Mathematics of Discrete Structures for Computer Science

This book provides a comprehensive treatment of the Gross–Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the periodic potential. It takes the mean-field model of the Bose–Einstein condensation as the starting point of analysis and addresses the existence and stability of localized modes. The mean-field model is simplified further to the coupled nonlinear Schrödinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrödinger equations. One of the important features of such systems is the existence of band gaps in the wave transmission spectra, which support stationary localized modes known as the gap solitons. These localized modes realise a balance between periodicity, dispersion and nonlinearity of the physical system. Written for researchers in applied mathematics, this book mainly focuses on the mathematical properties of the Gross–Pitaevskii equation. It also serves as a reference for theoretical physicists inter

Mankin Mak's textbook provides a self-contained course on atmospheric dynamics. The first half is suitable for senior undergraduates, and develops the physical, dynamical and mathematical concepts at the fundamental level. The second half of the book is aimed at more advanced students who are already familiar with the basics. The contents have been developed from many years of the author's teaching at the University of Illinois. Discussions are supplemented with schematics, weather maps and statistical plots of the atmospheric general circulation. Students often find the connection between theoretical dynamics and atmospheric observation somewhat tenuous, and this book demonstrates a strong connection between the key dynamics and real observations. This textbook is an invaluable asset for courses in atmospheric dynamics for advanced students and researchers in atmospheric science, ocean science, weather forecasting, environmental science, and applied mathematics. Some background in mat

A guide to computational thinking education, with a focus on artificial intelligence literacy and the integration of computing and physical objects. Computing has become an essential part of today’s primary and secondary school curricula. In recent years, K–12 computer education has shifted from computer science itself to the broader perspective of computational thinking (CT), which is less about technology than a way of thinking and solving problems―“a fundamental skill for everyone, not just computer scientists,” in the words of Jeanette Wing, author of a foundational article on CT. This volume introduces a variety of approaches to CT in K–12 education, offering a wide range of international perspectives that focus on artificial intelligence (AI) literacy and the integration of computing and physical objects. The book first offers an overview of CT and its importance in K–12 education, covering such topics as the rationale for teaching CT; programming as a general problem-solving

This 1989 book is about chaos, fractals and complex dynamics, and is addressed to all people who have some familiarity with computers and enjoy using them. The mathematics has been kept simple, with few formulae, yet the reader is introduced to and can learn about an area of current scientific research which was scarcely possible before the availability of computers. The introduction is achieved through the extensive use of computer graphics. The book is divided into two main parts: in the first the most interesting problems are described, with, in each case, a solution in the form of a computer program. A large number of exercises enable the reader to undertake his or her own experimental work. In the second part, example programs are given for specific machines and operating systems; details refer to MS-DOC and Turbo-Pascal, UNIX 4.2 BSD with Berkley Pascal and C. Other implementations of the graphics routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST.

This 1989 book is about chaos, fractals and complex dynamics, and is addressed to all people who have some familiarity with computers and enjoy using them. The mathematics has been kept simple, with few formulae, yet the reader is introduced to and can learn about an area of current scientific research which was scarcely possible before the availability of computers. The introduction is achieved through the extensive use of computer graphics. The book is divided into two main parts: in the first the most interesting problems are described, with, in each case, a solution in the form of a computer program. A large number of exercises enable the reader to undertake his or her own experimental work. In the second part, example programs are given for specific machines and operating systems; details refer to MS-DOC and Turbo-Pascal, UNIX 4.2 BSD with Berkley Pascal and C. Other implementations of the graphics routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST.

Peter Goos, Department of Statistics, University of Leuven, Faculty of Bio-Science Engineering and University of Antwerp, Faculty of Applied Economics, BelgiumDavid Meintrup, Department of Mathematics

Providing in-depth coverage, this book covers the fundamentals of computation and programming in C language. Essential concepts including operators and expressions, input and output statements, loop statements, arrays, pointers, functions, strings and preprocessors are described in a lucid manner. A unique approach - 'Learn by quiz' - features questions based on confidence-based learning methodology. It helps the reader to identify the right answer with adequate explanation and reasoning as to why the other options are incorrect. Computer programs and review questions are interspersed throughout the text. The book is appropriate for undergraduate students of engineering, computer science and information technology. It can be used for self-study and assists in the understanding of theoretical concepts and their applications.

One of the motivating questions in materials research today is, how can elements be combined to produce a solid with specified properties? This book is intended to acquaint the reader with established principles of crystallography and cohesive forces that are needed to address the fundamental relationship between the composition, structure and bonding. Starting with an introduction to periodic trends, the book discusses crystal structures and the various primary and secondary bonding types, and finishes by describing a number of models for predicting phase stability and structure. Containing a large number of worked examples, exercises, and detailed descriptions of numerous crystal structures, this book is primarily intended as an advanced undergraduate or graduate level textbook for students of materials science. It will also be useful to scientists and engineers who work with solid materials.

Molecular- and Nano-Tubes?summarizes recent advancements in the synthesis, fabrication and applications of tubular structures.??An interdisciplinary overview of innovative science? focused on?tubular

Drawing together contributions from history, anthropology, sociology, political science and religious studies, this collection of original essays interrogates the new structures and conditions of Isla

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selecte

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selecte

This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.

Engineering Problem Solving with C++, 4e, is ideal for one/two semester courses in Engineering and Computer Science at the freshman/sophomore level. This text is a clear, concise introduc

Examines important discoveries and advances in the field of computer science and discusses their impact on civilization.

This book includes the probability of events, discrete random variables and their distribution, continuous random variables and their distribution, digital characteristics of random variables, law of large numbers and central limit theorem, sampling distribution, parameter estimation and hypothesis testing.All of the authors of this book have the background of visiting British and American university. The writing language is easy to understand, and the content has moderate difficulty.This book can be used for the teaching of probability and statistics courses of Sino-foreign cooperation projects and foreign student programs in universities of science and engineering (non-mathematics majors), as well as bilingual teaching of probability and statistics.本書內容包括事件的概率、離散型隨機變量及其分佈、連續型隨機變量及其分佈、隨機變量的數字特徵、大數定律與中心極限定理、抽樣分佈、參數估計和假設檢驗。本書編著者均有英美訪學背景，英文語言簡單易懂，寫作簡約，內容難易適中，便於學習。本書可供理工科大學(非數學專業)中外合作辦學項目和留

The applications of topological techniques for understanding molecular structures have become increasingly important over the past thirty years. In this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, while learning the role these play in understanding molecular structures. Most of the results that are described in the text are motivated by questions asked by chemists or molecular biologists, though the results themselves often go beyond answering the original question asked. There is no specific mathematical or chemical prerequisite; all the relevant background is provided. The text is enhanced by nearly 200 illustrations and more than 100 exercises. Reading this fascinating book, undergraduate mathematics students can escape the world of pure abstract theory and enter that of real molecules, while chemists and biologists will find simple, clear but rigorous definitions of mathematical concepts they handle intuitive

Throughout his life, Benjamin Banneker was known and admired for his work in science, mathematics, and astronomy, just to name a few pursuits. But even when he was born in Maryland in 1731, he was alr

A practical text suitable for an introductory or advanced course in formal methods, this book presents a mathematical approach to modelling and designing systems using an extension of the B formal method: Event-B. Based on the idea of refinement, the author's systematic approach allows the user to construct models gradually and to facilitate a systematic reasoning method by means of proofs. Readers will learn how to build models of programs and, more generally, discrete systems, but this is all done with practice in mind. The numerous examples provided arise from various sources of computer system developments, including sequential programs, concurrent programs and electronic circuits. The book also contains a large number of exercises and projects ranging in difficulty. Each of the examples included in the book has been proved using the Rodin Platform tool set, which is available free for download at www.event-b.org.

Excellent coverage of kinematics, momentum principle, Newtonian fluid, rotating fluids, compressibility, and more. Geared toward advanced undergraduate and graduate students of mathematics and science

"A first year undergraduate textbook for computer science majors, this book can also be used by anyone who wants to learn Java on their own. After reading the textbook and completing the attached proj

The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimensio

Numerical algorithms, modern programming techniques, and parallel computing are often taught serially across different courses and different textbooks. The need to integrate concepts and tools usually comes only in employment or in research - after the courses are concluded - forcing the student to synthesise what is perceived to be three independent subfields into one. This book provides a seamless approach to stimulate the student simultaneously through the eyes of multiple disciplines, leading to enhanced understanding of scientific computing as a whole. The book includes both basic as well as advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Some of the advanced topics include wavelets, high-order methods, non-symmetric systems, and parallelization of sparse systems. The material covered is suited to students from engineering, computer science, physics and mathematics.

This book brings together contributions from researchers within various social science disciplines who seek to redefine the methods and topics that constitute the study of work. They investigate work activity in ways that do not reduce it to a 'psychology' of individual cognition nor to a 'sociology' of societal structures and communication. A key theme in the material is the relationship between theory and practice. This is not an abstract problem of interest merely to social scientists. Rather, it is discussed as an issue that working people address when they attempt to understand a task and communicate its demands. Mindful practices and communicative interaction are examined as situated issues at work in the reproduction of communities of practice in a variety of settings including: courts of law, computer software design, the piloting of airliners, the coordination of air traffic control, and traffic management in underground railway systems.

Bayesian probability theory has emerged not only as a powerful tool for building computational theories of vision, but also as a general paradigm for studying human visual perception. This 1996 book provides an introduction to and critical analysis of the Bayesian paradigm. Leading researchers in computer vision and experimental vision science describe general theoretical frameworks for modelling vision, detailed applications to specific problems and implications for experimental studies of human perception. The book provides a dialogue between different perspectives both within chapters, which draw on insights from experimental and computational work, and between chapters, through commentaries written by the contributors on each others' work. Students and researchers in cognitive and visual science will find much to interest them in this thought-provoking collection.

Bayesian probability theory has emerged not only as a powerful tool for building computational theories of vision, but also as a general paradigm for studying human visual perception. This 1996 book provides an introduction to and critical analysis of the Bayesian paradigm. Leading researchers in computer vision and experimental vision science describe general theoretical frameworks for modelling vision, detailed applications to specific problems and implications for experimental studies of human perception. The book provides a dialogue between different perspectives both within chapters, which draw on insights from experimental and computational work, and between chapters, through commentaries written by the contributors on each others' work. Students and researchers in cognitive and visual science will find much to interest them in this thought-provoking collection.

Gale (political science, U. of Victoria, British Columbia) examines the structures and operation of the International Tropical Timber Organization (ITTO), created to balance tropical timber demand wit

Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a cookbook approach, giving concrete and geometric explanations, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.

Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a cookbook approach, giving concrete and geometric explanations, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.

A cornerstone of undergraduate mathematics, science, and engineering, this presentation of the fundamentals of linear algebra is unique in its emphasis and integration of computational skills and math

Cognitive scientists have a variety of approaches to studying cognition: experimental psychology, computer science, robotics, neuroscience, educational psychology, philosophy of mind, and psycholingu

Psycholinguistics – the field of science that examines the mental processes and knowledge structures involved in the acquisition, comprehension, and production of language – had a strong m

This book brings together the leading authors currently working at the intersection of social sciences and transport science and offers rich consideration of the issues, practices and structures of mu

This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.

Since 1985 Nell Dale's texts have helped shape the way computer science is taught. Now she and Henry Walker, an accomplished instructor and author in his own right, are proposing a new focus for the j

Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics.B

Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics.

This comprehensive biography traces the life and works of Robert Maillart, one of the most important engineers and designers of the twentieth century. His career developed around a central issue of modern technological society: the debate between two antithetical views of engineering opposing applied science, which relied on general mathematical theories for understanding structures against design, which Maillart championed. Maillart considered structures not merely works of utility but also as works of art. As utilitarian objects, he created a series of innovations of lasting significance. Aesthetically, Maillart shaped his three innovations in concrete to create surprising and often stunning new forms. Providing an analysis of these innovations, this biography also connects Maillart's aesthetic ideas with the private and professional context in which he worked.

This book examines tends in modern biotechnology. It covers all aspects of this interdisciplinary technology, from chemistry to computer science.