Download or read book Julia Sets of Rational Functions with Special Emphasis on Chebyshev Families Connectedness and Visualization on the Computer written by Christoph Martin Stroh and published by . This book was released on 2000 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Self Similar Groups written by Volodymyr Nekrashevych and published by American Mathematical Soc.. This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians.
Download or read book Dynamics in One Non Archimedean Variable written by Robert L. Benedetto and published by American Mathematical Soc.. This book was released on 2019-03-05 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of complex dynamics in one variable, initiated by Fatou and Julia in the early twentieth century, concerns the iteration of a rational function acting on the Riemann sphere. Building on foundational investigations of p-adic dynamics in the late twentieth century, dynamics in one non-archimedean variable is the analogous theory over non-archimedean fields rather than over the complex numbers. It is also an essential component of the number-theoretic study of arithmetic dynamics. This textbook presents the fundamentals of non-archimedean dynamics, including a unified exposition of Rivera-Letelier's classification theorem, as well as results on wandering domains, repelling periodic points, and equilibrium measures. The Berkovich projective line, which is the appropriate setting for the associated Fatou and Julia sets, is developed from the ground up, as are relevant results in non-archimedean analysis. The presentation is accessible to graduate students with only first-year courses in algebra and analysis under their belts, although some previous exposure to non-archimedean fields, such as the p-adic numbers, is recommended. The book should also be a useful reference for more advanced students and researchers in arithmetic and non-archimedean dynamics.
Download or read book Polynomial Root finding and Polynomiography written by Bahman Kalantari and published by World Scientific. This book was released on 2009 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Algorithms written by Justin Solomon and published by CRC Press. This book was released on 2015-06-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Download or read book Complex Dynamics written by Lennart Carleson and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. Focusing on the analytic side of this contemporary subject, the text was developed from a course taught over several semesters and aims to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration, classification of periodic components, critical points and expanding maps, some applications of conformal mappings, the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set.
Download or read book Mathematica in Action written by Stan Wagon and published by Springer Science & Business Media. This book was released on 1999 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematica in Action, 2nd Edition," is designed both as a guide to the extraordinary capabilities of Mathematica as well as a detailed tour of modern mathematics by one of its leading expositors, Stan Wagon. Ideal for teachers, researchers, mathematica enthusiasts. This second edition of the highly sucessful W.H. Freeman version includes an 8 page full color insert and 50% new material all organized around Elementary Topics, Intermediate Applications, and Advanced Projects. In addition, the book uses Mathematica 3.0 throughtout. Mathematica 3.0 notebooks with all the programs and examples discussed in the book are available on the TELOS web site (www.telospub.com). These notebooks contain materials suitable for DOS, Windows, Macintosh and Unix computers. Stan Wagon is well-known in the mathematics (and Mathematica) community as Associate Editor of the "American Mathematical Monthly," a columnist for the "Mathematical Intelligencer" and "Mathematica in Education and Research," author of "The Banach-Tarski Paradox" and "Unsolved Problems in Elementary Geometry and Number Theory (with Victor Klee), as well as winner of the 1987 Lester R. Ford Award for Expository Writing.
Download or read book Python for Scientists written by John M. Stewart and published by Cambridge University Press. This book was released on 2017-07-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific Python is taught from scratch in this book via copious, downloadable, useful and adaptable code snippets. Everything the working scientist needs to know is covered, quickly providing researchers and research students with the skills to start using Python effectively.
Download or read book The Mathematica GuideBook for Programming written by Michael Trott and published by Springer. This book was released on 2013-12-21 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive, detailed reference provides readers with both a working knowledge of Mathematica in general and a detailed knowledge of the key aspects needed to create the fastest, shortest, and most elegant implementations possible. It gives users a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The three volumes -- Programming, Graphics, and Mathematics, total 3,000 pages and contain more than 15,000 Mathematica inputs, over 1,500 graphics, 4,000+ references, and more than 500 exercises. This first volume begins with the structure of Mathematica expressions, the syntax of Mathematica, its programming, graphic, numeric and symbolic capabilities. It then covers the hierarchical construction of objects out of symbolic expressions, the definition of functions, the recognition of patterns and their efficient application, program flows and program structuring, and the manipulation of lists. An indispensible resource for students, researchers and professionals in mathematics, the sciences, and engineering.
Download or read book Essentials of Mathematica written by Nino Boccara and published by Springer Science & Business Media. This book was released on 2007-10-17 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book teaches how to use Mathematica to solve a wide variety of problems in mathematics and physics. It is based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students. The book is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs. The first part, in which the reader learns how to use a variety of Mathematica commands, contains examples, not long explanations; the second part contains attractive applications.
Download or read book Probability for Statisticians written by Galen R. Shorack and published by Springer. This book was released on 2017-09-21 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: The choice of examples used in this text clearly illustrate its use for a one-year graduate course. The material to be presented in the classroom constitutes a little more than half the text, while the rest of the text provides background, offers different routes that could be pursued in the classroom, as well as additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Steins method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function, with both the bootstrap and trimming presented. The section on martingales covers censored data martingales.
Download or read book An Introduction to Data Structures and Algorithms written by J.A. Storer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data structures and algorithms are presented at the college level in a highly accessible format that presents material with one-page displays in a way that will appeal to both teachers and students. The thirteen chapters cover: Models of Computation, Lists, Induction and Recursion, Trees, Algorithm Design, Hashing, Heaps, Balanced Trees, Sets Over a Small Universe, Graphs, Strings, Discrete Fourier Transform, Parallel Computation. Key features: Complicated concepts are expressed clearly in a single page with minimal notation and without the "clutter" of the syntax of a particular programming language; algorithms are presented with self-explanatory "pseudo-code." * Chapters 1-4 focus on elementary concepts, the exposition unfolding at a slower pace. Sample exercises with solutions are provided. Sections that may be skipped for an introductory course are starred. Requires only some basic mathematics background and some computer programming experience. * Chapters 5-13 progress at a faster pace. The material is suitable for undergraduates or first-year graduates who need only review Chapters 1 -4. * This book may be used for a one-semester introductory course (based on Chapters 1-4 and portions of the chapters on algorithm design, hashing, and graph algorithms) and for a one-semester advanced course that starts at Chapter 5. A year-long course may be based on the entire book. * Sorting, often perceived as rather technical, is not treated as a separate chapter, but is used in many examples (including bubble sort, merge sort, tree sort, heap sort, quick sort, and several parallel algorithms). Also, lower bounds on sorting by comparisons are included with the presentation of heaps in the context of lower bounds for comparison-based structures. * Chapter 13 on parallel models of computation is something of a mini-book itself, and a good way to end a course. Although it is not clear what parallel
Download or read book NIST Handbook of Mathematical Functions Hardback and CD ROM written by Frank W. J. Olver and published by Cambridge University Press. This book was released on 2010-05-17 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.
Download or read book Experimentation in Mathematics written by Jonathan M. Borwein and published by CRC Press. This book was released on 2004-04-12 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of
Download or read book Conformal Invariants written by Lars V. Ahlfors and published by American Mathematical Soc.. This book was released on with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Walks on Infinite Graphs and Groups written by Wolfgang Woess and published by Cambridge University Press. This book was released on 2000-02-13 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
Download or read book Numerical Python written by Robert Johansson and published by Apress. This book was released on 2018-12-24 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leverage the numerical and mathematical modules in Python and its standard library as well as popular open source numerical Python packages like NumPy, SciPy, FiPy, matplotlib and more. This fully revised edition, updated with the latest details of each package and changes to Jupyter projects, demonstrates how to numerically compute solutions and mathematically model applications in big data, cloud computing, financial engineering, business management and more. Numerical Python, Second Edition, presents many brand-new case study examples of applications in data science and statistics using Python, along with extensions to many previous examples. Each of these demonstrates the power of Python for rapid development and exploratory computing due to its simple and high-level syntax and multiple options for data analysis. After reading this book, readers will be familiar with many computing techniques including array-based and symbolic computing, visualization and numerical file I/O, equation solving, optimization, interpolation and integration, and domain-specific computational problems, such as differential equation solving, data analysis, statistical modeling and machine learning. What You'll Learn Work with vectors and matrices using NumPy Plot and visualize data with Matplotlib Perform data analysis tasks with Pandas and SciPy Review statistical modeling and machine learning with statsmodels and scikit-learn Optimize Python code using Numba and Cython Who This Book Is For Developers who want to understand how to use Python and its related ecosystem for numerical computing.
