Mathematics of Discrete Structures for Computer Science

Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of info

This is my 2nd collection of 50 STEM (Science, Technology, Engineering, & Mathematics) science experiments for kids. Recommended for grades 3 and up. Each one has a snappy title, a brief descr

This is a collection of 50 STEM (Science, Technology, Engineering, & Mathematics) science experiments for kids. Recommended for grades 3 and up. Each one has a snappy title, a brief descriptio

This book is ideal for engineering, physical science and applied mathematics students and professionals who want to enhance their mathematical knowledge. Advanced Topics in Applied Mathematics covers four essential applied mathematics topics: Green's functions, integral equations, Fourier transforms and Laplace transforms. Also included is a useful discussion of topics such as the Wiener–Hopf method, finite Hilbert transforms, the Cagniard–De Hoop method and the proper orthogonal decomposition. This book reflects Sudhakar Nair's long classroom experience and includes numerous examples of differential and integral equations from engineering and physics to illustrate the solution procedures. The text includes exercise sets at the end of each chapter and a solutions manual, which is available for instructors.

How does nature work in our human-created city, suburb, and exurb/peri-urb? Indeed how is ecology - including its urban water, soil, air, plant, and animal foundations - spatially entwined with this great human enterprise? And how can we improve urban areas for both nature and people? Urban Ecology: Science of Cities explores the entire urban area: from streets, lawns, and parks to riversides, sewer systems, and industrial sites. The book presents models, patterns, and examples from hundreds of cities worldwide. Numerous illustrations enrich the presentation. Cities are analyzed, not as ecologically bad or good, but as places with concentrated rather than dispersed people. Urban ecology principles, traditionally adapted from natural-area ecology, now increasingly emerge from the distinctive features of cities. Spatial patterns and flows, linking organisms, built structures, and the physical environment highlight a treasure chest of useful principles. This pioneering interdisciplinary b

This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of re

Computational science is an exciting new field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and

The main objective of CSAIT 2013 is to provide a forum for researchers, educators, engineers and government officials involved in the general areas of Computational Sciences and Information Technology

There is a common misconception in educational circles that spelling and mathematics are opposites. A familiar cry of the struggling speller, "I can’t spell because I have a maths brain."Actually spel

The book investigates the rhetorical nature of scientific computer simulations, and it discusses the implications of those rhetorical strategies for how we understand, use and evaluate simulated evide

The study of astronomy offers an unlimited opportunity for us to gain a deeper understanding of our planet, the Solar System, the Milky Way Galaxy and the known Universe. Using the plain-language approach that has proven highly popular in Fleisch's other Student's Guides, this book is ideal for non-science majors taking introductory astronomy courses. The authors address topics that students find most troublesome, on subjects ranging from stars and light to gravity and black holes. Dozens of fully worked examples and over 150 exercises and homework problems help readers get to grips with the concepts in each chapter. An accompanying website features a host of supporting materials, including interactive solutions for every exercise and problem in the text and a series of video podcasts in which the authors explain the important concepts of every section of the book.

Mobile Robotics offers comprehensive coverage of the essentials of the field suitable for both students and practitioners. Adapted from Alonzo Kelly's graduate and undergraduate courses, the content of the book reflects current approaches to developing effective mobile robots. Professor Kelly adapts principles and techniques from the fields of mathematics, physics and numerical methods to present a consistent framework in a notation that facilitates learning and highlights relationships between topics. This text was developed specifically to be accessible to senior level undergraduates in engineering and computer science, and includes supporting exercises to reinforce the lessons of each section. Practitioners will value Kelly's perspectives on practical applications of these principles. Complex subjects are reduced to implementable algorithms extracted from real systems wherever possible, to enhance the real-world relevance of the text.

The study of astronomy offers an unlimited opportunity for us to gain a deeper understanding of our planet, the Solar System, the Milky Way Galaxy and the known Universe. Using the plain-language approach that has proven highly popular in Fleisch's other Student's Guides, this book is ideal for non-science majors taking introductory astronomy courses. The authors address topics that students find most troublesome, on subjects ranging from stars and light to gravity and black holes. Dozens of fully worked examples and over 150 exercises and homework problems help readers get to grips with the concepts in each chapter. An accompanying website features a host of supporting materials, including interactive solutions for every exercise and problem in the text and a series of video podcasts in which the authors explain the important concepts of every section of the book.

A book for those interested in how modern graphics programs work and how they can generate realistic-looking objects. It emphasises the mathematics behind computer graphics, most of which is included

Data and Computer Communications, 10e, is a two-time winner of the best Computer Science and Engineering textbook of the year award from the Textbook and Academic Authors Association. It is ideal for

For computer scientists, especially those in the security field, the use of chaos has been limited to the computation of a small collection of famous but unsuitable maps that offer no explanation of w

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of th

Unifying a range of topics that are currently scattered throughout the literature, this book offers a unique and definitive review of mathematical aspects of quantization and quantum field theory. The authors present both basic and more advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. They begin with a discussion of the mathematical structures underlying free bosonic or fermionic fields, like tensors, algebras, Fock spaces, and CCR and CAR representations (including their symplectic and orthogonal invariance). Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in-depth coverage, this text is essential reading for graduate students and rese

Efficient transfer between science and society is crucial for their future development. The rapid progress of information technology and computer systems offers a large potential and new perspectives

Computational methods for the modeling and simulation of the dynamic response and behavior of particles, materials and structural systems have had a profound influence on science, engineering and tech

The self-taught mathematician Hua Loo-Keng (1910–1985) has been credited with inspiring generations of mathematicians, while his papers on number theory are regarded as some of the most significant contributions made to the subject during the first half of the twentieth century. An Introduction to Higher Mathematics is based on the lectures given by Hua at the University of Science and Technology of China from 1958. The course reflects Hua's instinctive technique, using the simplest tools to tackle even the most difficult problems, and contains both pure and applied mathematics, emphasising the interdependent relationships between different branches of the discipline. With hundreds of diagrams, examples and exercises, this is a wide-ranging reference text for university mathematics and a testament to the teaching of one of the most eminent mathematicians of his generation.

An understanding of the senses - vision, hearing, touch, chemical and other non-human senses - is important not only for many fields of biology but also in applied areas such as human-computer interaction, robotics and computer games. Using information theory as a unifying framework, this is a wide-ranging survey of sensory systems, covering all known senses. The book draws on three unifying principles to examine senses: the Nyquist sampling theorem, Shannon's information theory, and the creation of different streams of information to subserve different tasks. This framework is used to discuss the fascinating role of sensory adaptation in the context of environment and lifestyle. Providing a fundamental grounding in sensory perception, the book then demonstrates how this knowledge can be applied to the design of human-computer interfaces and virtual environments. It is an ideal resource for both graduate and undergraduate students of biology, engineering (robotics) and computer science

Computer simulation has become an important means for obtaining knowledge about nature. The practice of scientific simulation and the frequent use of uncertain simulation results in public policy rais

Praise for the First Edition". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews". . . a very well writt

Turbulence pervades our world, from weather patterns to the air entering our lungs. This book describes methods that reveal its structures and dynamics. Building on the existence of coherent structures – recurrent patterns – in turbulent flows, it describes mathematical methods that reduce the governing (Navier–Stokes) equations to simpler forms that can be understood more easily. This second edition contains a new chapter on the balanced proper orthogonal decomposition: a method derived from control theory that is especially useful for flows equipped with sensors and actuators. It also reviews relevant work carried out since 1995. The book is ideal for engineering, physical science and mathematics researchers working in fluid dynamics and other areas in which coherent patterns emerge.

Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this bo

The design and analysis of data structures and efficient algorithms has gained considerable importance in recent years. The concept of "algorithm" is central in computer science, and "efficiency" is c

Raster graphics differs from the more traditional vector or line graphics in the sense that images are not made up from line segments but from discrete elements orderly arranged in a two-dimensional r

These proceedings will be of interest to Mathematicians, Applied Mathematicians, Computer Scientists, Physicists, Chemists, Engineers. The importance for the reader is that with this book one can find

Most of the contributors here are teachers of mathematics, though a few are from computer science and education generally--a reverse proportion from most books about computers in education. They discu

This well-balanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced error-correcting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masters-level students studying mathematics, computer science, electrical engineering or physics.

This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of re

This well-balanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced error-correcting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masters-level students studying mathematics, computer science, electrical engineering or physics.

This book blends traditional teaching approaches with the use of mathematics, together with the use of a hardware description language and a concrete processor as vehicles for "hands-on" modelling and

The typical computational approach to object understanding derives shape information from the 2D outline of the objects. For complex object structures, however, such a planar approach cannot determine

Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected e

This book provides a rigorous presentation of the mathematical theory underlying subdivision surfaces as it is used in computer graphics and animation. It is excellent preparation for reading more adv

For general readers, Lerner, who has degrees in history and library science from Columbia U., provides a brief and selective history of libraries and how people have collected and organized records of

Visualization is one of the most active and exciting areas of Mathematics and Computing Science, and indeed one which is only beginning to mature. Current visualization algorithms break down for very