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Go Math!, Grade 8, Middle School: Student Interactive Worktext (Go Math! STA)
by Edward B. Burger Juli K. Dixon Timothy D. KanoldNIMAC-sourced textbook
Go Math! [Grade K] Volume 1
by Juli K. Dixon Edward B. Burger Steven J. LeinwandNIMAC-sourced textbook
Go Math! [Grade K] Volume 2
by Juli K. Dixon Edward B. Burger Steven J. LeinwandNIMAC-sourced textbook
Go Math, Middle School, Accelerated Grade 7
by Edward B. Burger Juli K. Dixon Timothy D. KanoldNIMAC-sourced textbook
Go Math, Middle School, Grade 6
by Edward B. Burger Juli K. Dixon Timothy D. KanoldNIMAC-sourced textbook
Go Math, Middle School, Grade 6
by Edward B. Burger Juli K. Dixon Timothy D. KanoldNIMAC-sourced textbook
Go Math, Middle School, Grade 7
by Edward B. Burger Juli K. Dixon Timothy D. KanoldNIMAC-sourced textbook
Go Math, Middle School, Grade 8
by Edward B. Burger Juli K. Dixon Timothy D. KanoldNIMAC-sourced textbook
Go Math, Middle School, Grade 8
by Edward B. Burger Juli K. Dixon Timothy D. KanoldNIMAC-sourced textbook
Go Math! Student Interactive Worktext (Grade #7)
by Edward B. Burger Juli K. Dixon Timothy D. KanoldGo Math ¡Vivan las matemáticas! escuela intermedia, Grado 6
by Edward B. Burger Juli K. Dixon Timothy D. KanoldNIMAC-sourced textbook
Go Math ¡Vivan las matemáticas! Escuela intermedia, Grado 7
by Edward B. Burger Juli K. Dixon Timothy D. KanoldNIMAC-sourced textbook
Go Math! ¡Vivan las matemáticas! Grado 5, Cuaderno de práctica de los estándares, Para el hogar o la escuela: Standards Practice Book Grade 5 (Go Math! Spanish)
by Houghton Mifflin Harcourt StaffNIMAC-sourced textbook
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 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.
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. "
The Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs
by Raymond M. SmullyanThese brand-new recreational logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. Created by the celebrated logician Raymond Smullyan, the puzzles require no background in formal logic and will delight readers of all ages.The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious systems related to Gödel's theorem. The first three chapters of Part II contain generalized Gödel theorems. Symbolic logic is deferred until the last three chapters, which give explanations and examples of first-order arithmetic, Peano arithmetic, and a complete proof of Gödel's celebrated result involving statements that cannot be proved or disproved. The book also includes a lively look at decision theory, better known as recursion theory, which plays a vital role in computer science.
Gödel's Proof
by Ernest Nagel James R Newman Douglas R. HofstadterAn accessible explanation of Kurt Gödel&’s groundbreaking work in mathematical logic: &“An excellent nontechnical account.&” —Bulletin of the American Mathematical Society In 1931 Kurt Gödel published his fundamental paper, &“On Formally Undecidable Propositions of Principia Mathematica and Related Systems.&” This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he received the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as &“one of the greatest contributions to the sciences in recent times.&” However, few mathematicians of the time were equipped to understand the young scholar&’s complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. New York University Press is proud to publish this special edition of one of its bestselling books. With a new foreword by Douglas R. Hofstadter, Pulitzer Prize-winning author of Gödel, Escher, Bach, who also updated the text, this book will be of interest to students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.
Gödel's Theorem: An Incomplete Guide to Its Use and Abuse
by Torkel Franzén"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
Goedel's Way: Exploits into an undecidable world
by Gregory Chaitin Francisco Doria Newton da CostaKurt 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.
The Golden Ratio: The Story of PHI, the World's Most Astonishing Number
by Mario LivioThroughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.From the Hardcover edition.