A Mathematical Mosaic: Patterns & Problem Solving by Ravi Vakil is a must for teachers seeking to challenge their best students, and for students preparing for mathematics competitions. In this exciting book, Vakil, a preeminent winner of International Mathematics Olympiads, develops some of the powerful problem-solving ideas underpinning the major branches of mathematics and weaves them into a mosaic that reveals their interconnections.The mathematics is presented at the level of the capable high school mathematics student, but there is much substance for the advanced undergraduate and the intelligent lay reader. You will find this book an invaluable source of enrichment problems and ideas. The style is informal, friendly, and often humorous. In this book, Vakil profiles seven other mathematics olympiad winners including Noam Elkies, the youngest professor to receive tenure at Harvard.