As exciting as any action/adventure novel, this is actually the story of incredible individuals and engrossing tales behind the most profound, enduring mathematical theorems.Archimedes famously ran naked through the streets shouting, “Eureka, eureka!” after finding a method for measuring the volume of an irregular-shaped object. René Descartes was not only a great French mathematician, philosopher, physicist, and natural scientist; he was also an expert swordsman who traveled with European armies from town to town, dressed in green taffeta and accompanied by a valet. Georg Cantor grappled with mental illness as he explored the highly counterintuitive, bizarre properties of infinite sets and numbers. Emmy Noether struggled to find employment as she laid the mathematical groundwork for modern theoretical physics. And Alexander Grothendieck taught himself mathematics while interned in Nazi concentration camps, only to disappear into the Pyrenees at the zenith of his career.These are just a few stories recounted in this absorbing narrative. In probing the lives of the preeminent mathematicians in history, a Strange Wilderness will leave you entertained and enlightened, with a newfound appreciation of the tenacity, complexity, and brilliance of the mathematical genius.

    Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    The study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory. Colin Adams’s The Knot Book is the first book to make cutting-edge research in knot theory accessible to a non-specialist audience. Starting with the simplest knots, Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians can now solve, as well as those that remain open. He also explores how knot theory is providing important insights in biology, chemistry, physics, and other fields. The new paperback edition has been updated to include the latest research results, and includes hundreds of illustrations of knots, as well as worked examples, exercises and problems. With a simple piece of string, an elementary mathematical background, and The Knot Book, anyone can start learning about some of the most advanced ideas in contemporary mathematics.

    story of the predecessors of Christians

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

     Three and a half billion years ago, Mars resembled earth. It was warm and wet and could have supported primitive organisms. If life once existed on Mars, might it have originated there and traveled to earth inside meteorites blasted into space by cosmic impacts? Davies builds on recent scientific discoveries and theories to address larger questions of existence: What, exactly, is life? Is it the inevitable by-product of physical laws, as many scientists maintain, or an almost miraculous accident? Are we alone in the universe, or will life emerge on all earthlike planets? And if there is life elsewhere in the universe, is it preordained to evolve toward greater complexity and intelligence? Through his search for answers to these questions, Davies explores the ultimate mystery of mankind's existence -- who we are and what our place might be in the unfolding drama of the cosmos.

    Right? Wrong, says Alex Rosenberg in How History Gets Things Wrong. Feeling especially well-informed after reading a book of popular history on the best-seller list? Don't. Narrative history is always, always wrong. It's not just incomplete or inaccurate but deeply wrong, as wrong as Ptolemaic astronomy. We no longer believe that the earth is the center of the universe. Why do we still believe in historical narrative? Our attachment to history as a vehicle for understanding has a long Darwinian pedigree and a genetic basis. Our love of stories is hard-wired. Neuroscience reveals that human evolution shaped a tool useful for survival into a defective theory of human nature.Stories historians tell, Rosenberg continues, are not only wrong but harmful. Israel and Palestine, for example, have dueling narratives of dispossession that prevent one side from compromising with the other. Henry Kissinger applied lessons drawn from the Congress of Vienna to American foreign policy with disastrous results. Human evolution improved primate mind reading—the ability to anticipate the behavior of others, whether predators, prey, or cooperators—to get us to the top of the African food chain. Now, however, this hard-wired capacity makes us think we can understand history—what the Kaiser was thinking in 1914, why Hitler declared war on the United States—by uncovering the narratives of what happened and why. In fact, Rosenberg argues, we will only understand history if we don't make it into a story.

    Geared to philosophers, biologists, and students of both, the book provides sophisticated and innovative coverage of the central topics and many of the latest developments in the field. Emphasizing connections between biological theories and other areas of philosophy, and carefully explaining both philosophical and biological terms, Peter Godfrey-Smith discusses the relation between philosophy and science; examines the role of laws, mechanistic explanation, and idealized models in biological theories; describes evolution by natural selection; and assesses attempts to extend Darwin's mechanism to explain changes in ideas, culture, and other phenomena. Further topics include functions and teleology, individuality and organisms, species, the tree of life, and human nature. The book closes with detailed, cutting-edge treatments of the evolution of cooperation, of information in biology, and of the role of communication in living systems at all scales.Authoritative and up-to-date, this is an essential guide for anyone interested in the important philosophical issues raised by the biological sciences.

    He was trying to find an equation that explained all physical reality - a theory of everything. He failed, but others have taken up the challenge in a remarkable quest that is shedding light on unsuspected secrets of the cosmos.Experimental physicist and award-winning educator Dr. Don Lincoln of the Fermi National Accelerator Laboratory takes you on this exciting journey in The Theory of Everything: The Quest to Explain All Reality. Suitable for the intellectually curious at all levels and assuming no background beyond basic high-school math, these 24 half-hour lectures cover recent developments at the forefront of particle physics and cosmology, while delving into the history of the centuries-long search for this holy grail of science.You trace the dream of a theory of everything through Newton, Maxwell, Einstein, Bohr, Schrödinger, Feynman, Gell-Mann, Weinberg, and other great physicists, charting their progress toward an all-embracing, unifying theory. Their resulting equations are the masterpieces of physics, which Dr. Lincoln explains in fascinating and accessible detail. Studying them is like touring a museum of great works of art - works that are progressing toward an ultimate, as-yet-unfinished masterpiece.Listening Length: 12 hours and 21 minutes

    Inspired by and expanding on a series of lectures presented by Leonard Peikoff, David Harriman presents a fascinating answer to the problem of induction-the epistemological question of how we can know the truth of inductive generalizations.Ayn Rand presented her revolutionary theory of concepts in her book Introduction to Objectivist Epistemology. As Dr. Peikoff subsequently explored the concept of induction, he sought out David Harriman, a physicist who had taught philosophy, for his expert knowledge of the scientific discovery process.Here, Harriman presents the result of a collaboration between scientist and philosopher. Beginning with a detailed discussion of the role of mathematics and experimentation in validating generalizations in physics-looking closely at the reasoning of scientists such as Galileo, Kepler, Newton, Lavoisier, and Maxwell-Harriman skillfully argues that the inductive method used in philosophy is in principle indistinguishable from the method used in physics.

    A remarkable pictorial discussion of the curved space-time we call home, it achieves even greater impact through the use of 141 excellent illustrations. This is the first sustained visual account of many important topics in relativity theory that up till now have only been treated separately.Finding a perfect analogy in the situation of the geometrical characters in Flatland, Professor Rucker continues the adventures of the two-dimensional world visited by a three-dimensional being to explain our three-dimensional world in terms of the fourth dimension. Following this adventure into the fourth dimension, the author discusses non-Euclidean geometry, curved space, time as a higher dimension, special relativity, time travel, and the shape of space-time. The mathematics is sound throughout, but the casual reader may skip those few sections that seem too purely mathematical and still follow the line of argument. Readable and interesting in itself, the annotated bibliography is a valuable guide to further study.Professor Rucker teaches mathematics at the State University of New York in Geneseo. Students and laymen will find his discussion to be unusually stimulating. Experienced mathematicians and physicists will find a great deal of original material here and many unexpected novelties. Annotated bibliography. 44 problems.

    Julia Diggins masterfully recreates the atmosphere of ancient times, when men, using three simple tools, the string, the straightedge, and the shadow, discovered the basic principles and constructions of elementary geometry. Her book reveals how these discoveries related to the early civilizations of Mesopotamia, Egypt, and Greece.The fabric of the story is woven out of archeological and historical records and legends about the major men of mathematics. By reconstructing the events as they might have happened, Diggins enables the attentive reader to easily follow the pattern of reasoning that leads to an ingenious proof of the Pythagorean theorem, an appreciation of the significance of the Golden Mean in art and architecture, and the construction of the five regular solids.Out of print for 34 years, Julia Diggins' classic book is back and is a must-read for middle school students or for parents helping their children through their first geometry course. You will be fascinated with the graphic illustrations and written depiction of how the knowledge and wisdom of so many cultures helped shape our civilization today. This book is popular with teachers and parents who use Jamie York's Making Math Meaningful curriculum books.

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    To Alexander the Great, the country was a place of clever naked philosophers and massive armies mounted on elephants – which eventually forced his army to retreat. To ancient Rome, it was a source of luxuries, mainly spices and textiles, paid for in gold—hence the enormous numbers of Roman gold coins excavated in India. At the height of the Mughal empire in 1700, India boasted 24 percent of the world economy—a share virtually equal to Europe’s 25 percent. But then its economy declined. Colonial India was known for its extremes of wealth and poverty, epitomized by the Taj Mahal and famines, maharajas and untouchables, and also for its spirituality: many-armed Hindu gods and Buddhist philosophy, Mahatma Gandhi and Rabindranath Tagore.India: A Short History places as much emphasis on individuals, ideas and cultures as on the rise and fall of kingdoms, political parties and economies. Anyone curious about a great civilization, and its future, will find this an ideal introduction, at times controversial, written by an author who has been strongly engaged with India for more than three decades.