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 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 Monthly observed, “[ 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.”
Ravi Vakil is one of the most promising young pure mathematicians. In high school, 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.
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.
The main idea of this book is to introduce the reader to many mathematical ideas, but in a very shallow way. A few problems follow these ideas, giving the reader the opportunity to rediscover many mathematical gems. Beware, the problems are often quite hard. Although not the best source for problems or ideas, this book makes itself unique by a few reasons. First, it contains several sessions "Food for thought", with simple problems to think very deeply. Second, it contains several interesting biographies, from famous mathematicians and not-so famous math students. Finally, it has well chosen subjects and it is fun!