Ravi Vakil

Excerpt from a review in the "Mathematics Teacher." A Mathematical Mosaic is a collection of wonderful topics from nmber theory through combinatorics to game theory, presented in a fashion that seventh- and eighth- grade students can handle yet high school students will find challenging." John Cocharo, Saint Mark's School of Texas, Dallas, TX

Patterns & Problem Solving

A Mathematical Mosaic

Ravi Vakil, described in the San Francisco Chronicle as “a legend in the world of math competitions” has finally 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 has received wide acclaim from mathematics teachers, professors and the mathematics community at large. 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.”

Jason Starr

Brendan Hassett

James McKernan

This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

A Celebration of Algebraic Geometry

Kiran S. Kedlaya

Bjorn Poonen

This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.

Ravi Vakil

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