Mathematics of Discrete Structures for Computer Science

What is abstraction? To what extent can it account for the existence and identity of abstract objects? And to what extent can it be used as a foundation for mathematics? Kit Fine provides rigorous and

"This man could plainly do for mathematics what Brian Cox has done for physics." (Sunday Times). How does a genius see the world? Where and how does inspiration strike? Cedric Villani takes us on a me

Discrete optimization problems are everywhere, from traditional operations research planning (scheduling, facility location and network design); to computer science databases; to advertising issues in viral marketing. Yet most such problems are NP-hard; unless P = NP, there are no efficient algorithms to find optimal solutions. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first section is devoted to a single algorithmic technique applied to several different problems, with more sophisticated treatment in the second section. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithm courses

Since its publication in 1982 Sir Bernard Feilden's Conservation of Historic Buildings has become the standard text for architects and others involved in the conservation of historic structures. Leadi

Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one indepen

Fortified structures have been in existence for thousands of years. In ancient and medieval times castles were the ultimate symbol of power, dominating their surroundings, and marking the landscape wi

Textile fabrics of various structures are being increasingly used by engineers of different disciplines for working out elegant solution of problems, be it in designing a spacecraft, an automobile, a

What biological and cognitive forces have shaped humankind's musical behavior and therich global repertoire of musical structures? What is music for, and why does every human culturehave it? What are

Originally published in 2000, this is the first volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which is unifying across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 1 includes the abstract parabolic theory for the finite and infinite cases and corresponding PDE illustrations as well as various abstract hyperbolic settings in the finite case. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering

Alexander von Humboldt (1769–1859) was a naturalist, explorer and philanthropist now well known for his multidisciplinary approach to science. First published in English in 1873, this two-volume biography was translated from the German edition of 1872, edited by Karl Bruhns, which had been compiled in commemoration of the centenary of Humboldt's birth. Incorporating numerous extracts of Humboldt's own warmly written letters and anecdotes from his many acquaintances, it charts his travels in South America, Asia and Europe. Volume 1 covers his early exploratory trips and some of his lesser known exploits, including becoming Superintendent of Mines in Northern Bavaria and his research on the sixteenth-century eruption of Nevado del Altar in Ecuador. Volume 2 covers his later life, exploring an impecunious period in Paris at the École Polytechnique, where he shared rooms with the French chemist Gay-Lussac, and his later association with Frederick William IV of Prussia.

This new Springer handbook has authoritative, detailed chapters addressing the physics, mathematics, experimental evidence, and cosmological implications of the profound idea that gravity is not a for

For courses in Music Theory A text/workbook combination that gives students the tools to understand harmonic structures With an emphasis on learning by doing, The Practice of Harmony, Seventh Edit

The ultimate aim of IUPAC nomenclature is to provide unequivocal and comprehensible names for all kinds of chemical structures. This requires a rational basis from which comprehensible names can be de

Indispensable for students of modern physics, this text provides the necessary background in mathematics to study the concepts of electromagnetic theory and quantum mechanics. Topics include vector al

This classic in film theory, presents a systematic study of the techniques of the film medium and of their potential uses for creating formal structures in individual films such as Dovzhenko's Earth,

This classic in film theory, presents a systematic study of the techniques of the film medium and of their potential uses for creating formal structures in individual films such as Dovzhenko's Earth,

The Uses of Haiti tells the truth about uncomfortable matters—uncomfortable, that is, for the structures of power and the doctrinal framework that protects them from scrutiny. It tells the truth about

This classic is an ideal introduction for students into the methodology and thinking of higher mathematics. It covers material not usually taught in the more technically-oriented introductory classes

This book is intended for the undergraduate one or two semester course in modern algebra, also called abstract algebra. It follows that basic plan, using the axioms or rules to understand structures s

Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. On

Oswald Spengler was born in 1880 at Blankenburg, Germany. He studied mathematics, philosophy, and history at Munich and Berlin. Except for his doctor's thesis on Heraclitus, he published nothing befor

Introduction to digital imaging covering core techniques of image capture and the display of monochrome and color images. Basic tools required to describe sampling and image display on real devices are presented within a powerful mathematical framework. Starting with an overview of digital imaging, mathematical representation, and the elementary display of images, the topics progressively move to quantization, spatial sampling, photometry and colorimetry, and color sampling, and conclude with the estimation of image model parameters, and image restoration. The characterization of input and output devices is also covered. The reader will learn the processes used to generate accurate images, and appreciate the mathematical basis required to test and evaluate new devices. Contains illustrations, real-world examples, and end-of-chapter homework problems. Suitable for advanced undergraduate and graduate courses in digital imaging in electrical engineering and computer science departments.

Elementary real analysis deserves its place as a core subject in the undergraduate mathematics curriculum because of the way it provides a rigorous foundation for the theory of calculus through logica

The Library of Alexandria was the largest library of its time and a major center for learning and scholarly research, particularly in the fields of astronomy, geography, mathematics, and medicine. Ca

This monograph deals with the structure, generation and stability of flames from a mathematical point of view. It uses a specific mathematical approach to provide a unified theoretical description of fundamental flame phenomena. Its importance stems from the fact that it provides the first clear evidence that combustion can be legitimately treated as a mathematical science as well as an empirical one. The book will be of interest to researchers in combustion, fluid mechanics and applied mathematics, as well as to graduate students taking advanced courses in these areas.

This updated textbook provides a balanced, seamless treatment of both classic, analytic methods and contemporary, computer-based techniques for conceptualizing and designing a structure. New to the se

This updated textbook provides a balanced, seamless treatment of both classic, analytic methods and contemporary, computer-based techniques for conceptualizing and designing a structure. New to the se

Details the history of the computer software and consumer electronics company known for such innovative and popular products as the iPod, iPhone, iPad, and Macintosh line of computers.

Elements of Fluid Dynamics is intended to be a basic textbook, useful for undergraduate and graduate students in different fields of engineering, as well as in physics and applied mathematics. The mai

Elements of Fluid Dynamics is intended to be a basic textbook, useful for undergraduate and graduate students in different fields of engineering, as well as in physics and applied mathematics. The mai

From one of the foremost interpreters for lay readers of the history and meaning of mathematics: a stimulating account of the origins of mathematical thought and the development of numerical theory. I

This book is concerned with the ionosphere and the magnetosphere, and the theory of their effect on radio waves. It includes accounts of some mathematical topics now widely used in this study, particularly W. K. B. approximations, Airy integral functions and integration by steepest descents. The subject is divided into ray theory and full wave theory. Ray theory is useful for high frequencies when the ionosphere is treated as a horizonally stratified medium. The discussion of the magnetosphere, whose structure is more complicated, includes an account of whistlers and ion cyclotron whistlers. The book has been planned both for final year undergraduates and as a reference book for research. It is suitable as a course book on radio propagation for students of physics or electrical engineering or mathematics. Some of the topics are presented from an elementary viewpoint so as to help undergraduates new to the subject. The later parts are more advanced. Because the subject is so large and h

Model checking is a computer-assisted method for the analysis of dynamical systems that can be modeled by state-transition systems. Drawing from research traditions in mathematical logic, programming

With the rise of multi-core architecture, parallel programming is an increasingly important topic for software engineers and computer system designers. Written by well-known researchers Larry Snyder a

This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. The first half of the book provides a basic background in numerical analysis

This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's toti

This is a comprehensive, authoritative and innovative account of Pythagoras and Pythagoreanism, one of the most enigmatic and influential philosophies in the West. In twenty-one chapters covering a timespan from the sixth century BC to the seventeenth century AD, leading scholars construct a number of different images of Pythagoras and his community, assessing current scholarship and offering new answers to central problems. Chapters are devoted to the early Pythagoreans, and the full breadth of Pythagorean thought is explored including politics, religion, music theory, science, mathematics and magic. Separate chapters consider Pythagoreanism in Plato, Aristotle, the Peripatetics and the later Academic tradition, while others describe Pythagoreanism in the historical tradition, in Rome and in the pseudo-Pythagorean writings. The three great lives of Pythagoras by Diogenes Laertius, Porphyry and Iamblichus are also discussed in detail, as is the significance of Pythagoras for the Middle

This is a comprehensive, authoritative and innovative account of Pythagoras and Pythagoreanism, one of the most enigmatic and influential philosophies in the West. In twenty-one chapters covering a timespan from the sixth century BC to the seventeenth century AD, leading scholars construct a number of different images of Pythagoras and his community, assessing current scholarship and offering new answers to central problems. Chapters are devoted to the early Pythagoreans, and the full breadth of Pythagorean thought is explored including politics, religion, music theory, science, mathematics and magic. Separate chapters consider Pythagoreanism in Plato, Aristotle, the Peripatetics and the later Academic tradition, while others describe Pythagoreanism in the historical tradition, in Rome and in the pseudo-Pythagorean writings. The three great lives of Pythagoras by Diogenes Laertius, Porphyry and Iamblichus are also discussed in detail, as is the significance of Pythagoras for the Middle

The book of nature is written in the language of mathematics ?-- Galileo Galilei?How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it

The purpose of this book is to examine three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. It is ideal for a "capstone" co