A Mathematical Mosaic: Patterns & Problem Solving (Revised Edition)

The Ideal Gift for the Math Wiz in your family from the President of the American Mathematical Society

Ravi Vakil, described in the San Francisco Chronicle as “a legend in the world of math competitions” has released his long-awaited second edition of A Mathematical Mosaic: Patterns & Problem Solving. Regarded by many as a seminal book in the field of mathematics competitions, the first edition of A Mathematical Mosaic received such wide acclaim from mathematics teachers, professors and the mathematics community at large that a second edition was updated and published a decade later..

In a review in The Mathematics Teacher, high school teacher John Cocharo wrote, “Without a doubt, this book is a must for any library, teacher’s reference or student’s amusement.” André Toom in his review in the Mathematical Monthlyobserved, “[A Mathematical Mosaic] speaks in an interesting and understandable way about number theory, combinatorics, game theory, geometry, and calculus, to say nothing about magic tricks, puzzles and other digressions. What is most important is that whenever Vakil starts to discuss something, he never leaves the reader without a piece of exact, rigorous knowledge.”

In high school, Ravi Vakil was already a promising mathematician. He placed first in the USA Mathematical Olympiad, and at the International Mathematical Olympiad won two gold medals and one silver medal, and wrote a perfect paper. As an undergraduate, he won the top award of "Putnam Fellow" in the William Lowell Putnam Mathematical Competition in each of his four years. This is a feat achieved by only 8 competitors since the inception of the Putnam competition in 1938. Ravi subsequently received his Ph.D. from Harvard, taught at Princeton and MIT, and is now Full Professor of Mathematics at Stanford University and President of the American Mathematical Society.

A Mathematical Mosaic is used extensively by students in high school gifted programs that run during the summer at various universities in the United States and Canada.

Ravi Vakil s resume reads like a dictionary of superlatives. During his high school years he won every major mathematics competition. These include first place standing in the Canadian Mathematical Olympiad for two successive years, first place standing in North America on the USA Mathematical Olympiad, and two gold medals and one silver medal in the International Mathematical Olympiad (including a perfect score). He also won first prize in the Canadian Association of Physicists Competition and led his high school computer team to three provincial championships. During his undergraduate years at the University of Toronto, Ravi raised his brilliant achievements to new heights. In all four years he placed among the top five competitors in the prestigious North American William Lowell Putnam Mathematical Competition, earning him the top award of Putnam Fellow in each year. He graduated in 1992 with B. Sc. and M. Sc. degrees; for his B. Sc., he was awarded the Governor General s Medal for the highest graduating marks at the University of Toronto. Ravi s extraordinary achievements have not prevented him from pursuing his many other interests. These include squash, debating, student government, journalism, and Amnesty International. For this breadth of involvement he has received numerous scholarships including the John H. Moss Scholarship for the best all-round graduating student at the University of Toronto. Ravi Vakil is a compassionate person with an eager willingness to help others. He has coached the Canadian Team at the International Mathematical Olympiad from 1989 through 1996. He was also cofounder of Mathematical Mayhem, a mathematical problem-solving journal for high school and undergraduate students the only student-run journal of its kind in the English-speaking world. This book was written while Ravi was a graduate student. Since the first edition was completed, Ravi received his Ph.D. in pure mathematics at Harvard in 1997, and subsequently taught at Princeton and M.I.T. before moving to Stanford in 2001. He is an algebraic geometer, and his work touches on many other parts of mathematics, including topology, string theory, applied mathematics, combinatorics, number theory, and more. His awards include the Alfred P. Sloan Research Fellowship, the National Science Foundation CAREER Award, the American Mathematical Society Centennial Fellowship, and the Dean s Award for Distinguished Teaching. In 2004, he traveled to the White House to receive the Presidential Early Career Award for Scientists and Engineers. He continues to work extensively with talented younger mathematicians at all levels, from high school (through math circles, camps, and olympiads) through recent Ph.D. s.