Pattern Calculus

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Pattern Calculus

Author : Barry Jay
Publisher : Springer Science & Business Media
ISBN 13 : 3540891854
Total Pages : 217 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Pattern Calculus by : Barry Jay

Download or read book Pattern Calculus written by Barry Jay and published by Springer Science & Business Media. This book was released on 2009-07-30 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over time, basic research tends to lead to specialization – increasingly narrow t- ics are addressed by increasingly focussed communities, publishing in increasingly con ned workshops and conferences, discussing increasingly incremental contri- tions. Already the community of programming languages is split into various s- communities addressing different aspects and paradigms (functional, imperative, relational, and object-oriented). Only a few people manage to maintain a broader view, and even fewer step back in order to gain an understanding about the basic principles, their interrelation, and their impact in a larger context. The pattern calculus is the result of a profound re-examination of a 50-year - velopment. It attempts to provide a unifying approach, bridging the gaps between different programming styles and paradigms according to a new slogan – compu- tion is pattern matching. It is the contribution of this book to systematically and elegantly present and evaluate the power of pattern matching as the guiding paradigm of programming. Patterns are dynamically generated, discovered, passed, applied, and automatically adapted, based on pattern matching and rewriting technology, which allows one to elegantly relate things as disparate as functions and data structures. Of course, pattern matching is not new. It underlies term rewriting – it is, for example, inc- porated in, typically functional, programming languages, like Standard ML – but it has never been pursued as the basis of a unifying framework for programming.

Nature’s Patterns and the Fractional Calculus

Author : Bruce J. West
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110534274
Total Pages : 213 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Nature’s Patterns and the Fractional Calculus by : Bruce J. West

Download or read book Nature’s Patterns and the Fractional Calculus written by Bruce J. West and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-09-11 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus

Term Rewriting and Applications

Author : Franz Baader
Publisher : Springer
ISBN 13 : 354073449X
Total Pages : 422 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Term Rewriting and Applications by : Franz Baader

Download or read book Term Rewriting and Applications written by Franz Baader and published by Springer. This book was released on 2007-08-14 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 18th International Conference on Rewriting Techniques and Applications, held in Paris, France in June 2007, featured presentations and discussions centering on some of the latest advances in the field. This volume presents the proceedings from that meeting. Papers cover current research on all aspects of rewriting, including applications, foundational issues, frameworks, implementations, and semantics.

Pre-Calculus For Dummies

Author : Krystle Rose Forseth
Publisher : John Wiley & Sons
ISBN 13 : 0470169842
Total Pages : 410 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Pre-Calculus For Dummies by : Krystle Rose Forseth

Download or read book Pre-Calculus For Dummies written by Krystle Rose Forseth and published by John Wiley & Sons. This book was released on 2008-04-07 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an introduction to the principles of pre-calculus, covering such topics as functions, law of sines and cosines, identities, sequences, series, and binomials.

The Complete Idiot's Guide to Calculus

Author : W. Michael Kelley
Publisher : Penguin
ISBN 13 : 1592574718
Total Pages : 354 pages
Book Rating : 4.5/5 (925 download)

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Book Synopsis The Complete Idiot's Guide to Calculus by : W. Michael Kelley

Download or read book The Complete Idiot's Guide to Calculus written by W. Michael Kelley and published by Penguin. This book was released on 2006 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let's face it- most students don't take calculus because they find it intellectually stimulating. It's not . . . at least for those who come up on the wrong side of the bell curve! There they are, minding their own business, working toward some non-science related degree, when . . . BLAM! They get next semester's course schedule in the mail, and first on the list is the mother of all loathed college courses . . . CALCULUS! Not to fear-The Complete Idiot's Guide to Calculus, Second Edition, like its predecessor, is a curriculum-based companion book created with this audience in mind. This new edition continues the tradition of taking the sting out of calculus by adding more explanatory graphs and illustrations and doubling the number of practice problems! By the time readers are finished, they will have a solid understanding (maybe even a newfound appreciation) for this useful form of math. And with any luck, they may even be able to make sense of their textbooks and teachers.

Mathematical Approaches to Neural Networks

Author : J.G. Taylor
Publisher : Elsevier
ISBN 13 : 9780080887395
Total Pages : 381 pages
Book Rating : 4.8/5 (873 download)

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Book Synopsis Mathematical Approaches to Neural Networks by : J.G. Taylor

Download or read book Mathematical Approaches to Neural Networks written by J.G. Taylor and published by Elsevier. This book was released on 1993-10-27 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of Neural Networks is being seen to be coming of age, after its initial inception 50 years ago in the seminal work of McCulloch and Pitts. It is proving to be valuable in a wide range of academic disciplines and in important applications in industrial and business tasks. The progress being made in each approach is considerable. Nevertheless, both stand in need of a theoretical framework of explanation to underpin their usage and to allow the progress being made to be put on a firmer footing. This book aims to strengthen the foundations in its presentation of mathematical approaches to neural networks. It is through these that a suitable explanatory framework is expected to be found. The approaches span a broad range, from single neuron details to numerical analysis, functional analysis and dynamical systems theory. Each of these avenues provides its own insights into the way neural networks can be understood, both for artificial ones and simplified simulations. As a whole, the publication underlines the importance of the ever-deepening mathematical understanding of neural networks.

Design Pattern Formalization Techniques

Author : Taibi, Toufik
Publisher : IGI Global
ISBN 13 : 1599042215
Total Pages : 400 pages
Book Rating : 4.5/5 (99 download)

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Book Synopsis Design Pattern Formalization Techniques by : Taibi, Toufik

Download or read book Design Pattern Formalization Techniques written by Taibi, Toufik and published by IGI Global. This book was released on 2007-04-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many formal approaches for pattern specification are emerging as a means to cope with the inherent shortcomings of informal description. Design Pattern Formalization Techniques presents multiple mathematical, formal approaches for pattern specification, emphasizing on software development processes for engineering disciplines. Design Pattern Formalization Techniques focuses on formalizing the solution element of patterns, providing tangible benefits to pattern users, researchers, scholars, academicians, practitioners and students working in the field of design patterns and software reuse.Design Pattern Formalization Techniques explains details on several specification languages, allowing readers to choose the most suitable formal technique to solve their specific inquiries.

Learning Mathematics

Author : Anthony Orton
Publisher : A&C Black
ISBN 13 : 1441140018
Total Pages : 241 pages
Book Rating : 4.4/5 (411 download)

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Book Synopsis Learning Mathematics by : Anthony Orton

Download or read book Learning Mathematics written by Anthony Orton and published by A&C Black. This book was released on 2004-10-01 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: • Why do some students achieve more than others? • Do we have to wait until pupils are "ready"? • Can children discover math for themselves? • Does language interfere with the learning of math? This classic text, written from the viewpoint of the math teacher, provides answers to these and many more questions. Each chapter explores a particular issue that illustrates the interaction between theory and practice. New chapters have been included on cognition, pattern, and ICT.

Discrete Calculus

Author : Carlo Mariconda
Publisher : Springer
ISBN 13 : 3319030388
Total Pages : 659 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Discrete Calculus by : Carlo Mariconda

Download or read book Discrete Calculus written by Carlo Mariconda and published by Springer. This book was released on 2016-12-01 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet user-friendly approach. This is particularly useful in combinatorics, a field where, all too often, exercises are solved by means of ad hoc tricks. The book contains more than 400 examples and about 300 problems, and the reader will be able to find the proof of every result. To further assist students and teachers, important matters and comments are highlighted, and parts that can be omitted, at least during a first and perhaps second reading, are identified.

Approximately Calculus

Author : Shahriar Shahriari
Publisher : American Mathematical Soc.
ISBN 13 : 0821837508
Total Pages : 314 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Approximately Calculus by : Shahriar Shahriari

Download or read book Approximately Calculus written by Shahriar Shahriari and published by American Mathematical Soc.. This book was released on 2006 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there always a prime number between $n$ and $2n$? Where, approximately, is the millionth prime? And just what does calculus have to do with answering either of these questions? It turns out that calculus has a lot to do with both questions, as this book can show you. The theme of the book is approximations. Calculus is a powerful tool because it allows us to approximate complicated functions with simpler ones. Indeed, replacing a function locally with a linear--or higher order--approximation is at the heart of calculus. The real star of the book, though, is the task of approximating the number of primes up to a number $x$. This leads to the famous Prime Number Theorem--and to the answers to the two questions about primes. While emphasizing the role of approximations in calculus, most major topics are addressed, such as derivatives, integrals, the Fundamental Theorem of Calculus, sequences, series, and so on. However, our particular point of view also leads us to many unusual topics: curvature, Pade approximations, public key cryptography, and an analysis of the logistic equation, to name a few. The reader takes an active role in developing the material by solving problems. Most topics are broken down into a series of manageable problems, which guide you to an understanding of the important ideas. There is also ample exposition to fill in background material and to get you thinking appropriately about the concepts. Approximately Calculus is intended for the reader who has already had an introduction to calculus, but wants to engage the concepts and ideas at a deeper level. It is suitable as a text for an honors or alternative second semester calculus course.

More Calculus of a Single Variable

Author : Peter R. Mercer
Publisher : Springer
ISBN 13 : 1493919261
Total Pages : 419 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis More Calculus of a Single Variable by : Peter R. Mercer

Download or read book More Calculus of a Single Variable written by Peter R. Mercer and published by Springer. This book was released on 2014-10-17 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus — such as the real numbers, differentiation and integration, mean value theorems, the exponential function — are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for π. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization. More Calculus of a Single Variable is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for self-study by students, instructors, and, indeed, all connoisseurs of ingenious calculations.

Calculus

Author : David Warren Cohen
Publisher : Jones & Bartlett Learning
ISBN 13 : 9780763729479
Total Pages : 1014 pages
Book Rating : 4.7/5 (294 download)

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Book Synopsis Calculus by : David Warren Cohen

Download or read book Calculus written by David Warren Cohen and published by Jones & Bartlett Learning. This book was released on 2005 with total page 1014 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptable to courses for non-engineering majors, this textbook illustrates the meaning of a curve through graphs and tests predictions through numerical values of change, before formally defining the limit of a sequence and function, the derivative, and the integral. The second half of the book develops techniques for integrating functions, approxi

Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding

Author : Terrance J Quinn
Publisher : World Scientific
ISBN 13 : 9811222584
Total Pages : 250 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding by : Terrance J Quinn

Download or read book Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding written by Terrance J Quinn and published by World Scientific. This book was released on 2020-07-24 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.

Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition

Author : Dan Kalman
Publisher : American Mathematical Soc.
ISBN 13 : 1470450011
Total Pages : 509 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition by : Dan Kalman

Download or read book Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition written by Dan Kalman and published by American Mathematical Soc.. This book was released on 2019-08-02 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Mathematical Models offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses. Presuming only a background of exposure to high school algebra, the text introduces students to the methodology of mathematical modeling, which plays a role in nearly all real applications of mathematics. A course based on this text would have as its primary goal preparing students to be competent consumers of mathematical modeling in their future studies. Such a course would also provide students with an understanding of the modeling process and a facility with much of the standard, non-trigonometric, content of college algebra and precalculus. This book builds, successively, a series of growth models defined in terms of simple recursive patterns of change corresponding to arithmetic, quadratic, geometric, and logistic growth. Students discover and come to understand linear, polynomial, exponential, and logarithmic functions in the context of analyzing these models of intrinsically—and scientifically—interesting phenomena including polar ice extent, antibiotic resistance, and viral internet videos. Students gain a deep appreciation for the power and limitations of mathematical modeling in the physical, life, and social sciences as questions of modeling methodology are carefully and constantly addressed. Realistic examples are used consistently throughout the text, and every topic is illustrated with models that are constructed from and compared to real data. The text is extremely attractive and the exposition is extraordinarily clear. The lead author of this text is the recipient of nine MAA awards for expository writing including the Ford, Evans, Pólya, and Allendoerfer awards and the Beckenbach Book prize. Great care has been taken by accomplished expositors to make the book readable by students. Those students will also benefit from more than 1,000 carefully crafted exercises.

A Calculus of Ideas

Author : Ulf Grenander
Publisher : World Scientific
ISBN 13 : 981438318X
Total Pages : 236 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis A Calculus of Ideas by : Ulf Grenander

Download or read book A Calculus of Ideas written by Ulf Grenander and published by World Scientific. This book was released on 2012 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.

Pre-Calculus For Dummies

Author : Yang Kuang
Publisher : John Wiley & Sons
ISBN 13 : 1118168887
Total Pages : 408 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Pre-Calculus For Dummies by : Yang Kuang

Download or read book Pre-Calculus For Dummies written by Yang Kuang and published by John Wiley & Sons. This book was released on 2012-06-26 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an introduction to the principles of pre-calculus, covering such topics as functions, law of sines and cosines, identities, sequences, series, and binomials.

Pre-Calculus For Dummies

Author : Mary Jane Sterling
Publisher : John Wiley & Sons
ISBN 13 : 1119508770
Total Pages : 419 pages
Book Rating : 4.1/5 (195 download)

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Book Synopsis Pre-Calculus For Dummies by : Mary Jane Sterling

Download or read book Pre-Calculus For Dummies written by Mary Jane Sterling and published by John Wiley & Sons. This book was released on 2018-11-13 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Get ahead in pre-calculus Pre-calculus courses have become increasingly popular with 35 percent of students in the U.S. taking the course in middle or high school. Often, completion of such a course is a prerequisite for calculus and other upper level mathematics courses. Pre-Calculus For Dummies is an invaluable resource for students enrolled in pre-calculus courses. By presenting the essential topics in a clear and concise manner, the book helps students improve their understanding of pre-calculus and become prepared for upper level math courses. Provides fundamental information in an approachable manner Includes fresh example problems Practical explanations mirror today’s teaching methods Offers relevant cultural references Whether used as a classroom aid or as a refresher in preparation for an introductory calculus course, this book is one you’ll want to have on hand to perform your very best.