Mathematics : History & Philosophy

In How Math Explains the World , mathematician Stein reveals how seemingly arcane mathematical investigations and discoveries have led to bigger, more world-shaking insights into the nature of our world. In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time. Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick. more...

Price: $19.95

Die Urspr??nge mathematischen Denkens, d.h. die Bildung abstrakter Begriffe und die Herstellung von Beziehungen zwischen ihnen, liegen nach heutigem Wissen in den Hochkulturen Mesopotamiens und ??gyptens im 4. Jahrtausend v. Chr. Hier beginnt der Autor seine Zeitreise durch die Mathematik und verfolgt ihre Geschichte bis in ausgehende 20. Jahrhundert. Mathematische Ideen, Methoden und Ergebnisse sowie die sie tragenden Menschen werden ebenso pr??gnant und lebendig geschildert, wie die Kulturen und das Umfeld, in denen Mathematik entstand und sich in Wechselwirkung mit der Gesellschaft entwickelte. Ein spannendes Lesevergn??gen f??r Mathematiker und alle an Mathematik und seiner Geschichte als Teil unserer Kultur Interessierte Der erste Band umfasst die Zeit von den Urspr??ngen bis Zeit der wissenschaftlichen Revolution des 17. Jahrhunderts. more...

Price: $39.95

Agenda Relevance is the first volume in the authors' omnibus investigation of. the logic of practical reasoning, under the collective title, A Practical Logic. of Cognitive Systems. In this highly original approach, practical reasoning is. identified as reasoning performed with comparatively few cognitive assets,. including resources such as information, time and computational capacity. Unlike. what is proposed in optimization models of human cognition, a practical reasoner. lacks perfect information, boundless time and unconstrained access to. computational complexity. The practical reasoner is therefore obliged to be a. cognitive economizer and to achieve his cognitive ends with considerable. efficiency. Accordingly, the practical reasoner avails himself of various. scarce-resource compensation strategies. He also possesses neurocognitive. traits that abet him in his reasoning tasks. Prominent among these is the. practical agent's striking (though not perfect) adeptness at evading irrelevant. information and staying on task. On the approach taken here, irrelevancies are. impediments to the attainment of cognitive ends. Thus, in its most basic sense,. relevant information is cognitively helpful information. Information can then be. said to be relevant for a practical reasoner to the extent that it advances or. closes some cognitive agenda of his. The book explores this idea with a. conceptual detail and nuance not seen the standard semantic, probabilistic and. pragmatic approaches to relevance; but wherever possible, the authors seek to. integrate alternative conceptions rather than reject them outright. A further. attraction of the agenda-relevance approach is the extent to which its principal. conceptual findings lend themselves to technically sophisticated re-expression. in formal models that marshal the resources of time and action logics and. label led deductive systems. Agenda Relevance is necessary reading for researchers in logic, belief. dynamics, more...

Price: $165.00

A sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the author’s intensive and ground breaking studies of the long history of Mesopotamian mathematics, from the late 4th to the late 1st millennium BC. It is argued in the book that several of the most famous Greek mathematicians appear to have been familiar with various aspects of Babylonian “metric algebra,” a convenient name for an elaborate combination of geometry, metrology, and quadratic equations that is known from both Babylonian and pre-Babylonian mathematical clay tablets. The book’s use of “metric algebra diagrams” in the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstract “lettered diagrams” in the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The author’s comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics. more...

Price: $127.40

A mind-bending excursion to the limits of science and mathematics Are some scientific problems insoluble? In Beyond Reason, internationally acclaimed math and science author A. K. Dewdney answers this question by examining eight insurmountable mathematical and scientific roadblocks that have stumped thinkers across the centuries, from ancient mathematical conundrums such as "squaring the circle," first attempted by the Pythagoreans, to G?del's vexing theorem, from perpetual motion to the upredictable behavior of chaotic systems such as the weather. A. K. Dewdney, PhD (Ontario, Canada), was the author of Scientific American's "Computer Recreations" column for eight years. He has written several critically acclaimed popular math and science books, including A Mathematical Mystery Tour (0-471-40734-8); Yes, We Have No Neutrons (0-471-29586-8); and 200% of Nothing (0-471-14574-2). more...

Price: $27.95