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The Pea and the Sun
Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.
Unexpected Expectations
Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball explores how paradoxical challenges involving mathematical expectation often necessitate a reexamination of basic premises. The author takes you through mathematical paradoxes associated with seemingly straightforward applications of mathematical expectation and shows how these unexpected contradictions may push you to reconsider the legitimacy of the applications. The book requires only an understanding of basic algebraic operations and includes supplemental mathematical background in chapter appendices. After a history of probability theory, it introduces the basic laws of probability as well as the definition and appl...
The Outer Limits of Reason
This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, ...
Why Beliefs Matter
In the follow-up to his acclaimed Science in the Looking Glass, Brian Davies discusses deep problems about our place in the world, using a minimum of technical jargon. The book argues that 'absolutist' ideas of the objectivity of science, dating back to Plato, continue to mislead generations of both theoretical physicists and theologians. It explains that the multi-layered nature of our present descriptions of the world is unavoidable, not because of anything about the world, but because of our own human natures. It tries to rescue mathematics from the singular and exceptional status that it has been assigned, as much by those who understand it as by those who do not. Working throughout from direct quotations from many of the important contributors to its subject, it concludes with a penetrating criticism of many of the recent contributions to the often acrimonious debates about science and religions.
Heinz Werner and Developmental Science
Heinz Werner (1890-1964) was one of the three key developmental psychologists of the 20th century – along with Jean Piaget and Lev Vygotsky. This book is a new exploration of Werner’s ideas and their social contexts – in Vienna in his student years, in Hamburg up to 1933, followed by the years of transit as an immigrant to America at times of economic depression, finally culminating in his establishment of the prominent "Clark tradition" in American psychology in the 1950s. The book offers an in-depth analysis of Werner’s ideas as they were originally formulated in Vienna and Hamburg, and how they were changed by North American influences. Werner’s pivotal role between European and...
The Mathematics of Various Entertaining Subjects
The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics. This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, com...
The Shape of Inner Space
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
UN Peacekeeping in Civil Wars
An in-depth 2007 analysis of the sources of success and failure in UN peacekeeping missions in civil wars.
An Introduction to Mathematical Reasoning
This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
Third World Political Ecology
An effective response to contemporary environmental problems demands an approach that integrates political, economic and ecological issues. Third World Political Ecology provides an introduction to an exciting new research field that aims to develop an integrated understanding of the political economy of environmental change in the Third World. The authors review the historical development of the field, explain what is distinctive about Third World political ecology, and suggest areas for future development. Clarifying the essentially politicised condition of environmental change today, the authors explore the role of various actors - states, multilateral institutions, businesses, environmen...
