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Go To: The Story of the Math Majors, Bridge Players, Engineers, Chess Wizards, Maverick Scientists and Iconoclasts- the Programmers Who Created the Software Revolution
by Steve LohrIn Go To, Steve Lohr chronicles the history of software from the early days of complex mathematical codes mastered by a few thousand to today's era of user-friendly software and over six million professional programmers worldwide. Lohr maps out the unique seductions of programming, and gives us an intimate portrait of the peculiar kind of genius that is drawn to this blend of art, science, and engineering, introducing us to the movers and shakers of the 1950s and the open-source movement of today. With original reporting and deft storytelling, Steve Lohr shows us how software transformed the world, and what it holds in store for our future.
God Created the Integers: The Mathematical Breakthroughs that Changed History
by Stephen HawkingBestselling author and physicist Stephen Hawking explores the masterpieces of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians. "
God and the Mathematics of Infinity: What Irreducible Mathematics Says about Godhood
by H. Chris RansfordDrawing on the science and mathematics of infinity, H. Chris Ransford analyzes the traditional concept of godhood and reaches surprising conclusions. He addresses humankind's abiding core debate on the meaning of spirituality and God. Using mathematics, he explores key questions within this debate: for instance, why does evil exist if there is a God? The book fastidiously does not take sides nor proffers opinions, it only follows allowable mathematics wherever it leads. By doing so, it makes a major contribution to an understanding of the nature of reality.
Goedel's Way: Exploits into an undecidable world
by Gregory Chaitin Newton da Costa Francisco DoriaKurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines.The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8
Gold Medal Physics: The Science of Sports
by John Eric GoffNothing is quite as thrilling as watching superior athletes do the seemingly impossible. From Doug Flutie's "Hail Mary" pass to Lance Armstrong's record-breaking climb of Alp d'Huez to David Beckham's astounding ability to bend a soccer kick, we marvel and wonder, "How did they do that?" Well, physics professor John Eric Goff has the answers.This tour of the wide world of sports uses some of the most exhilarating feats in recent athletic history to make basic physics concepts accessible and fun. Goff discusses the science behind American football, soccer, cycling, skating, diving, long jumping, and a host of other competitive sports. Using elite athletes such as Greg Louganis and Bob Beamon as starting points, he explains in clear, lively language the basic physical properties involved in amazing and everyday athletic endeavors. Accompanied by illustrations and mathematical equations, each chapter builds on knowledge imparted in earlier portions of the book to provide a firm understanding of the concepts involved.Fun, witty, and imbued throughout with admiration for the simple beauty of physics, Gold Medal Physics is sure to inspire readers to think differently about the next sporting event they watch.
Gold Medal Physics: The Science of Sports
by John Eric GoffA physicist explains the science behind some of the greatest feats in sports history—from diving like Greg Louganis to bending it like Beckham.Nothing is quite as thrilling as watching superior athletes do the seemingly impossible. From Doug Flutie's "Hail Mary" pass to Lance Armstrong's record-breaking climb of Alp d'Huez to David Beckham's astounding ability to bend a soccer kick, we marvel and wonder, "How did they do that?" Well, physics professor John Eric Goff has the answers.In this scientific tour of the wide world of sports, John Eric Goff discusses the science behind American football, soccer, cycling, skating, diving, long jumping, and a host of other competitive sports. Using elite athletes as starting points, Goff explains the basic physical properties involved in amazing and everyday athletic endeavors. Accompanied by illustrations and mathematical equations, each chapter builds on knowledge imparted in earlier chapters to provide a firm understanding of the concepts involved.Fun, witty, and imbued throughout with admiration for the simple beauty of physics, Gold Medal Physics is sure to inspire readers to think differently about the next sporting event they watch.
Goldbach’s Problem
by Michael Th. RassiasImportant results surrounding the proof of Goldbach's ternary conjecture are presented in this book. Beginning with an historical perspective along with an overview of essential lemmas and theorems, this monograph moves on to a detailed proof of Vinogradov's theorem. The principles of the Hardy-Littlewood circle method are outlined and applied to Goldbach's ternary conjecture. New results due to H. Maier and the author on Vinogradov's theorem are proved under the assumption of the Riemann hypothesis. The final chapter discusses an approach to Goldbach's conjecture through theorems by L. G. Schnirelmann. This book concludes with an Appendix featuring a sketch of H. Helfgott's proof of Goldbach's ternary conjecture. The Appendix also presents some biographical remarks of mathematicians whose research has played a seminal role on the Goldbach ternary problem. The author's step-by-step approach makes this book accessible to those that have mastered classical number theory and fundamental notions of mathematical analysis. This book will be particularly useful to graduate students and mathematicians in analytic number theory, approximation theory as well as to researchers working on Goldbach's problem.
Golden Numbers: A California Number Book
by David DomeniconiCalifornia's symbols, facts, landscapes, and history are introduced using numbers. Each subject is introduced with a poem, followed by more detailed information. Topics include volcanoes, presidios, the desert tortoise, frogs, and monarch butterflies.
Golf by the Numbers: How Stats, Math, and Physics Affect Your Game
by Roland MintonHow do the world’s greatest golfers improve their game? Practice, sure, but Roland Minton says mathematics and statistics are also key to their success. Golf by the Numbers analyzes the mathematical strategies behind the sport, giving fans a behind-the-scenes look at how numbers drive the game.Computers, GPS trackers, swing simulators, and high-speed cameras have introduced new and exciting ways of seeing and understanding the complicated and endlessly fascinating game of golf. Players like Phil Mickelson are so good because they review the results of every swing they take. Minton’s comprehensive analysis of statistics taken from the PGA Tour’s ShotLink system walks readers through the mountains of data that pros use to inform and refine their play. The result is an insider’s perspective of how the world’s greatest golfers apply mathematics to the sport.Minton discusses randomness in golf (especially how much luck is involved in putting) as well as aggressive and cautious strategies both on and off the greens, and he explains, by the numbers, just how Tiger Woods was so dominant from 2004 to 2009.Here is a book that tells some truly engaging stories of modern golf, featuring famous players and memorable tournaments, all through the lens of elementary probability theory. Minton’s informal style and clear and direct explanations make even the most detailed discussions accessible to all curious-minded golfers. His mathematical morsels are not only enjoyable to read—they may even help you improve your game.
Good Math: A Geek's Guide to the Beauty of Numbers, Logic, and Computation
by Mark C. Chu-CarrollMathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you.Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird.Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing.If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.
Good Vibrations: The Physics of Music
by Barry ParkerWhy does a harpsichord sound different from a piano? For that matter, why does middle C on a piano differ from middle C on a tuning fork, a trombone, or a flute? Good Vibrations explains in clear, friendly language the out-of-sight physics responsible not only for these differences but also for the whole range of noises we call music.The physical properties and history of sound are fascinating to study. Barry Parker's tour of the physics of music details the science of how instruments, the acoustics of rooms, electronics, and humans create and alter the varied sounds we hear. Using physics as a base, Parker discusses the history of music, how sounds are made and perceived, and the various effects of acting on sounds. In the process, he demonstrates what acoustics can teach us about quantum theory and explains the relationship between harmonics and the theory of waves.Peppered throughout with anecdotes and examples illustrating key concepts, this invitingly written book provides a firm grounding in the actual and theoretical physics of music.
Goodness-of-Fit-Techniques
by RalphB. D'AgostinoConveniently grouping methods by techniques, such as chi-squared and empirical distributionfunction , and also collecting methods of testing for specific famous distributions, this usefulreference is the fust comprehensive.review of the extensive literature on the subject. It surveysthe leading methods of testing fit . .. provides tables to make the tests available . .. assessesthe comparative merits of different test procedures . .. and supplies numerical examples to aidin understanding these techniques.Goodness-of-Fit Techniques shows how to apply the techniques . .. emphasizes testing for thethree major distributions, normal, exponential, and uniform . .. discusses the handling of censoreddata .. . and contains over 650 bibliographic citations that cover the field.Illustrated with tables and drawings, this volume is an ideal reference for mathematical andapplied statisticians, and biostatisticians; professionals in applied science fields, including psychologists,biometricians , physicians, and quality control and reliability engineers; advancedundergraduate- and graduate-level courses on goodness-of-fit techniques; and professional seminarsand symposia on applied statistics, quality control, and reliability.
Google's PageRank and Beyond: The Science of Search Engine Rankings
by Amy N. Langville Carl D. MeyerWhy doesn't your home page appear on the first page of search results, even when you query your own name? How do other web pages always appear at the top? What creates these powerful rankings? And how? The first book ever about the science of web page rankings, Google's PageRank and Beyond supplies the answers to these and other questions and more. The book serves two very different audiences: the curious science reader and the technical computational reader. The chapters build in mathematical sophistication, so that the first five are accessible to the general academic reader. While other chapters are much more mathematical in nature, each one contains something for both audiences. For example, the authors include entertaining asides such as how search engines make money and how the Great Firewall of China influences research. The book includes an extensive background chapter designed to help readers learn more about the mathematics of search engines, and it contains several MATLAB codes and links to sample web data sets. The philosophy throughout is to encourage readers to experiment with the ideas and algorithms in the text. Any business seriously interested in improving its rankings in the major search engines can benefit from the clear examples, sample code, and list of resources provided. Many illustrative examples and entertaining asides MATLAB code Accessible and informal style Complete and self-contained section for mathematics review
Gorenstein Homological Algebra
by Alina IacobGorenstein homological algebra is an important area of mathematics, with applications in commutative and noncommutative algebra, model category theory, representation theory, and algebraic geometry. While in classical homological algebra the existence of the projective, injective, and flat resolutions over arbitrary rings are well known, things are a little different when it comes to Gorenstein homological algebra. The main open problems in this area deal with the existence of the Gorenstein injective, Gorenstein projective, and Gorenstein flat resolutions. Gorenstein Homological Algebra is especially suitable for graduate students interested in homological algebra and its applications.
Gottfried Wilhelm Leibniz: The Polymath Who Brought Us Calculus
by M. B. W. TentGottfried Wilhelm Leibniz: The Polymath Who Brought Us Calculus focuses on the life and accomplishments of one of the seventeenth century's most influential mathematicians and philosophers. The book, which draws on Leibniz's written works and translations, and reconstructs dialogues Leibniz may have had based on the historical record of his life ex
Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces
by Marek Golasiński Juno MukaiThis is a monograph that details the use of Siegel's method and the classical results of homotopy groups of spheres and Lie groups to determine some Gottlieb groups of projective spaces or to give the lower bounds of their orders. Making use of the properties of Whitehead products, the authors also determine some Whitehead center groups of projective spaces that are relevant and new within this monograph.
Governance and Opportunity in Metropolitan America
by National Research CouncilAmerica's cities have symbolized the nation's prosperity, dynamism, and innovation. Even with the trend toward suburbanization, many central cities attract substantial new investment and employment. Within this profile of health, however, many urban areas are beset by problems of economic disparity, physical deterioration, and social distress.This volume addresses the condition of the city from the perspective of the larger metropolitan region. It offers important, thought-provoking perspectives on the structure of metropolitan-level decisionmaking, the disadvantages faced by cities and city residents, and expanding economic opportunity to all residents in a metropolitan area. The book provides data, real-world examples, and analyses in key areas: Distribution of metropolitan populations and what this means for city dwellers, suburbanites, whites, and minorities.How quality of life depends on the spatial structure of a community and how problems are based on inequalities in spatialopportunity--with a focus on the relationship between taxes and services.The role of the central city today, the rationale for revitalizing central cities, and city-suburban interdependence. The book includes papers that provide in-depth examinations of zoning policy in relation to patterns of suburban development; regionalism in transportation and air quality; the geography of economic and social opportunity; social stratification in metropolitan areas; and fiscal and service disparities within metropolitan areas.
Government Consolidation and Economic Development in Allegheny County and the City of Pittsburgh
by Sally Sleeper Rae W. ArchibaldThis report concludes that, although evidence is mixed and effects difficult to measure, consolidating the City of Pittsburgh and Allegheny County could enhance economic development by unifying leadership, improving policy direction and coordination, and sharpening economic-development initiatives. Increased collaboration with the private sector also is important, and combining only two governments still leaves the region highly fragmented.
Grade 1 Math Speed Drills: Beginning Arithmetic
by Rod and Staff PublishersThis small tablet of 72 speed drills provides timed practice of addition and subtractions facts. These drills begin at lesson 28 and continue through lesson 170. Speed drills are to be given every other day. Directions for using this tablet are in the teacher's manual.
Grade 5: Getting Ready for High Stakes Assessments
by Houghton Mifflin Harcourt Publishing CompanyGo Math! Getting Ready for High Stakes Assessments Student Edition Grade 5
Grade 7 Common Core Assessment Readiness
by Holt McdougalMathematics: Assessment Readiness Workbook Grade 7
Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains (Surveys and Tutorials in the Applied Mathematical Sciences #10)
by Hengguang LiThis book develops a class of graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains. It provides an approachable and self-contained presentation of the topic, including both the mathematical theory and numerical tools necessary to address the major challenges imposed by the singular solution. Moreover, by focusing upon second-order equations with constant coefficients, it manages to derive explicit results that are accessible to the broader computation community. Although written with mathematics graduate students and researchers in mind, this book is also relevant to applied and computational mathematicians, scientists, and engineers in numerical methods who may encounter singular problems.
Graded Rings and Graded Grothendieck Groups
by Roozbeh HazratThis study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.
Gradually-varied Flow Profiles in Open Channels
by Chyan-Deng JanGradually-varied flow (GVF) is a steady non-uniform flow in an open channel with gradual changes in its water surface elevation. The evaluation of GVF profiles under a specific flow discharge is very important in hydraulic engineering. This book proposes a novel approach to analytically solve the GVF profiles by using the direct integration and Gaussian hypergeometric function. Both normal-depth- and critical-depth-based dimensionless GVF profiles are presented. The novel approach has laid the foundation to compute at one sweep the GVF profiles in a series of sustaining and adverse channels, which may have horizontal slopes sandwiched in between them.
Graham Priest on Dialetheism and Paraconsistency (Outstanding Contributions to Logic #18)
by Can Başkent Thomas Macaulay FergusonThis book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth.This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes.