Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Infinite Processes PDF full book. Access full book title Infinite Processes by A. Gardiner. Download full books in PDF and EPUB format.
Author: A. Gardiner Publisher: Springer Science & Business Media ISBN: 1461256542 Category : Mathematics Languages : en Pages : 309
Book Description
What shall we say of this metamorphosis in passing from finite to infinite? Galileo, Two New Sciences As its title suggests, this book was conceived as a prologue to the study of "Why the calculus works"--otherwise known as analysis. It is in fact a critical reexamination of the infinite processes arising in elementary math ematics: Part II reexamines rational and irrational numbers, and their representation as infinite decimals; Part III examines our ideas of length, area, and volume; and Part IV examines the evolution of the modern function-concept. The book may be used in a number of ways: firstly, as a genuine pro logue to analysis; secondly, as a supplementary text within an analysis course, providing a source of elementary motivation, background and ex amples; thirdly, as a kind of postscript to elementary analysis-as in a senior undergraduate course designed to reinforce students' understanding of elementary analysis and of elementary mathematics by considering the mathematical and historical connections between them. But the contents of the book should be of interest to a much wider audience than this including teachers, teachers in training, students in their last year at school, and others interested in mathematics.
Author: A. Gardiner Publisher: Springer Science & Business Media ISBN: 1461256542 Category : Mathematics Languages : en Pages : 309
Book Description
What shall we say of this metamorphosis in passing from finite to infinite? Galileo, Two New Sciences As its title suggests, this book was conceived as a prologue to the study of "Why the calculus works"--otherwise known as analysis. It is in fact a critical reexamination of the infinite processes arising in elementary math ematics: Part II reexamines rational and irrational numbers, and their representation as infinite decimals; Part III examines our ideas of length, area, and volume; and Part IV examines the evolution of the modern function-concept. The book may be used in a number of ways: firstly, as a genuine pro logue to analysis; secondly, as a supplementary text within an analysis course, providing a source of elementary motivation, background and ex amples; thirdly, as a kind of postscript to elementary analysis-as in a senior undergraduate course designed to reinforce students' understanding of elementary analysis and of elementary mathematics by considering the mathematical and historical connections between them. But the contents of the book should be of interest to a much wider audience than this including teachers, teachers in training, students in their last year at school, and others interested in mathematics.
Author: Anthony Gardiner Publisher: Courier Corporation ISBN: 9780486425382 Category : Mathematics Languages : en Pages : 324
Book Description
Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.
Author: Horst Osswald Publisher: Cambridge University Press ISBN: 1107016142 Category : Mathematics Languages : en Pages : 429
Book Description
After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.
Author: Gennady Samoradnitsky Publisher: Routledge ISBN: 1351414801 Category : Mathematics Languages : en Pages : 632
Book Description
This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.
Author: Olaf Burkart Publisher: Springer ISBN: 3540696784 Category : Computers Languages : en Pages : 169
Book Description
A common approach in software engineering is to apply during the design phase a variety of structured techniques like top-down design, decomposition and abstraction, while only subsequently, in the implementation phase, is the design tested to ensure reliability. But this approach neglects that central aspects of software design and program development have a strong formal character which admits tool support for the construction of reliable and correct computer systems based on formal reasoning. This monograph provides much information both for theoreticians interested in algebraic theories, and for software engineers building practically relevant tools. The author presents the theoretical foundations needed for the verification of reactive, sequential infinite-state systems.
Author: Evarist Giné Publisher: Cambridge University Press ISBN: 1009022784 Category : Mathematics Languages : en Pages : 706
Book Description
In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
Author: Zo Peacemaker Publisher: ISBN: 9780983383383 Category : Self-Help Languages : en Pages : 364
Book Description
"Peacemaker succeeds in addressing the sacred needs of every human being within this practical and honest guide. He begins to untangle the messes we create in our lives daily, and does so through sound advice and compassion for those in search of a more positive lifestyle. By the last page, it feels as though the world is an entirely new thing to be experienced. It deserves a place on the bookshelf, right next to The Four Agreements and Way of the Peaceful Warrior." -Rayla Gomez, Freelance Editor "Reading this book is as if I were sitting at the foot of a Native Elder, listening to the wisdom passed down through centuries of observation, experience and wonder. Not only does Zo expose our self-limiting beliefs, but he gives us simple and effective answers as to how we can begin to change our lives from the inside out." Jake Ducey, Author of Into the Wind "Zo has succeeded in communicating the message that happiness and peace must come from within instead of depending on things outside of ourselves. His message about our power to turn garbage into gold gives us the knowing that living an accountable life can in turn create world peace. Communicating this message to the world is an increasingly important endeavor as humanity continues to wake up and realize in order to create world peace we must first find our own peace within." Daniel Pettegrew, Founder of World Peace Gardens
Author: Kôhei Uchiyama Publisher: Springer Nature ISBN: 3031410203 Category : Electronic books Languages : en Pages : 277
Book Description
This book studies the potential functions of one-dimensional recurrent random walks on the lattice of integers with step distribution of infinite variance. The central focus is on obtaining reasonably nice estimates of the potential function. These estimates are then applied to various situations, yielding precise asymptotic results on, among other things, hitting probabilities of finite sets, overshoot distributions, Green functions on long finite intervals and the half-line, and absorption probabilities of two-sided exit problems. The potential function of a random walk is a central object in fluctuation theory. If the variance of the step distribution is finite, the potential function has a simple asymptotic form, which enables the theory of recurrent random walks to be described in a unified way with rather explicit formulae. On the other hand, if the variance is infinite, the potential function behaves in a wide range of ways depending on the step distribution, which the asymptotic behaviour of many functionals of the random walk closely reflects. In the case when the step distribution is attracted to a strictly stable law, aspects of the random walk have been intensively studied and remarkable results have been established by many authors. However, these results generally do not involve the potential function, and important questions still need to be answered. In the case where the random walk is relatively stable, or if one tail of the step distribution is negligible in comparison to the other on average, there has been much less work. Some of these unsettled problems have scarcely been addressed in the last half-century. As revealed in this treatise, the potential function often turns out to play a significant role in their resolution. Aimed at advanced graduate students specialising in probability theory, this book will also be of interest to researchers and engineers working with random walks and stochastic systems.
Author: Fred W. Steutel Publisher: CRC Press ISBN: 020301412X Category : Mathematics Languages : en Pages : 562
Book Description
Infinite Divisibility of Probability Distributions on the Real Line reassesses classical theory and presents new developments, while focusing on divisibility with respect to convolution or addition of independent random variables. This definitive, example-rich text supplies approximately 100 examples to correspond with all major chapter topics and reviews infinite divisibility in light of the central limit problem. It contrasts infinite divisibility with finite divisibility, discusses the preservation of infinite divisibility under mixing for many classes of distributions, and investigates self-decomposability and stability on the nonnegative reals, nonnegative integers, and the reals.
Author: A. Gardiner
Author: A. Gardiner
Author: Anthony Gardiner
Author: Horst Osswald
Author: Gennady Samoradnitsky
Author: Olaf Burkart
Author: Evarist Giné
Author: Sato Ken-Iti
Author: Zo Peacemaker
Author: Kôhei Uchiyama
Author: Fred W. Steutel