Mathematics of Discrete Structures for Computer Science

This book explores questions about the nature of an interlanguage grammar, i.e. the grammar of a bilingual. John Archibald approaches these questions within a cognitive science perspective that draws upon abstract representational structures in demonstrating that phonological knowledge underlies the surface phonetic properties of L2 speech. Specifically, he proposes that interlanguage grammars are not 'impaired', 'fundamentally different', or 'shallow' (as some have argued); the phonological grammars are complex, hierarchically-structured, mental representations that are governed by the principles of linguistic theory, including those of Universal Grammar. The book outlines a model that addresses Plato's problem (learning in the absence of evidence) and Orwell's problem (resistance to learning in the face of abundant evidence). Furthermore, the study of grammatical interfaces--phonetics/phonology; phonology/morphology; phonology/syntax--reveals the necessary design conditions foran int

Want to learn the in-demand skill of PHP programming… AND do it fast?Are you new to computer programming or just want to brush up on some skills? If so, this book is a wonderful resource for you. PHP

The collection is for courses in the history of science and technology, or science and society courses. The 28 essays cover thinking about technology, debating technology 1960s style and 21st-century

Proceedings in Nonlinear Science Centre for Nonlinear Studies, The University, Leeds LS2 9NQ, UK Series co-ordinator: Arun V. Holden Proceedings in Nonlinear Science deal with all areas of nonlinear s

The flow of granular materials such as sand, snow, coal, and catalyst particles is common occurrence in natural and industrial settings. The mechanics of these materials is not well understood. They are important since a large fraction of the materials handled and processed in the chemical, metallurgical, pharmaceutical, and food processing industries are granular in nature. This book describes the theories for granular flow based mainly on continuum models although alternative discrete models are also discussed briefly. The level is appropriate for advanced undergraduates or beginning graduate students. The goal is to inform the reader about observed phenomena, some available models, and their shortcomings and to visit some issues that remain unresolved. There is a selection of problems at the end of the chapters to encourage exploration, and extensive references are provided.

This text focuses on a variety of topics in mathematics in common usage in graduate engineering programs including vector calculus, linear and nonlinear ordinary differential equations, approximation methods, vector spaces, linear algebra, integral equations and dynamical systems. The book is designed for engineering graduate students who wonder how much of their basic mathematics will be of use in practice. Following development of the underlying analysis, the book takes students through a large number of examples that have been worked in detail. Students can choose to go through each step or to skip ahead if they so desire. After seeing all the intermediate steps, they will be in a better position to know what is expected of them when solving assignments, examination problems, and when on the job. Chapters conclude with exercises for the student that reinforce the chapter content and help connect the subject matter to a variety of engineering problems. Students have grown up with com

Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations. In this book the authors give elementary accounts of many aspects of classical complex function theory including Möbius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics. This book is based on lectures given to advanced undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread applic

This book provides attorneys and research assistants with quick and easy access to information previously found only by searching multiple sources. The format of the book includes a careful balance of text describing anatomic structures and illustrations enhancing those descriptions. The text is placed on one page with its corresponding illustrations on the opposing page. Information is grouped into separate sections of arteries, bones, muscles, nerves, and veins. These anatomic structures are alphabetized, by Latin nomenclature, to expedite access to them. Although the Latin and English terms are sufficiently similar, an index of the English equivalents has been added at the end of the book. Each illustration is coordinated with the text by means of colour and a large bold letter for easy identification. The book provides clear and concise descriptions of technical anatomic information.

From Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus.

Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.

Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.

For this third edition of a text for undergraduate and graduate students of library and information science, Chowdhury (information and knowledge management, the University of Technology-Sydney, Austr

This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and exhaustively both the statement and proof of all the standard inequalities of analysis. The authors were well known for their powers of exposition and were able here to make the subject accessible to a wide audience of mathematicians.

First published in 1972, this book combines concepts from the philosophy of science and statistics with social science techniques to form a methodological text for all those engaged in the social scie

A campaigning handbook, a thrilling work of popular science, and a call to arms for doctors, researchers and patients from Britain's finest writer on the science behind medicine. Statins are the singl

Seymour Simon has written more than 150 award-winning science books about animals, anatomy, astronomy, earth science, and vehicles! Named after the Roman god of war, Mars has fascinated people for t

With an increasing emphasis on creativity and innovation in the twenty-first century, teachers need to be creative professionals just as students must learn to be creative. And yet, schools are institutions with many important structures and guidelines that teachers must follow. Effective creative teaching strikes a delicate balance between structure and improvisation. The authors draw on studies of jazz, theater improvisation and dance improvisation to demonstrate that the most creative performers work within similar structures and guidelines. By looking to these creative genres, the book provides practical advice for teachers who wish to become more creative professionals.

With an increasing emphasis on creativity and innovation in the twenty-first century, teachers need to be creative professionals just as students must learn to be creative. And yet, schools are institutions with many important structures and guidelines that teachers must follow. Effective creative teaching strikes a delicate balance between structure and improvisation. The authors draw on studies of jazz, theater improvisation and dance improvisation to demonstrate that the most creative performers work within similar structures and guidelines. By looking to these creative genres, the book provides practical advice for teachers who wish to become more creative professionals.

Clarity, readability, and rigor combine in the third edition of this widely used textbook to provide the first step into general relativity for advanced undergraduates with a minimal background in mathematics. Topics within relativity that fascinate astrophysics researchers and students alike are covered with Schutz's characteristic ease and authority, from black holes to relativistic objects, from pulsars to the study of the Universe as a whole. This third edition contains discoveries by astronomers that require general relativity for their explanation; two chapters on gravitational waves, including direct detections of gravitational waves and their observations' impact on cosmological measurements; new information on black holes and neutron stars; and greater insight into the expansion of the Universe. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, while the informal writing style and worked ex

This book is an introduction to the theory of partial differential operators. It assumes that the reader has a knowledge of introductory functional analysis, up to the spectral theorem for bounded linear operators on Banach spaces. However, it describes the theory of Fourier transforms and distributions as far as is needed to analyse the spectrum of any constant coefficient partial differential operator. A completely new proof of the spectral theorem for unbounded self-adjoint operators is followed by its application to a variety of second-order elliptic differential operators, from those with discrete spectrum to Schrödinger operators acting on L2(RN). The book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on the subjec

This book provides a detailed introduction to the ergodic theory of equilibrium states giving equal weight to two of its most important applications, namely to equilibrium statistical mechanics on lattices and to (time discrete) dynamical systems. It starts with a chapter on equilibrium states on finite probability spaces which introduces the main examples for the theory on an elementary level. After two chapters on abstract ergodic theory and entropy, equilibrium states and variational principles on compact metric spaces are introduced emphasizing their convex geometric interpretation. Stationary Gibbs measures, large deviations, the Ising model with external field, Markov measures, Sinai-Bowen-Ruelle measures for interval maps and dimension maximal measures for iterated function systems are the topics to which the general theory is applied in the last part of the book. The text is self contained except for some measure theoretic prerequisites which are listed (with references to the

The two volumes that comprise this work provide a comprehensive guide and source book on the marine use of composite materials. This second volume, Practical Considerations, examines how the theory can be used in the design and construction of marine structures, including ships, boats, offshore structures and other deep-ocean installations. Areas covered in this second volume include design, the role of adhesives, fabrication techniques and operational aspects such as response to slam loads and fatigue performance. The final three chapters of the book cover regulatory aspects of design, quality and safety assessment and management and organisation. These volumes will provide an introduction to this important and fast-growing area for students and researchers in naval architecture and maritime engineering. It will also be of value to practising engineers as comprehensive reference book.

Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.

Gottfried Leibniz was a remarkable thinker who made fundamental contributions not only to philosophy, but also to the development of modern mathematics and science. At the centre of Leibniz's philosophy stands his metaphysics, an ambitious attempt to discover the nature of reality through the use of unaided reason. This volume provides a systematic and comprehensive account of the full range of Leibniz's thought, exploring the metaphysics in detail and showing its subtle and complex relationship to his views on logic, language, physics, and theology. Other chapters examine the intellectual context of his thought and its reception in the eighteenth century. New readers and nonspecialists will find this the most accessible and comprehensive guide to Leibniz currently available. Advanced students and specialists will find a conspectus of recent developments in the interpretation of Leibniz.

Gottfried Leibniz was a remarkable thinker who made fundamental contributions not only to philosophy, but also to the development of modern mathematics and science. At the centre of Leibniz's philosophy stands his metaphysics, an ambitious attempt to discover the nature of reality through the use of unaided reason. This volume provides a systematic and comprehensive account of the full range of Leibniz's thought, exploring the metaphysics in detail and showing its subtle and complex relationship to his views on logic, language, physics, and theology. Other chapters examine the intellectual context of his thought and its reception in the eighteenth century. New readers and nonspecialists will find this the most accessible and comprehensive guide to Leibniz currently available. Advanced students and specialists will find a conspectus of recent developments in the interpretation of Leibniz.

Science meets magic in this funny new fiction series, starring Izzy the Inventor and a lovable unicorn.Meet Izzy the Inventor in a laugh-out-loud series that brings together science, magic and a very lovable unicorn. Packed full of illustrations and easy-to-read text, this series is perfect for beginner readers and fans of Isadora Moon and The Naughtiest Unicorn.Every book contains ideas for science experiments and a QR code with links for more to try at home.#1 Izzy the Inventor and the Unexpected Unicorn#2 Izzy the Inventor and the Curse of Doom#3 Izzy the Inventor and the Time Travelling Gnome#4 Izzy the Inventor and the Teeny Tiny Ogres

Hyperirrealism is a merger of the disciplines of science and art for research in architecture.

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

This book surveys the application of the recently developed technique of the wavelet transform to a wide range of physical fields, including astrophysics, turbulence, meteorology, plasma physics, atomic and solid state physics, multifractals occurring in physics, biophysics (in medicine and physiology) and mathematical physics. The wavelet transform can analyze scale-dependent characteristics of a signal (or image) locally, unlike the Fourier transform, and more flexibly than the windowed Fourier transform developed by Gabor fifty years ago. The continuous wavelet transform is used mostly for analysis, but the discrete wavelet transform allows very fast compression and transmission of data and speeds up numerical calculation, and is applied, for example, in the solution of partial differential equations in physics. This book will be of interest to graduate students and researchers in many fields of physics, and to applied mathematicians and engineers interested in physical application.

This book surveys the application of the recently developed technique of the wavelet transform to a wide range of physical fields, including astrophysics, turbulence, meteorology, plasma physics, atomic and solid state physics, multifractals occurring in physics, biophysics (in medicine and physiology) and mathematical physics. The wavelet transform can analyze scale-dependent characteristics of a signal (or image) locally, unlike the Fourier transform, and more flexibly than the windowed Fourier transform developed by Gabor fifty years ago. The continuous wavelet transform is used mostly for analysis, but the discrete wavelet transform allows very fast compression and transmission of data and speeds up numerical calculation, and is applied, for example, in the solution of partial differential equations in physics. This book will be of interest to graduate students and researchers in many fields of physics, and to applied mathematicians and engineers interested in physical application.

Babies who love science can be anything! Move over Wonder Woman and Superman—here come Aerospace Engineer and Particle Physicist!Baby loves to explore the world of science! What’s next for Baby after

Human activity is undeniably affecting the rates of change of many parts of the global system. How this global change develops into the future is vitally important, but modelling these changes requires a complex, integrated assessment of a wide range of disciplines in science and social science. This book describes the structure, assumptions, philosophy and results of an advanced global integrated assessment model: TARGETS. For a number of future directions selected on the basis of divergent cultural perspectives, the model charts global implications in terms of population and health, energy, land- and water-use and biogeochemical cycles. This integrated assessment approach has led to innovative fresh insights into global change. The book will help policymakers formulate the strategies required for a sustainable global future. It will be of interest to a broad audience, from researchers and modellers of global change in science and social science, to policy analysts, decision makers an

Introduction to Atmospheric Chemistry is a concise, clear review of the fundamental aspects of atmospheric chemistry. In ten succinct chapters, it reviews our basic understanding of the chemistry of the Earth's atmosphere and discusses current environmental issues, including air pollution, acid rain, the ozone hole, and global change. Written by a well-known atmospheric science teacher, researcher, and author of several established textbooks, this book is an introductory textbook for beginning university courses in atmospheric chemistry. Also suitable for self instruction, numerous exercises and solutions make this textbook accessible to students covering atmospheric chemistry as a part of courses in atmospheric science, meteorology, environmental science, geophysics and chemistry. Together with its companion volume, Basic Physical Chemistry for the Atmospheric Sciences (second edition 2000; Cambridge University Press), Introduction to Atmospheric Chemistry provides a solid introductio

This book addresses key topics in social theory such as the basic structures of social life, the character of human activity, and the nature of individuality. Drawing on the work of Wittgenstein, the author develops an account of social existence that argues that social practices are the fundamental phenomenon in social life. This approach offers insight into the social formation of individuals, surpassing and critiquing the existing practice theories of Bourdieu, Giddens, Lyotard and Oakeshott. In bringing Wittgenstein's work to bear on issues of social theory the book shows the relevance of his work to a body of thought to which it has never been applied. The book will be of particular interest to philosophers of the social sciences, a wide range of social theorists in political science and sociology, as well as some literary theorists.

This book addresses key topics in social theory such as the basic structures of social life, the character of human activity, and the nature of individuality. Drawing on the work of Wittgenstein, the author develops an account of social existence that argues that social practices are the fundamental phenomenon in social life. This approach offers insight into the social formation of individuals, surpassing and critiquing the existing practice theories of Bourdieu, Giddens, Lyotard and Oakeshott. In bringing Wittgenstein's work to bear on issues of social theory the book shows the relevance of his work to a body of thought to which it has never been applied. The book will be of particular interest to philosophers of the social sciences, a wide range of social theorists in political science and sociology, as well as some literary theorists.

Recipient of the Prize of the Minister of Science, Culture, and Sport [of the State of Israel] for classical literature for the year 5762 [2001].The commentary, which accompanies the Hebrew biblical t

An incomparably useful examination of statistical methods for comparisonThe nature of doing science, be it natural or social, inevitably calls for comparison. Statistical methods are at the heart of s

With 25 million social media followers, I F'ing Love Science is the world's favorite source of science on the web, loved for its irreverent but celebratory approach to nerdy subject matter. In its fir

If science fiction stages the battle between humans and non-humans, whether alien or machine, who is elected to fight for us? In the classics of science fiction cinema, humanity is nearly always repre