Mathematics of Discrete Structures for Computer Science

Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text

There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics.

The book consists of 29 extended chapters which have been selected and invited from the submissions to the 1st International Conference on Computer Science, Applied Mathematics and Applications (ICCSA

While the structures of the Church of England provide practical resources for clergy as they make changes and transitions in their 'careers', very little has been done in the area of theological refle

King (statistics, Tarleton State U., Texas) explains how to apply research and statistical methods to current problems in a number of fields but with a special emphasis on computer science and informa

Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

This book deals with several topics in algebra useful for computer science applications and the symbolic treatment of algebraic problems, pointing out and discussing their algorithmic nature. The topi

Information Visualization: Perception for Design is a comprehensive guide to what the science of human perception tells us about how we should display information. The human brain is a super-computer

"This book presents high quality research on the design and implementation of information systems in the fields of agronomics, mathematics, economics, computer science, and the environment, offering h

In the 1860s and 1870s, leading neurologists used animal experimentation to establish that discrete sections of the brain regulate specific mental and physical functions. These discoveries had immediate medical benefits: David Ferrier's detailed cortical maps, for example, saved lives by helping surgeons locate brain tumors and haemorrhages without first opening up the skull. These experiments both incited controversy and stimulated creative thought, because they challenged the possibility of an extra-corporeal soul. This book examines the cultural impact of neurological experiments on late-Victorian Gothic romances by Robert Louis Stevenson, Bram Stoker, H. G. Wells and others. Novels like Dracula and Dr Jekyll and Mr Hyde expressed the deep-seated fears and visionary possibilities suggested by cerebral localization research, and offered a corrective to the linearity and objectivity of late Victorian neurology.

Mechatronics is a multidisciplinary field combining Mechanical, Electronic, Computer, and other Engineering fields to develop intelligent processes and products. Based on thirty years of extensive wor

Industrial optimization lies on the crossroads between mathematics, computer science, engineering and management. This book presents these fields in interdependence as a conversation between theoretic

Adler (mathematics, U. of Utah) provides a third edition of his textbook on calculus, probability, and statistics designed to teach freshman and sophomore level college life science students how mathe

Since computer scientists make decisions every day that have societal context and influence, an understanding of society and computing together should be integrated into computer science education. Sh

The past decade has seen a revolution in the field of spoken dialogue systems. As in other areas of Computer Science and Artificial Intelligence, data-driven methods are now being used to drive new me

Lamon (emerita, mathematics, statistics, and computer science; Marquette U.) presents a reference for researchers and curriculum developers in mathematics education, pre-service and in-service teacher

Signal processing applications have burgeoned in the past decade. During the same time, signal processing techniques have matured rapidly and now include tools from many areas of mathematics, computer

Blended learning is defined here as a combination of face-to-face teaching with computer-mediated instruction. Scholars mostly of education and psychology, but also mathematics, medicine, law, and lan

Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their i

Robert Willis (1800–1875) was a scientist, inventor and architectural historian of international repute. As Jacksonian Professor of Natural and Experimental Philosophy at Cambridge, he demonstrated specially made mechanical devices to huge audiences. First published in 1841, Principles of Mechanism provided the theory behind the demonstrations. He defined mechanism as the means by which any relations of motion could be realised. The book was extremely influential, with all books in English, French, and German on the subject for the next generation adopting Willis' classification and nomenclature. He worked closely with William Whewell, whose Mechanics of Engineering was published in the same year. These two books established the science of mechanism, and provided study materials for the rapidly growing engineering profession. The work became a standard textbook for engineering and mathematics students, with a second edition issued in 1870.

In operations research and computer science it is common practice to evaluate the performance of optimization algorithms on the basis of computational results, and the experimental approach should fol

Designed to address a lack of computer skills training in biological science education, this volume presents problem-centered instruction for using basic computer programming in biological research an

Clustering and Classification, Data Analysis, Data Handling and Business Intelligence are research areas at the intersection of statistics, mathematics, computer science and artificial intelligence. T

The Local Group of galaxies consists of the Milky Way and all of its neighbours. The proximity of these galaxies allows for detailed studies of the processes that have led to their formation, structures, and evolution. In particular, studies of the Local Group can test predictions of structure formation that are based on dark energy and cold dark matter. This book presents a collection of review papers, written by world experts, on some of the most important aspects of Local Group Astrophysics. It is an invaluable resource for both professional researchers and graduate students in this fascinating area of research.

Researchers (most of them from Brazil) in mathematics, computer science, and a range of biological and agricultural sciences survey mathematical and computational methods used in agriculture research.

Efficient signal processing algorithms are important for embedded and power-limited applications since, by reducing the number of computations, power consumption can be reduced significantly. Similarly, efficient algorithms are also critical to very large scale applications such as video processing and four-dimensional medical imaging. This self-contained guide, the only one of its kind, enables engineers to find the optimum fast algorithm for a specific application. It presents a broad range of computationally-efficient algorithms, describes their structure and implementation, and compares their relative strengths for given problems. All the necessary background mathematics is included and theorems are rigorously proved, so all the information needed to learn and apply the techniques is provided in one convenient guide. With this practical reference, researchers and practitioners in electrical engineering, applied mathematics, and computer science can reduce power dissipation for low-

The LNCS series reports state-of-the-art results in computer science research, development, and education, at a high level and in both printed and electronic form. Enjoying tight cooperation with the

With the onward march of science and technology, and the continuing quest for improvement, there is a growing curiosity about the world around us. Close examination of structures in nature can be rew

Writing with healthcare researchers in mind, Patricia Cerrito (mathematics, U. of Louisville) and John Cerrito, a retail and consulting pharmacist, describe how the investigation of healthcare databas

Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.

The present collection of formulas has been composed for students of economics or management science at universities, colleges and trade schools. It contains basic knowledge in mathematics, financial

Scholars of education from all over the world--many specializing in science and mathematics education, but others in, for example childhood or adult education--grapple with issues that arise from teac

Thin-film silicon materials and their alloys underpin a diverse range of electronic systems, from active matrix flat-panel displays, through solar panels for the 'green-power' generation, to surface micromanaged MEMS devices. Thin-film silicon can possess a diverse range of structures, from being fully amorphous to fully polycrystalline, as well as allowing mixed-phase states, such as micro- and nanocrystalline silicon. Such diversity has made large-area electronics one of the fastest growing semiconductor technologies, although not without introducing some complexity. This book addresses issues related to both fundamental materials science and applied technology and offers an overview of studies on film growth and crystallization, materials characterization, defects, metastability and carrier transport, as well as devices such as solar cells and thin-film transistors. The importance of developing efficient solar cells is reflected in the number of reports that seek to improve lifetime

This is a title on the foundations of defeasible logic, which explores the formal properties of everyday reasoning patterns whereby people jump to conclusions, reserving the right to retract them in the light of further information. Although technical in nature the book contains sections that outline basic issues by means of intuitive and simple examples. This book is primarily targeted at philosophers interested in the foundations of defeasible logic, logicians, and specialists in artificial intelligence and theoretical computer science.

Artificial intelligence (AI) is a field within computer science that is attempting to build enhanced intelligence into computer systems. This book traces the history of the subject, from the early dreams of eighteenth-century (and earlier) pioneers to the more successful work of today's AI engineers. AI is becoming more and more a part of everyone's life. The technology is already embedded in face-recognizing cameras, speech-recognition software, Internet search engines, and health-care robots, among other applications. The book's many diagrams and easy-to-understand descriptions of AI programs will help the casual reader gain an understanding of how these and other AI systems actually work. Its thorough (but unobtrusive) end-of-chapter notes containing citations to important source materials will be of great use to AI scholars and researchers. This book promises to be the definitive history of a field that has captivated the imaginations of scientists, philosophers, and writers for ce

Artificial intelligence (AI) is a field within computer science that is attempting to build enhanced intelligence into computer systems. This book traces the history of the subject, from the early dreams of eighteenth-century (and earlier) pioneers to the more successful work of today's AI engineers. AI is becoming more and more a part of everyone's life. The technology is already embedded in face-recognizing cameras, speech-recognition software, Internet search engines, and health-care robots, among other applications. The book's many diagrams and easy-to-understand descriptions of AI programs will help the casual reader gain an understanding of how these and other AI systems actually work. Its thorough (but unobtrusive) end-of-chapter notes containing citations to important source materials will be of great use to AI scholars and researchers. This book promises to be the definitive history of a field that has captivated the imaginations of scientists, philosophers, and writers for ce

The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.

Fifty-nine international academics, researchers, and computer science and engineering professionals contribute 15 chapters addressing the issues of which modeling languages are good for embedded syste