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'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the GalaxyWe human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the inf...

This book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdoes, B.L. van der Waerden, and Henry Baudet.

One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the numb...

George Birtwistle (1877-1929) published The New Quantum Mechanics in 1928. His stated aim was to give a detailed account of work which had brought the relatively new subject of quantum mechanics to the fore in the previous few years. The earlier chapters give a restatement of Alfred Lande's theory of multiplets which reconciles it with the new mechanics which follow. Later chapters present the matrix theory of Heisenberg, the q-number theory of Dirac and the wave mechanics of Schroedinger, and s...

Though there are a number of well-written works on Chinese divination, there are none that deal with the three sophisticated devices that were employed by the Chinese Astronomical Bureau in the eleventh century and for hundreds of years thereafter. Chinese experts applied the methods associated with these devices to both weather forecasting and to the interpretation of human affairs. Hidden by a veil of secrecy, these methods have always been relatively little known other than by their names....

A philosopher, scholar of the natural world, and gifted mathematician, Thomas Reid holds a distinctive place in the Scottish Enlightenment. This volume reconstructs Reid's lifelong engagement with the physical sciences and makes clear why these fields were central to his epistemology and moral and social philosophy.Placing Reid's "Essay on Quantity" alongside his previously unpublished writings on mathematics and the physical sciences, Paul Wood shows that, in contrast to Francis Hutcheson and D...

This is the ultimate collection of challenging high-school-level mathematics problems. It is the result of a two year long collaboration to rescue these problems from old and scattered manuscripts, and produce the definitive source of IMO practice problems in book form for the first time. This book attempts to gather all the problems and solutions appearing on the IMO and contains a grand total of 1900 problems. It is an invaluable resource for high-school students preparing for mathematics comp...

There is a long tradition of relating the history of mathematics to its teaching, and increasingly this has extended throughout mathematical education. This volume brings together articles from well known figures in this area, and provides many insights, both in particular cases and in generality, into how the history of mathematics can find application in the teaching of mathematics itself. Educators at all levels, and mathematicians interested in the history of their subject, will find much of...

Praise for Five Golden Rules "Casti is one of the great science writers of the 1990s...If you'd like to have fun while giving your brain a first-class workout, then check this book out."-Keay Davidson in the San Francisco Examiner. "Five Golden Rules is caviar for the inquiring reader...There is joy here in watching the unfolding of these intricate and beautiful techniques. Casti's gift is to be able to let the nonmathematical reader share in his understanding of the beauty of a good theory." -C...

For thousands of years, algebra consisted solely of expanding the list of problem-solving algorithms-a list of procedures similar in concept to the quadratic formula. But much of contemporary algebra focuses on identifying and describing the logical structures upon which mathematics is built. It is now clear that identifying and exploiting these structures is just as important for mathematical and scientific progress as the development of new algorithms. Algebra, Revised Edition describes the hi...

Despite the rapidly expanding ambit of physical research and the continual appearance of new branches of physics, the main thrust in its development was and is the attempt at a theoretical synthesis of the entire body of physical knowledge. The main triumphs in physical science were, as a rule, associ ated with the various phases of this synthesis. The most radical expression of this tendency is the program of construction of a unified physical theory. After Maxwellian electrodynamics had unifi...

This unique compilation includes more than 225 problems from Mathematics Teaching in the Middle School, ranging from "appetisers" (warm-up problems) through "main courses" (more challenging problems) and "desserts" (suitable for students with more experience in solving problems). The problems are conveniently grouped by topic or theme for easy selection.