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The Golden Section
The Golden Section has played a part since antiquity in many parts of geometry, architecture, music, art and philosophy. However, it also appears in the newer domains of technology and fractals. This book aims both to describe examples of the Golden Section, and to show some paths to further developments.
I, Mathematician
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.
Proofs and Confirmations
This is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author recounts the story of the search for and discovery of a proof of a formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While apparent that the conjecture must be true, the proof was elusive. Researchers became drawn to this problem, making connections to aspects of invariant theory, to symmetric functions, to hypergeometric and basic hypergeometric series, and, finally, to the six-vertex model of statistical mechanics. All these threads are brought together in Zeilberger's 1996 proof of the original conjecture. The book is accessible to anyone with a knowledge of linear algebra. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something new here.
Half a Century of Pythagoras Magazine
Half a Century of Pythagoras Magazine is a selection of the best and most inspiring articles from this Dutch magazine for recreational mathematics. Founded in 1961 and still thriving today, Pythagoras has given generations of high school students in the Netherlands a perspective on the many branches of mathematics that are not taught in schools. The book contains a mix of easy, yet original puzzles, more challenging - and at least as original – problems, as well as playful introductions to a plethora of subjects in algebra, geometry, topology, number theory and more. Concepts like the sudoku and the magic square are given a whole new dimension. One of the first editors was a personal frien...
How Euler Did It
How Euler Did It is a collection of 40 monthly columns that appeared on MAA Online between November 2003 and February 2007 about the mathematical and scientific work of the great 18th-century Swiss mathematician Leonhard Euler. Inside we find interesting stories about Euler's work in geometry and his solution to Cramer's paradox and its role in the early days of linear algebra. We see Euler's first proof of Fermat's little theorem for which he used mathematical induction, as well as his discovery of over a hundred pairs of amicable numbers, and his work on odd perfect numbers, about which little is known even today. Professor Sandifer based his columns on Euler's own words in the original language in which they were written. In this way, the author was able to uncover many details that are not found in other sources.
Mathematics in Historical Context
What would Newton see if he looked out his bedroom window? This book describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society. It takes the reader on a grand tour of history from the ancient Egyptians to the twentieth century to show how mathematicians and mathematics were affected by the outside world, and at the same time how the outside world was affected by mathematics and mathematicians. Part biography, part mathematics, and part history, this book provides the interested layperson the background to understand mathematics and the history of mathematics, and is suitable for supplemental reading in any history of mathematics course.
Mathematical Apocrypha
Collection of stories about famous contemporary mathematicians, with illustrations.
