Describes learning environments which allow children to master mathematical concepts through the use of computer assisted instruction.

All the statistical tables you need, right at your fingertips.

A new copy with a bit of shelf-wear to the covers from less-than-optimal storage. Otherwise a quite nice edition with a sewn binding, thick spine (the book opens flat without problems) and bright, smooth, good-quality paper.

Following his popular books "The Armchair Economist" and "More Sex Is Safer Sex", Slate columnist Landsburg uses concepts from mathematics, economics, and physics to address the big questions in philosophy.

"This mind-blowing illustrated collection showcases hundreds of tattoos dedicated to numerous scientific arenas, from evolutionary biology and neuroscience to mathematics and astrophysics, with a brief note from each inked individual highlighting the reasons for selecting the tattoo. Best of all, each example is a leaping-off point for best-selling science essayist and lecturer Zimmer to muse about the subject, whether it's the importance of a tattoo of Darwin's finches or the significance of the uranium atom inked into the chest of a young radiologist"--

Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises.--

Anyone who gambles, plays cards, loves puzzles, or simply seeks an intellectual challenge will love this amusing and thought-provoking book. With wit and clarity, the authors deftly progress from simple arithmetic to calculus and non-Euclidean geometry. "Charming and exciting." -- "Saturday Review of Literature." Includes 169 figures.

"Solving problems", writes Polya, "is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice. This book cannot offer you a magic key that opens all the doors and solves all the problems, but it offers you good examples for imitation and many opportunities for practice: If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems." "In enough cases to allay . . . discouragement over not immediately discovering a solution, Professor Polya masterfully leads the reader down several unproductive paths. At the end of each chapter he provides examples for the render to solve. By means of these carefully selected and arranged problems, many of them directly related to others that precede, and guided by just the right suggestions at just the proper time, the reader's own ability is developed and extended. Solutions to the examples and, in many cases, outlines of procedures for discovering solutions. arc given at the back of the book. With striking promise for effectiveness, the entire book as a unit is one great experience in learning processes for problem solving through participation. The author has captured with great success the implication of his basic premise stated in the preface ..." The Mathematics Teacher

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 was awarded 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. Marking the 50th anniversary of the original publication of Gödel's Proof , New York University Press is proud to publish this special anniversary edition of one of its bestselling and most frequently translated books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

Mlodinow, Leonard

Do high-speed, complicated arithmetic in your head using the Trachtenberg Speed System.Ever find yourself struggling to check a bill or a payslip? With The Trachtenberg Speed System you can. Described as the 'shorthand of mathematics', the Trachtenberg system only requires the ability to count from one to eleven. Using a series of simplified keys it allows anyone to master calculations, giving greater speed, ease in handling numbers and increased accuracy.Jakow Trachtenberg believed that everyone is born with phenomenal abilities to calculate. He devised a set of rules that allows every child to make multiplication, division, addition, subtraction and square-root calculations with unerring accuracy and at remarkable speed. It is the perfect way to gain confidence with numbers.

There has been an explosive growth in the field of combinatorial algorithms. These algorithms depend not only on results in combinatorics and especially in graph theory, but also on the development of new data structures and new techniques for analyzing algorithms. Four classical problems in network optimization are covered in detail, including a development of the data structures they use and an analysis of their running time. Data Structures and Network Algorithms attempts to provide the reader with both a practical understanding of the algorithms, described to facilitate their easy implementation, and an appreciation of the depth and beauty of the field of graph algorithms.

Functional analysis is the study of certain topological-algebraic structures and of the methods by which knowledge of these structures can be applied to analytic problems. A good introductory text on this subject should include a presentation of its axiomatics (i.e., of the general theory of topological vector spaces), it should treat at least a few topics in some depth, and it should contain some interesting applications to other branches of mathematics. I hope that the present book meets these criteria. The subject is huge and is growing rapidly. (The bibliography in volume I of [4] contains 96 pages and goes only to 1957.) In order to write a book of moderate size, it was therefore necessary to select certain areas and to ignore others. I fully realize that almost any expert who looks at the table of contents will find that some of his or her (and my) favorite topics are missing, but this seems unavoidable. It was not my intention to write an encyclopedic treatise. I wanted to write a book that would open the way to further exploration. This is the reason for omitting many of the more esoteric topics that might have been included in the presentation of the general theory of topo-logical vector spaces. For instance, there is no discussion of uniform spaces, of Moore-Smith convergence, of nets, or of filters. The notion of complete-ness occurs only in the context of metric spaces. Bornological spaces are not mentioned, nor are barreled ones. Duality is of course presented, but not in its utmost generality. Integration of vector-valued functions is treated strictly as a tool; attention is confined to continuous integrands, with values in a Frechet space. Nevertheless, the material of Part I is fully adequate for almost all applications to concrete problems. And this is what ought to be stressed in such a course:

From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991

This is a classic book, representing the first major breakthrough in the field of modern financial theory. In effect, it created the mathematics of portfolio selection in a model which has turned out to be the indispensable building block from which the theory of the demand for risky securities is constructed. It also became an essential reference for individuals and financial institutions actually selecting optimal portfolios. Long out of print and unavailable to numerous recent entrants to both financial theory and financial practice, this new edition leaves the existing text as it stands but adds substantial new material including a new bibliography and a fascinating biographical piece on the birth of the field of finance.

"Max Tegmark leads us on an astonishing journey through past, present, and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and ground-breaking science, he not only helps us grasp his often mind-boggling theories (his website gives a flavor of how they might boggle the mind), but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last--here is a book for the full science-reading spectrum"--

This introductory text covers the key areas of computer science, including recursive function theory, formal languages, and automata. It assumes a minimal background in formal mathematics. The book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability. * Computability theory is introduced in a manner that makes maximum use of previous programming experience, including a "universal" program that takes up less than a page. * The number of exercises included has more than tripled. * Automata theory, computational logic, and complexity theory are presented in a flexible manner, and can be covered in a variety of different arrangements.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Indisputably recognized as a classic in its field, Statistics of Extremes was the first book to exclusively evaluate the relevance of maximum and minimum (extreme) values. More than fifty years after publication, it remains relevant and helpful to the contemporary work of statisticians, engineers, and scientists. In this far-sighted and important work, Gumbel explains the applications of statistical extremes and reinforces its main ideas with generalized exercises. Key topics in this book include: Aims and tools Order statistics and their exceedances Exact distribution of extremes Analytical study of extremes First asymptotic distribution Uses of the first, second, and third asymptotes Range To remain relevant to a wide audience of statisticians, Professor Gumbel relies on elementary language to convey highly technical concepts. With 47 tables and 97 graphs, the focus is on graphical procedures rather than calculations. Gumbel's original research in the 1940s was developed to predict natural disasters, but as he further refined his theory and tools of extreme statistics, it became clear it has applications in numerous fields.

The Essential Guide that Introduced Fractals to the World Explore the wondrously complex repeating shapes of the natural world in The Fractal Geometry of Nature. Written in a style that is accessible to a wide audience, computer scientist, professor, mathematician, economist, and visionary Benoit B Mandelbrot's fascinating work has inspired popular interest in the geometry inherent in the natural world. Unlike the squares, circles, spheres, and cones of fundamental geometry, nature has rough edges and no straight lines or perfect curves. Mandelbrot observed that, even with this roughness, there still exists a kind of symmetry, which he dedicated his work to document and study. This became the basis for his development of a new kind of geometry; indeed, he coined the term "fractal." Mandelbrot spent 35 years with IBM, which allowed him access to the level of computing power that would enable him to manipulate computer-generated images and develop his theory of a geometry found throughout our natural environment. He was among the first to use computer graphics to illustrate and test these kinds of concepts, demonstrating that natural phenomena which appear to be rough or chaotic actually have a certain degree of order and predictability. This definitive overview builds on Mandelbrot's 1977 work, Fractals: Form, Chance and Dimension (also published by Echo Point Books), revealing an in depth look at this still-emerging field. Richly illustrated and presented in an engaging manner which embraces geometric and visual dimensions interspersed with aspects of theory, this book will inspire curiosity and wonder in artists, mathematicians and naturalists alike. This book is also available from Echo Point Books in hardcover (ISBN 1648370403). Be sure to check out Benoit Mandelbrot's other definitive work, also availabe from Echo Point books: Fractals: Form, Chance and Dimension (use the web address https: //www.amazon.com/dp/1635619025/).