The Art of Problem Solving: Volume 1: The BASICS Solutions

Rating:
Summary: The best collection of problems for math competitions.
Review: There are many books designed to teach the basics of solving math problems. While the coverage is generally the same, quite naturally, some are much better than others. When attempting to explain basic mathematical concepts, style is very important, almost as much as in a novel. For without a fluid and captivating style, a problem-solving book is just a list of problems and a novel is just a set of sentences with a common theme.
I found the style of this book to be captivating, the authors clearly have a great deal of experience in teaching these topics to a wide variety of audiences. They waste very few words, although they do converge to a humor point on occasion. Their treatment of the topics is very well done, as I read it I was reminded of some of the classic results that I have not used for some time. The topics covered include linear and quadratic equations; exponents and logarithms; complex numbers, triangles and quadrilaterals; three dimensional geometry, functions, sequences, series and basic combinatorics.
There are many examples in the book, and they are used to reinforce the topic. Many problems, nearly all of which appeared in a problem-solving contest, are included at the end of each chapter. A separate manual of detailed solutions is also available. While this book could be used as a textbook, it would be an excellent choice for study material when preparing a group for a problem-solving contest. Since most of the exercises have been used in contests, you get a complete sampling of the kinds of problems used in the competitions. The contests where the problems were used are the MATHCOUNTS competition, the Mandelbroit Competition, the American Mathematical Competitions and the American Regions Mathematics League competition.
Success in problem solving is largely achieved the way it is in sports. By practicing, starting with the simpler problems and working your way up to more complex tasks, it is possible for nearly everybody to become proficient in solving problems. This book contains one of the best collections of practice problems that you will ever find.

Rating:
Summary: Problem Solving for the Advanced Student
Review: This is an excellent book for the advanced middle school or early high school student. Students who did excellenet in pre-algebra and/or algebra who also love math will gain a lot from this book. This book is also excellent for the teacher who's administration allows for more than the standard boring Algebra content to be taught in class or for a math team.

Rating:
Summary: Problem Solving for the Advanced Student
Review: This is an excellent book for the advanced middle school or early high school student. Students who did excellenet in pre-algebra and/or algebra who also love math will gain a lot from this book. This book is also excellent for the teacher who's administration allows for more than the standard boring Algebra content to be taught in class or for a math team.