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"Assuming a minimum of technical expertise beyond basic matrix theory, the authors introduce inertial frames and Minkowski diagrams to explain the nature of simultaneity, why faster-than-light travel is impossible, and the proper way to add velocities. We resolve the twin paradox, the train-in-tunnel paradox, the pra-shooter paradox along with the lesser-known bug-rivet paradox that shows how rigidity is incompatible with special relativity. Since Einstein in his seminal 1905 paper introducing special relativity, acknowledged his debt to Clerk Maxwell, we fully develop Maxwell's four equations that unify the theories of electricity, optics, and magnetism. These equations also lead to a simple calculation for the frame independent speed of electromagnetic waves in a vacuum."--Cover.
Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard’s The Psychology of Invention in the Mathematical Field. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting and thought-provoking. Not all respondents addressed the question directly. Michael Atiyah reflects on the tension between truth and beauty in mathematics. T.W. Körner, Alan Schoenfeld and Hyman Bass chose to write, reflectively and thoughtfully, about teaching and learning. Others, including Ian Stewart and Jane Hawkins, write about the sociology of our community. Many of the contributions range into philosophy of mathematics and the nature of our thought processes. Any mathematician will find much of interest here.
Illustrated book showing that there are few degrees of separation between mathematics and topics that provoke interesting conversations.
A historical introduction to non-Euclidean geometry.
Do you know precisely how your creativity happens? Can you coach other people to be more creative? This book is a how-to guide focused on helping you to generate great—or even greater—ideas by showing you “how to do it” and how to teach others how to do it, too. Written specifically for those working in the mathematical sciences, this book provides a proven process for idea generation and a wide range of mathematically oriented examples. Building on the authors’ many years of experience running creativity workshops, How to Be Creative: A Practical Guide for the Mathematical Sciences gives a six-step process for generating great ideas that can be used by individuals or groups, provides examples demonstrating how these concepts have been or might be used in practice in the mathematical sciences, presents seven tried and tested briefs that can be used at creativity workshops, and offers guidance on to how to evaluate ideas wisely and how to build a team culture in which creativity flourishes. This book is for anyone in the mathematical sciences who wants to be more creative or who wishes to train others in creativity.
This book describes and analyses how a mathematics student can develop into a sophisticated and rigorous thinker.
Numerical Methods that Work, originally published in 1970, has been reissued by the MAA with a new preface and some additional problems. Acton deals with a commonsense approach to numerical algorithms for the solution of equations: algebraic, transcendental, and differential. He assumes that a computer is available for performing the bulk of the arithmetic. The book is divided into two parts, either of which could form the basis of a one-semester course in numerical methods. Part I discusses most of the standard techniques: roots of transcendental equations, roots of polynomials, eigenvalues of symmetric matrices, and so on. Part II cuts across the basic tools, stressing such commonplace problems as extrapolation, removal of singularities, and loss of significant figures. The book is written with clarity and precision, intended for practical rather than theoretical use. This book will interest mathematicians, both pure and applied, as well as any scientist or engineer working with numerical problems.