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Author: A. Gardiner
Publisher: Springer Science & Business Media
ISBN: 1461256542
Category : Mathematics
Languages : en
Pages : 309
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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
Get Book
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: Lloyd Leroy Smail
Publisher:
ISBN:
Category : Processes, Infinite
Languages : en
Pages : 192
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Book Description
Author: Olaf Burkart
Publisher: Springer
ISBN: 3540696784
Category : Computers
Languages : en
Pages : 166
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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: Horst Osswald
Publisher: Cambridge University Press
ISBN: 1107016142
Category : Mathematics
Languages : en
Pages : 429
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Book Description
After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.
Author: Anthony Gardiner
Publisher: Courier Corporation
ISBN: 9780486425382
Category : Mathematics
Languages : en
Pages : 324
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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: Kôhei Uchiyama
Publisher: Springer Nature
ISBN: 3031410203
Category : Electronic books
Languages : en
Pages : 277
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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: Gennady Samoradnitsky
Publisher: Routledge
ISBN: 1351414801
Category : Mathematics
Languages : en
Pages : 632
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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: Analysis on Infinit Ams Special Session
Publisher: American Mathematical Soc.
ISBN: 0821832026
Category : Mathematics
Languages : en
Pages : 224
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Book Description
This book contains the proceedings of the special session in honor of Leonard Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The speakers were specialists in a variety of fields, and many were Professor Gross' former Ph.D. students and their descendants. Papers in this volume present results from several areas of mathematics. They illustrate applications of powerful ideas that originated in Gross' work and permeate diverse fields. Topics of this title include stochastic partial differential equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat kernels, and some applications. The volume should be useful to graduate students and researchers. It provides perspective on current activity and on central ideas and techniques in the topics covered.
Author: Robert F. Nagaev
Publisher: World Scientific
ISBN: 9789810235048
Category : Technology & Engineering
Languages : en
Pages : 268
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Book Description
Mapping out a “family constellation,” explains Dr. Joy Manné, encompasses exploring previous powerful life events from accidents to adoptions and accessing the deepest dynamics in that family system. This process helps us recognize and then resolve deeply seated family patterns. For example, in order to understand a person’s inability to trust, the family history of betrayal must be uncovered and released. These insights replace resentment with respect, pain with understanding.Dr. Manné uses the knowledge gained from her own practice as well as her educational experiences with Bert Hellinger, the founder of Family Constellations therapy, to clearly describe this technique. Most family constellation sessions are carried out in a group setting, with the facilitator first seeking clarity regarding the issue or problem the client has come to work out. Representatives are then chosen from among the group and the constellation is set up and worked in until it comes to resolution. This may be followed by a closing ritual and advice about how to integrate what the constellation has revealed. Through the use of real-life examples of family constellations, Dr. Manné makes this increasingly popular practice understandable and relatable.
Author: Fred W. Steutel
Publisher: CRC Press
ISBN: 020301412X
Category : Mathematics
Languages : en
Pages : 562
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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.
