils.
Polynomial Root Finding And Polynomiography
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Author : Bahman Kalantari
language : en
Publisher: World Scientific
Release Date : 2009
Polynomial Root Finding And Polynomiography written by Bahman Kalantari and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the well-known polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations.
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
Methods For Finding Zeros In Polynomials
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Author :
language : en
Publisher: Bookboon
Release Date :
Methods For Finding Zeros In Polynomials written by and has been published by Bookboon this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Fundamental Theorem Of Algebra
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Author : Benjamin Fine
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Fundamental Theorem Of Algebra written by Benjamin Fine 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 2012-12-06 with Mathematics categories.
The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.
Algebra Zero To Hero A Modern Guide To Mathematical Mastery
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Author : Lexa N. Palmer
language : en
Publisher: Book Lovers HQ
Release Date : 2025-01-02
Algebra Zero To Hero A Modern Guide To Mathematical Mastery written by Lexa N. Palmer and has been published by Book Lovers HQ this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-02 with Mathematics categories.
Algebra Zero to Hero: A Modern Guide to Mathematical Mastery is the ultimate resource for mastering algebra, whether you’re a student facing complex equations for the first time, a parent seeking to guide your child, or an adult ready to refresh your mathematical skills. This book transforms algebra from a daunting subject into an engaging journey of discovery, delivering practical tools and insights to help you succeed. Algebra is more than just solving equations—it’s a way of thinking critically, solving problems efficiently, and unlocking a world of opportunities in science, technology, business, and beyond. Algebra Zero to Hero bridges the gap between confusion and clarity with modern teaching methods, real-world applications, and an empowering growth mindset that ensures every reader can grasp the core concepts of algebra. In this book, you’ll begin with the basics—decoding symbols, simplifying expressions, and mastering equations. From there, you’ll progress to tackling functions, inequalities, polynomials, and quadratic equations with confidence. You’ll learn not only how to solve problems but also why these methods work, making algebra an intuitive tool you can use in everyday life and professional pursuits. What you will find in this book: A step-by-step approach to understanding algebraic fundamentals Clear explanations of equations, graphing, and problem-solving techniques Real-world applications that demonstrate the relevance of algebra in science, business, and technology Mastery of advanced topics like exponents, logarithms, and systems of equations Tips, tricks, and proven strategies for simplifying complex problems Practice problems and worked examples to build confidence and deepen understanding With Algebra Zero to Hero, you’ll not only conquer the subject but also build the confidence to apply algebraic thinking in every area of life. Whether you’re looking to improve your grades, sharpen your problem-solving skills, or enhance your career, this book will be your guide to success. Take the first step toward becoming a true algebra hero—your mathematical mastery starts here!