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.

Download or read book Advanced Calculus Revised Edition written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Download or read book Calculus for Computer Graphics written by John Vince and published by Springer. This book was released on 2019-03-12 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students studying different branches of computer graphics have to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces and as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems. In this 2nd edition, the author extends the scope of the original book to include applications of calculus in the areas of arc-length parameterisation of curves, geometric continuity, tangent and normal vectors, and curvature. The author draws upon his experience in teaching mathematics to undergraduates to make calculus appear no more challenging than any other branch of mathematics. He introduces the subject by examining how functions depend upon their independent variables, and then derives the appropriate mathematical underpinning and definitions. This gives rise to a function’s derivative and its antiderivative, or integral. Using the idea of limits, the reader is introduced to derivatives and integrals of many common functions. Other chapters address higher-order derivatives, partial derivatives, Jacobians, vector-based functions, single, double and triple integrals, with numerous worked examples, and over a hundred and seventy colour illustrations. This book complements the author’s other books on mathematics for computer graphics, and assumes that the reader is familiar with everyday algebra, trigonometry, vectors and determinants. After studying this book, the reader should understand calculus and its application within the world of computer graphics, games and animation.

Download or read book Calculus for Engineering Students written by Jesus Martin Vaquero and published by Academic Press. This book was released on 2020-08-10 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus for Engineering Students: Fundamentals, Real Problems, and Computers insists that mathematics cannot be separated from chemistry, mechanics, electricity, electronics, automation, and other disciplines. It emphasizes interdisciplinary problems as a way to show the importance of calculus in engineering tasks and problems. While concentrating on actual problems instead of theory, the book uses Computer Algebra Systems (CAS) to help students incorporate lessons into their own studies. Assuming a working familiarity with calculus concepts, the book provides a hands-on opportunity for students to increase their calculus and mathematics skills while also learning about engineering applications. - Organized around project-based rather than traditional homework-based learning - Reviews basic mathematics and theory while also introducing applications - Employs uniform chapter sections that encourage the comparison and contrast of different areas of engineering

Download or read book Calculus With Applications written by Peter D. Lax and published by Springer Science & Business Media. This book was released on 2013-09-21 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory.

Download or read book Mathematics From the Birth of Numbers written by Jan Gullberg and published by W. W. Norton & Company. This book was released on 1997-01-07 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustrated exploration of mathematics and its history, beginning with a study of numbers and their symbols, and continuing with a broad survey that includes consideration of algebra, geometry, hyperbolic functions, fractals, and many other mathematical functions.

Download or read book Abstract Computing Machines written by Werner Kluge and published by Springer Science & Business Media. This book was released on 2005-02-18 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book emphasizes the design of full-fledged, fully normalizing lambda calculus machinery, as opposed to the just weakly normalizing machines.

Download or read book Concrete Mathematics written by Ronald L. Graham and published by Addison-Wesley Professional. This book was released on 1994-02-28 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.

Download or read book Discrete Calculus written by Leo J. Grady and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.

Download or read book Operator Calculus On Graphs Theory And Applications In Computer Science written by George Stacey Staples and published by World Scientific. This book was released on 2012-02-23 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science.Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.

Download or read book Sets Logic and Maths for Computing written by David Makinson and published by Springer Science & Business Media. This book was released on 2012-02-27 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.

Download or read book Calculus written by Morris Kline and published by Courier Corporation. This book was released on 2013-05-09 with total page 962 pages. Available in PDF, EPUB and Kindle. Book excerpt: Application-oriented introduction relates the subject as closely as possible to science with explorations of the derivative; differentiation and integration of the powers of x; theorems on differentiation, antidifferentiation; the chain rule; trigonometric functions; more. Examples. 1967 edition.

Download or read book Mathematics in Computing written by Gerard O’Regan and published by Springer Nature. This book was released on 2020-01-10 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction. Topics and features: includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus. This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.

Download or read book Stochastic Network Calculus written by Yuming Jiang and published by Springer Science & Business Media. This book was released on 2009-03-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Network calculus is a theory dealing with queuing systems found in computer networks. Its focus is on performance guarantees. Central to the theory is the use of alternate algebras such as the min-plus algebra to transform complex network systems into analytically tractable systems. To simplify the ana- sis, another idea is to characterize tra?c and service processes using various bounds. Since its introduction in the early 1990s, network calculus has dev- oped along two tracks—deterministic and stochastic. This book is devoted to summarizing results for stochastic network calculus that can be employed in the design of computer networks to provide stochastic service guarantees. Overview and Goal Like conventional queuing theory, stochastic network calculus is based on properly de?ned tra?c models and service models. However, while in c- ventional queuing theory an arrival process is typically characterized by the inter-arrival times of customers and a service process by the service times of customers, the arrival process and the service process are modeled in n- work calculus respectively by some arrival curve that (maybe probabilis- cally) upper-bounds the cumulative arrival and by some service curve that (maybe probabilistically) lower-bounds the cumulative service. The idea of usingboundstocharacterizetra?candservicewasinitiallyintroducedfor- terministic network calculus. It has also been extended to stochastic network calculus by exploiting the stochastic nature of arrival and service processes.

Download or read book Mathematics for Electrical Engineering and Computing written by Mary P Attenborough and published by Elsevier. This book was released on 2003-06-30 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and continuous systems - particularly vital for Digital Signal Processing (DSP). In addition, as most modern engineers are required to study software, material suitable for Software Engineering - set theory, predicate and prepositional calculus, language and graph theory - is fully integrated into the book.Excessive technical detail and language are avoided, recognising that the real requirement for practising engineers is the need to understand the applications of mathematics in everyday engineering contexts. Emphasis is given to an appreciation of the fundamental concepts behind the mathematics, for problem solving and undertaking critical analysis of results, whether using a calculator or a computer.The text is backed up by numerous exercises and worked examples throughout, firmly rooted in engineering practice, ensuring that all mathematical theory introduced is directly relevant to real-world engineering. The book includes introductions to advanced topics such as Fourier analysis, vector calculus and random processes, also making this a suitable introductory text for second year undergraduates of electrical, electronic and computer engineering, undertaking engineering mathematics courses.Dr Attenborough is a former Senior Lecturer in the School of Electrical, Electronic and Information Engineering at South Bank University. She is currently Technical Director of The Webbery - Internet development company, Co. Donegal, Ireland. - Fundamental principles of mathematics introduced and applied in engineering practice, reinforced through over 300 examples directly relevant to real-world engineering

Download or read book Calculus Using Mathematica written by K.D. Stroyan and published by Academic Press. This book was released on 2014-05-10 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus Using Mathematica: Scientific Projects and Mathematical Background is a companion to the core text, Calculus Using Mathematica. The book contains projects that illustrate applications of calculus to a variety of practical situations. The text consists of 14 chapters of various projects on how to apply the concepts and methodologies of calculus. Chapters are devoted to epidemiological applications; log and exponential functions in science; applications to mechanics, optics, economics, and ecology. Applications of linear differential equations; forced linear equations; differential equations from vector geometry; and to chemical reactions are presented as well. College students of calculus will find this book very helpful.

Download or read book An Introduction to Lambda Calculi for Computer Scientists written by Chris Hankin and published by College Publications. This book was released on 2004 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lambda-calculus lies at the very foundations of computer science. Besides its historical role in computability theory it has had significant influence on programming language design and implementation, denotational semantics, and domain theory. The book emphasises the proof theory for the type-free lambda-calculus. The first six chapters concern this calculus and cover the basic theory, reduction, models, computability, and the relationship between the lambda-calculus and combinatory logic. Chapter 7 presents a variety of typed calculi; first the simply typed lambda-calculus, then Milner-style polymorphism and, finally, the polymorphic lambda-calculus. Chapter 8 concerns two variants of the type-free lambda-calculus that have appeared in the research literature: the lazy lambda-calculus, and the lambda sigma-calculus. The final chapter contains references and a guide to further reading. There are exercises throughout. In contrast to earlier books on these topics, which were written by logicians, this book is written from a computer science perspective and emphasises the practical relevance of many of the key theoretical ideas. The book is intended as a course text for final year undergraduates or first year graduate students in computer science. Research students should find it a useful introduction to more specialist literature.