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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.

An accessible compendium of essays on the broad theme of mathematics and sports.

Originally published in 1893, this book was significantly revised and extended by the author (second edition, 1919) to cover the history of mathematics from antiquity to the end of World War I. Since then, three more editions were published, and the current volume is a reproduction of the fifth edition (1991). The book covers the history of ancient mathematics (Babylonian, Egyptian, Roman, Chinese, Japanese, Mayan, Hindu, and Arabic, with a major emphasis on ancient Greek mathematics). The chapters that follow explore European mathematics in the Middle Ages and the mathematics of the sixteenth, seventeenth, and eighteenth centuries (Vieta, Decartes, Newton, Euler, and Lagrange). The last and...

The curious property that John Farey observed in one of Henry Goodwyn's tables has enduring pratical and theoretic interest. This book traces the curious property, the mediant, from its initial sighting by Nicolas Chuquet and Charles Haros to its connection to the Riemann hypothesis by Jerome Franel.

Continuing its rich tradition of engaging students and demonstrating how mathematics applies to various fields of study, the new edition of this text is packed with real data and real-life applications to business, economics, social and life sciences. Users continually praise Sullivan and Mizrahi for their attention to conceptual development, well-graded and applied examples and exercise sets that include CPA, CMA, and Actuarial exam questions. The new Eighth Edition also features a new full color design and improved goal-oriented pedagogy to facilitate understanding, including: More opportunities for the use of graphing calculator, including screen shots and instructions. Icons clearly identify each opportunity for the use of spreadsheets or graphing calculator. Work problems appear throughout the text, giving the student the chance to immediately reinforce the concept or skill they have just learned. Chapter Reviews contain a variety of features to help synthesize the ideas of the chapter, including: Objectives Check, Important Terms and Concepts, True-False Items,Fill in the Blanks, Review Exercises, Mathematical Questions from Professional Exams (CPA).

Written for liberal arts students and based on the belief that learning to solve problems is the principal reason for studying mathematics, Karl Smith introduces students to Polya’s problem-solving techniques and shows them how to use these techniques to solve unfamiliar problems that they encounter in their own lives. Through the emphasis on problem solving and estimation, along with numerous in-text study aids, students are assisted in understanding the concepts and mastering the techniques. In addition to the problem-solving emphasis, THE NATURE OF MATHEMATICS is renowned for its clear writing, coverage of historical topics, selection of topics, level, and excellent applications problem...