Numerous photographs and diagrams explain mathematical phenomena in series of thought-provoking expositions. From simple puzzles to more advanced problems, topics include psychology of lottery players, new and larger prime numbers, and more. 391 illustrations.
Designed to present small mathematical challenges in everyday life. Only the first edition, printed in Poland with English and Polish issues contains the loose objects for demonstrations the reader can do. There are also 180 text illustrations some designed to show three dimensional effects with the two-colour glasses.
In the first edition of The Mathematical Tourist, renowned science journalist Ivars Peterson took readers on an unforgettable tour through the sometimes bizarre, but always fascinating, landscape of modern mathematics. Now the journey continues in a new, updated edition that includes all the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on * the relationship between mathematical knots and DNA * how computers based on quantum logic can significantly speed up the factoring of large composite numbers * the relationship between four-dimensional geometry and physical theories of the nature of matter * the application of cellular automata models to social questions and the peregrinations of virtual ants * a novel mathematical model of quasicrystals based on decagon-shaped tiles Blazing a trail through rows of austere symbols and dense lines of formulae, Peterson explores the central ideas behind the work of professional mathematicians-- how and where their pieces of the mathematical puzzle fit in, the sources of their ideas, their fountains of inspiration, and the images that carry them from one discovery to another.
We, the authors of this book, are three ardent devotees of chance, or some what more precisely, of discrete probability. When we were collecting the material, we felt that one special pleasure of the field lay in its evocation of an earlier age: many of our 'probabilistic forefathers' were dexterous solvers of discrete problems. We hope that this pleasure will be transmitted to the readers. The first problem-book of a similar kind as ours is perhaps Mosteller's well-known Fifty Challenging Problems in Probability (1965). Possibly, our book is the second. The book contains 125 problems and snapshots from the world of prob ability. A 'problem' generally leads to a question with a definite answer. A 'snapshot' is either a picture or a bird's-eye view of some probabilistic field. The selection is, of course, highly subjective, and we have not even tried to cover all parts of the subject systematically. Limit theorems appear only seldom, for otherwise the book would have become unduly large. We want to state emphatically that we have not written a textbook in probability, but rather a book for browsing through when occupying an easy-chair. Therefore, ideas and results are often put forth without a machinery of formulas and derivations; the conscientious readers, who want to penetrate the whole clockwork, will soon have to move to their desks and utilize appropriate tools.
In mathematical studies drawn from algebra, geometry, analysis, statistics and computational methodology, applications are discussed in separate chapters, each prefaced by a summary of content and relevance. Some branches of the mathematics covered might be regarded as old-fashioned but they are still vigorous and relevant today.
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Both a challenge to mathematically inclined readers and a useful supplementary text for high school and college courses, One Hundred Problems in Elementary Mathematics presents an instructive, stimulating collection of problems. Many problems address such matters as numbers, equations, inequalities, points, polygons, circles, ellipses, space, polyhedra, and spheres. An equal number deal with more amusing or more practical subjects, such as a picnic ham, blood groups, rooks on a chessboard, and the doings of the ingenious Dr. Abracadabrus. Are the problems in this book really elementary? Perhaps not in the lay reader’s sense, for anyone who desires to solve these problems must know a fair amount of mathematics, up to calculus. Nevertheless, Professor Steinhaus has given complete, detailed solutions to every one of his 100 problems, and anyone who works through the solutions will painlessly learn an astonishing amount of mathematics. A final chapter provides a true test for the most proficient readers: 13 additional unsolved problems, including some for which the author himself does not know the solutions.
Is it possible to make mathematical drawings that help to understand mathematical ideas, proofs, and arguments? The [Author];s of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece, and India, but only in the last thirty years has there been a growing interest in so-called ``proofs without words''. Hundreds of these have been published in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books, and on the internet. Often a person encountering a ``proof without words'' may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of an exceptional ingenuity on the part of the picture's creator. In this book, the [Author];s show that behind most of the pictures, ``proving'' mathematical relations are some well-understood methods. As the reader shall see, a given mathematical idea or relation may have many different images that justify it, so that depending on the teaching level or the objectives for producing the pictures, one can choose the best alternative.
Since it was first published three decades ago, Excursions Into Mathematics has been one of the most popular mathematical books written for a general audience. Taking the reader for short "excursions" into several specific disciplines of mathematics, it makes mathematical concepts accessible to a wide audience. The Millennium Edition is updated with current research and new solutions to outstanding problems that have been discovered since the last edition was printed, such as the solution to the well-known "four-color problem." Excursions Into Mathematics: The Millennium Edition is an exciting revision of the original, much-loved classic. Everyone with an interest in mathematics should read this book.