Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.

    Now, in The Unimaginable Mathematics of Borges' Library of Babel, William Goldbloom Bloch takes readers on a fascinating tour of the mathematical ideas hiddenwithin one of the classic works of modern literature.Written in the vein of Douglas R. Hofstadter's Pulitzer Prize-winning G�del, Escher, Bach, this original and imaginative book sheds light on one of Borges' most complex, richly layered works. Bloch begins each chapter with a mathematical idea--combinatorics, topology, geometry, informationtheory--followed by examples and illustrations that put flesh on the theoretical bones. In this way, he provides many fascinating insights into Borges' Library. He explains, for instance, a straightforward way to calculate how many books are in the Library--an easily notated but literallyunimaginable number--and also shows that, if each book were the size of a grain of sand, the entire universe could only hold a fraction of the books in the Library. Indeed, if each book were the size of a proton, our universe would still not be big enough to hold anywhere near all the books.Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but alsoexposes the reader--including those more inclined to the literary world--to many intriguing and entrancing mathematical ideas.

    D. Williams wrote this entertaining, witty introduction for the nonscientist, game theory was still a somewhat mysterious subject familiar to very few scientists beyond those researchers, like himself, working for the military. Now, over thirty years after its original publication as a Rand Corporation research study, his light-hearted though thoroughly effective primer is the recognized classic introduction to an increasingly applicable discipline. Used by amateurs, professionals, and students throughout the world in the classroom, on the job, and for personal amusement, the book has been through ten printings, and has been translated into at least five languages (including Russian and Japanese).Revised, updated, and available for the first time in an inexpensive paperback edition, The Compleat Strategyst is a highly entertaining text essential for anyone interested in this provocative and engaging area of modern mathematics. In fully illustrated chapters complete with everyday examples and word problems, Williams offers readers a working understanding of the possible methods for selecting strategies in a variety of situations, simple to complex. With just a basic understanding of arithmetic, anyone can grasp all necessary aspects of two-, three-, four-, and larger strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.As research and study continues not only in this new discipline but in the related areas of statistics, probability and behavioral science, understanding of games, decision making, and the development of strategies will be increasingly important. In the areas of economics, sociology, politics, and the military, game theory is sure to have an even wider impact. For students and amateurs fascinated by game theory's implications there is no better, immediately applicable, or more entertaining introduction to the subject than this engaging text by the late J. D. Williams, Professor of Mathematics at Princeton University and a member of the Research Council of The Rand Corporation.

    From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire.

    Features exceptionally clear explanations and descriptions, step-by-step examples, more than 50 practical applications, over 2000 easy-to-challenging practice problems, and comprehensive coverage of essentials. PSpice, OrCAd version 9.2 Lite Edition, Multisims 2001 version of Electronics Workbench, and MathCad software references and examples are used throughout. Computer programs (C++, BASIC and PSpice) are printed in color, as they run, at the point in the book where they are discussed. Current and Voltage. Resistance. Ohm's Law, Power, and Energy. Series Circuits. Parallel Circuits. Series-Parallel Networks. Methods of Analysis & Selected Topics. Network Theorems. Capacitors. Magnetic Circuits. Inductors. Sinusodial Alternating Waveforms. The Basic Elements and Phasors. Series and Parallel ac Circuits. Series-Parallel ac Networks. Methods of Analysis and Related Topics. Network Theorems (ac). Power (ac). Resonance. Transformers. Polyphase Systems. Decibels, Filters, and Bode Points. Pulse Waveforms and the R-C Response. Nonsinusodial Circuits. System Analysis: An Introduction. For those working in electronic technology.

    This text provides a simple and straightforward introduction to econometrics for the beginner. The book is designed to help students understand econometric techniques through extensive examples, careful explanations, and a wide variety of problem material. In each of the editions, I have tried to incorporate major developments in the field in an intuitive and informative way without resort to matrix algebra, calculus, or statistics beyond the introductory level. The fourth edition continues that tradition.

    Quantum paradoxes and the eventful life of Schroedinger's Cat are explained, along with the Many Universe explanation of quantum measurement in this newly revised edition. Updated throughout, the book also looks ahead to the nanotechnology revolution and describes quantum cryptography, computing and teleportation. Including an account of quantum mechanics and science fiction, this accessible book is geared to the general reader. Anthony Hey teaches at the University of Southampton, UK, and is the co-author of several books, including two with Patrick Walters, The Quantum Universe (Cambridge, 1987), and Einstein's Mirror (Cambridge, 1997). Patrick Walters is a Lecturer in Continuing Education at the University of Wales at Swansea. He co-ordinates the Physical Science Programme in DACE which includes the Astronomy Programme. His research interests include science education, and he also writes non-technical books on science for the general reader and beginning undergraduates. First Edition Pb (1987): 0-521-31845-9

    Never before in history have we been able to acquire, record, communicate, and use information in so many different forms. Never before have we had access to such vast quantities of data of every kind. This revolution goes far beyond the limitless content that fills our lives, because information also underlies our understanding of ourselves, the natural world, and the universe. It is the key that unites fields as different as linguistics, cryptography, neuroscience, genetics, economics, and quantum mechanics. And the fact that information bears no necessary connection to meaning makes it a profound puzzle that people with a passion for philosophy have pondered for centuries.Table of ContentsLECTURE 1The Transformability of Information 4LECTURE 2Computation and Logic Gates 17LECTURE 3Measuring Information 26LECTURE 4Entropy and the Average Surprise 34LECTURE 5Data Compression and Prefix-Free Codes 44LECTURE 6Encoding Images and Sounds 57LECTURE 7Noise and Channel Capacity 69LECTURE 8Error-Correcting Codes 82LECTURE 9Signals and Bandwidth 94LECTURE 10Cryptography and Key Entropy 110LECTURE 11Cryptanalysis and Unraveling the Enigma 119LECTURE 12Unbreakable Codes and Public Keys 130LECTURE 13What Genetic Information Can Do 140LECTURE 14Life’s Origins and DNA Computing 152LECTURE 15Neural Codes in the Brain 169LECTURE 16Entropy and Microstate Information 185LECTURE 17Erasure Cost and Reversible Computing 198LECTURE 18Horse Races and Stock Markets 213LECTURE 19Turing Machines and Algorithmic Information 226LECTURE 20Uncomputable Functions and Incompleteness 239LECTURE 21Qubits and Quantum Information 253LECTURE 22Quantum Cryptography via Entanglement 266LECTURE 23It from Bit: Physics from Information 281LECTURE 24The Meaning of Information 293

    Good stories are full of life: they engage our emotions and have subtlety and nuance, but they lack rigor and the truths they tell are elusive and subject to debate. As ways of understanding the world around us, numbers and stories seem almost completely incompatible. Once Upon a Number shows that stories and numbers aren't as different as you might imagine, and in fact they have surprising and fascinating connections. The concepts of logic and probability both grew out of intuitive ideas about how certain situations would play out. Now, logicians are inventing ways to deal with real world situations by mathematical means -- by acknowledging, for instance, that items that are mathematically interchangeable may not be interchangeable in a story. And complexity theory looks at both number strings and narrative strings in remarkably similar terms. Throughout, renowned author John Paulos mixes numbers and narratives in his own delightful style. Along with lucid accounts of cutting-edge information theory we get hilarious anecdotes and jokes; instructions for running a truly impressive pyramid scam; a freewheeling conversation between Groucho Marx and Bertrand Russell (while they're stuck in an elevator together); explanations of why the statistical evidence against OJ Simpson was overwhelming beyond doubt and how the Unabomber's thinking shows signs of mathematical training; and dozens of other treats. This is another winner from America's favorite mathematician.

    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.

    Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation — Classical Theory; Fourier Approximation — Modern Theory; and Exponential Approximation.