Fifty Lectures for American Mathematics Competitions Volume 4

While the books in this series are primarily designed for AMC competitors, they contain the most essential and indispensable concepts used throughout middle and high school mathematics. Some featured topics include key concepts such as equations, polynomials, exponential and logarithmic functions in Algebra, various synthetic and analytic methods used in Geometry, and important facts in Number Theory.

The topics are grouped in lessons focusing on fundamental concepts. Each lesson starts with a few solved examples followed by a problem set meant to illustrate the content presented. At the end, the solutions to the problems are discussed with many containing multiple methods of approach.

I recommend these books to not only contest participants, but also to young, aspiring mathletes in middle school who wish to consolidate their mathematical knowledge. I have personally used a few of the books in this collection to prepare some of my students for the AMC contests or to form a foundation for others.

By Dr. Titu Andreescu
US IMO Team Leader (1995 – 2002)
Director, MAA American Mathematics Competitions (1998 – 2003)
Director, Mathematical Olympiad Summer Program (1995 – 2002)
Coach of the US IMO Team (1993 – 2006)
Member of the IMO Advisory Board (2002 – 2006)
Chair of the USAMO Committee (1996 – 2004)

I love this book! I love the style, the selection of topics and the choice of problems to illustrate the ideas discussed. The topics are typical contest problem topics: divisors, absolute value, radical expressions, Veita’s Theorem, squares, divisibility, lots of geometry, and some trigonometry. And the problems are delicious.

Although the book is intended for high school students aiming to do well in national and state math contests like the American Mathematics Competitions, the problems are accessible to very strong middle school students.

The book is well-suited for the teacher-coach interested in sets of problems on a given topic. Each section begins with several substantial solved examples followed by a varied list of problems ranging from easily accessible to very challenging. Solutions are provided for all the problems. In many cases, several solutions are provided.

By Professor Harold Reiter
Chair of MATHCOUNTS Question Writing Committee.
Chair of SAT II Mathematics committee of the Educational Testing Service
Chair of the AMC 12 Committee (and AMC 10) 1993 to 2000.