Discrete Or Continuous

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Continuous and Discrete Modules

Saad H. Mohamed,Bruno J. Müller
Continuous and Discrete Modules Book PDF

Author : Saad H. Mohamed,Bruno J. Müller
Publisher : Cambridge University Press
Page : 141 pages
File Size : 52,6 Mb
Release : 1990-02-22
Category : Mathematics
ISBN : 9780521399753

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Continuous and Discrete Modules by Saad H. Mohamed,Bruno J. Müller Pdf

Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory.

The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics

John L. Bell
The Continuous the Discrete and the Infinitesimal in Philosophy and Mathematics Book PDF

Author : John L. Bell
Publisher : Springer Nature
Page : 313 pages
File Size : 42,7 Mb
Release : 2019-09-09
Category : Mathematics
ISBN : 9783030187071

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The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics by John L. Bell Pdf

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.

Discrete or Continuous?

Amit Hagar
Discrete or Continuous Book PDF

Author : Amit Hagar
Publisher : Cambridge University Press
Page : 281 pages
File Size : 47,9 Mb
Release : 2014-05
Category : Science
ISBN : 9781107062801

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Discrete or Continuous? by Amit Hagar Pdf

Novel conceptual analysis, fresh historical perspectives, and concrete physical examples illuminate one of the most thought-provoking topics in physics.

Discrete and Continuous Models in the Theory of Networks

Fatihcan M. Atay,Pavel B. Kurasov,Delio Mugnolo
Discrete and Continuous Models in the Theory of Networks Book PDF

Author : Fatihcan M. Atay,Pavel B. Kurasov,Delio Mugnolo
Publisher : Springer Nature
Page : 370 pages
File Size : 51,8 Mb
Release : 2020-09-03
Category : Mathematics
ISBN : 9783030440978

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Discrete and Continuous Models in the Theory of Networks by Fatihcan M. Atay,Pavel B. Kurasov,Delio Mugnolo Pdf

This book contains contributions from the participants of the research group hosted by the ZiF - Center for Interdisciplinary Research at the University of Bielefeld during the period 2013-2017 as well as from the conclusive conference organized at Bielefeld in December 2017. The contributions consist of original research papers: they mirror the scientific developments fostered by this research program or the state-of-the-art results presented during the conclusive conference. The volume covers current research in the areas of operator theory and dynamical systems on networks and their applications, indicating possible future directions. The book will be interesting to researchers focusing on the mathematical theory of networks; it is unique as, for the first time, continuous network models - a subject that has been blooming in the last twenty years - are studied alongside more classical and discrete ones. Thus, instead of two different worlds often growing independently without much intercommunication, a new path is set, breaking with the tradition. The fruitful and beneficial exchange of ideas and results of both communities is reflected in this book.

Problems from the Discrete to the Continuous

Ross G. Pinsky
Problems from the Discrete to the Continuous Book PDF

Author : Ross G. Pinsky
Publisher : Springer
Page : 154 pages
File Size : 53,9 Mb
Release : 2014-08-09
Category : Mathematics
ISBN : 9783319079653

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Problems from the Discrete to the Continuous by Ross G. Pinsky Pdf

The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.

Stochastic Analysis in Discrete and Continuous Settings

Nicolas Privault
Stochastic Analysis in Discrete and Continuous Settings Book PDF

Author : Nicolas Privault
Publisher : Springer
Page : 282 pages
File Size : 43,5 Mb
Release : 2009-07-14
Category : Mathematics
ISBN : 9783642023804

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Stochastic Analysis in Discrete and Continuous Settings by Nicolas Privault Pdf

This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.

Foundations of Discrete Mathematics

K. D. Joshi
Foundations of Discrete Mathematics Book PDF

Author : K. D. Joshi
Publisher : New Age International
Page : 768 pages
File Size : 53,5 Mb
Release : 1989
Category : Mathematics
ISBN : 8122401201

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Foundations of Discrete Mathematics by K. D. Joshi Pdf

This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.

Discrete, Continuous, and Hybrid Petri Nets

René David,Hassane Alla
Discrete Continuous and Hybrid Petri Nets Book PDF

Author : René David,Hassane Alla
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 43,5 Mb
Release : 2010-11-09
Category : Technology & Engineering
ISBN : 9783642106699

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Discrete, Continuous, and Hybrid Petri Nets by René David,Hassane Alla Pdf

Petri Nets were introduced and still successfully used to analyze and model discrete event systems especially in engineering and computer sciences such as in automatic control. Recently this discrete Petri Nets formalism was successfully extended to continuous and hybrid systems. This monograph presents a well written and clearly organized introduction in the standard methods of Petri Nets with the aim to reach an accurate understanding of continuous and hybrid Petri Nets, while preserving the consistency of basic concepts throughout the book. The book is a monograph as well as a didactic tool which is easy to understand due to many simple solved examples and detailed figures. In its second completely reworked edition various sections, concepts and recently developed algorithms are added as well as additional examples/exercises.

Nonlinear Hybrid Continuous/Discrete-Time Models

Marat Akhmet
Nonlinear Hybrid Continuous Discrete Time Models Book PDF

Author : Marat Akhmet
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 43,5 Mb
Release : 2011-05-03
Category : Mathematics
ISBN : 9789491216039

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Nonlinear Hybrid Continuous/Discrete-Time Models by Marat Akhmet Pdf

The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type.

Statistics For Dummies

Deborah J. Rumsey
Statistics For Dummies Book PDF

Author : Deborah J. Rumsey
Publisher : John Wiley & Sons
Page : 423 pages
File Size : 52,7 Mb
Release : 2016-06-07
Category : Mathematics
ISBN : 9781119293521

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Statistics For Dummies by Deborah J. Rumsey Pdf

The fun and easy way to get down to business with statistics Stymied by statistics? No fear? this friendly guide offers clear, practical explanations of statistical ideas, techniques, formulas, and calculations, with lots of examples that show you how these concepts apply to your everyday life. Statistics For Dummies shows you how to interpret and critique graphs and charts, determine the odds with probability, guesstimate with confidence using confidence intervals, set up and carry out a hypothesis test, compute statistical formulas, and more. Tracks to a typical first semester statistics course Updated examples resonate with today's students Explanations mirror teaching methods and classroom protocol Packed with practical advice and real-world problems, Statistics For Dummies gives you everything you need to analyze and interpret data for improved classroom or on-the-job performance.

Stochastic Control in Discrete and Continuous Time

Atle Seierstad
Stochastic Control in Discrete and Continuous Time Book PDF

Author : Atle Seierstad
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 55,6 Mb
Release : 2010-07-03
Category : Mathematics
ISBN : 9780387766171

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Stochastic Control in Discrete and Continuous Time by Atle Seierstad Pdf

This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1), piecewise - terministic control problems (Chapter 3), and control of Ito diffusions (Chapter 4). The chapters include treatments of optimal stopping problems. An Appendix - calls material from elementary probability theory and gives heuristic explanations of certain more advanced tools in probability theory. The book will hopefully be of interest to students in several ?elds: economics, engineering, operations research, ?nance, business, mathematics. In economics and business administration, graduate students should readily be able to read it, and the mathematical level can be suitable for advanced undergraduates in mathem- ics and science. The prerequisites for reading the book are only a calculus course and a course in elementary probability. (Certain technical comments may demand a slightly better background. ) As this book perhaps (and hopefully) will be read by readers with widely diff- ing backgrounds, some general advice may be useful: Don’t be put off if paragraphs, comments, or remarks contain material of a seemingly more technical nature that you don’t understand. Just skip such material and continue reading, it will surely not be needed in order to understand the main ideas and results. The presentation avoids the use of measure theory.

Discrete and Continuous Nonlinear Schrödinger Systems

M. J. Ablowitz,B. Prinari,A. D. Trubatch
Discrete and Continuous Nonlinear Schr dinger Systems Book PDF

Author : M. J. Ablowitz,B. Prinari,A. D. Trubatch
Publisher : Cambridge University Press
Page : 276 pages
File Size : 40,7 Mb
Release : 2004
Category : Mathematics
ISBN : 0521534372

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Discrete and Continuous Nonlinear Schrödinger Systems by M. J. Ablowitz,B. Prinari,A. D. Trubatch Pdf

This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.

Discrete and Continuous Boundary Problems

Atkinson
Discrete and Continuous Boundary Problems Book PDF

Author : Atkinson
Publisher : Academic Press
Page : 586 pages
File Size : 42,9 Mb
Release : 1964-01-01
Category : Computers
ISBN : 9780080955162

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Discrete and Continuous Boundary Problems by Atkinson Pdf

Discrete and Continuous Boundary Problems

Continuous and Discrete Dynamics near Manifolds of Equilibria

B. Aulbach
Continuous and Discrete Dynamics near Manifolds of Equilibria Book PDF

Author : B. Aulbach
Publisher : Springer
Page : 150 pages
File Size : 41,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540388531

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Continuous and Discrete Dynamics near Manifolds of Equilibria by B. Aulbach Pdf

Entfesseln Sie die Kreativität Ihres Kindes mit über 35 einzigartigen Seite zum Färben! Sie werden viele beliebte Dinosaurier-Typen hier zu finden. Dieses Buch ist eine erstaunliche Aktivität, um die Phantasie und Kreativität Ihres Kindes zu stimulieren. Dieses tolle Buch wird Ihrem Kind auch den Namen einiger Dinosaurier beibringen, während Sie Spaß beim Färben haben. Ein perfektes Geschenk für Dinosaurier-Fans! Jede Ausmalseite ist auf einer separaten Seite gedruckt, um ein Durchbluten zu vermeiden. Geeignet für Marker, Buntstifte, Wasserfarbe, Gelstifte. Große Größe - 8,5 x 11 Zoll

An Introduction to Dynamical Systems

Rex Clark Robinson
An Introduction to Dynamical Systems Book PDF

Author : Rex Clark Robinson
Publisher : American Mathematical Soc.
Page : 763 pages
File Size : 46,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891353

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An Introduction to Dynamical Systems by Rex Clark Robinson Pdf

This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course. The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally, chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems. The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets. In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book. This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations.