Gerald L. Alexanderson - Böcker

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.

Fascinating Mathematical People is a collection of informal interviews and memoirs of sixteen prominent members of the mathematical community of the twentieth century, many still active. The candid portraits collected here demonstrate that while these men and women vary widely in terms of their backgrounds, life stories, and worldviews, they all share a deep and abiding sense of wonder about mathematics. Featured here--in their own words--are major research mathematicians whose cutting-edge discoveries have advanced the frontiers of the field, such as Lars Ahlfors, Mary Cartwright, Dusa McDuff, and Atle Selberg. Others are leading mathematicians who have also been highly influential as teachers and mentors, like Tom Apostol and Jean Taylor. Fern Hunt describes what it was like to be among the first black women to earn a PhD in mathematics. Harold Bacon made trips to Alcatraz to help a prisoner learn calculus. Thomas Banchoff, who first became interested in the fourth dimension while reading a Captain Marvel comic, relates his fascinating friendship with Salvador Dali and their shared passion for art, mathematics, and the profound connection between the two.Other mathematical people found here are Leon Bankoff, who was also a Beverly Hills dentist; Arthur Benjamin, a part-time professional magician; and Joseph Gallian, a legendary mentor of future mathematicians, but also a world-renowned expert on the Beatles. This beautifully illustrated collection includes many photographs never before published, concise introductions by the editors to each person, and a foreword by Philip J. Davis.

This book is the second volume based on lectures for pre-college students given by prominent mathematicians in the Bay Area Mathematical Adventures (BAMA). This book reflects the flavor of the BAMA lectures and the excitement they have generated among the high school and middle school students in the Silicon Valley. The topics cover a wide range of mathematical subjects each treated by a leading proponent of the subject at levels designed to challenge and attract students whose mathematical interests are just beginning. In addition, the treatments given here will intrigue and enchant a more mature mathematician. It is hoped that the publication of these lectures will expose students outside of the San Francisco Bay Area to interesting mathematical topics and treatments outside of their normal experience in the classroom. Mathematical educators are encouraged to offer the students in their own localities similar opportunities to come into contact with exciting adventures in mathematics.

The MAA was founded in 1915 to serve as a home for The American Mathematical Monthly. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott.This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.

G. H. Hardy (1877-1947) ranks among the great mathematicians of the twentieth century. He did essential research in number theory and analysis, held professorships at Cambridge and Oxford, wrote important textbooks as well as the classic A Mathematician's Apology, and famously collaborated with J. E. Littlewood and Srinivasa Ramanujan. Hardy was a colorful character with remarkable expository skills. This book is a feast of G. H. Hardy's writing. There are selections of his mathematical papers, his book reviews, his tributes to departed colleagues. Some articles are serious, whereas others display a wry sense of humor. And there are recollections by those who knew Hardy, along with biographical and mathematical pieces written explicitly for this collection. Fans of Hardy should find much here to like. And for those unfamiliar with his work, The G. H. Hardy Reader provides an introduction to this extraordinary individual.

G. H. Hardy (1877-1947) ranks among the great mathematicians of the twentieth century. He did essential research in number theory and analysis, held professorships at Cambridge and Oxford, wrote important textbooks as well as the classic A Mathematician's Apology, and famously collaborated with J. E. Littlewood and Srinivasa Ramanujan. Hardy was a colorful character with remarkable expository skills. This book is a feast of G. H. Hardy's writing. There are selections of his mathematical papers, his book reviews, his tributes to departed colleagues. Some articles are serious, whereas others display a wry sense of humor. And there are recollections by those who knew Hardy, along with biographical and mathematical pieces written explicitly for this collection. Fans of Hardy should find much here to like. And for those unfamiliar with his work, The G. H. Hardy Reader provides an introduction to this extraordinary individual.

The Putnam Competition has been providing a challenge to gifted college mathematics students since 1928. This book, the second of the Putnam Competition volumes, contains problems with their solutions for the years 1965-1984. Additional solutions are presented for many of the problems. Included is an essay on recollections of the first Putnam Exam by Herbert Robbins, as well as appendices listing the winning teams and students from 1965 through 1984. This volume offers the problem solver an enticing sample of challenging problems and their solutions.