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First Steps for Math Olympians: Using the American Mathematics Competitions (MAA Problem Book Series) Hardcover – 21 Dec 2006

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'Within each chapter, three well-chosen examples illustrate a variety of problem-solving strategies and applications of concepts. The examples are followed by ten exercises, graduated in difficulty so that nearly every student reader will be able to solve at least one problem easily and nearly every reader will struggle with at least one. The thoughtful choice of examples and exercises is one of the book's strengths, providing a wealth of opportunity for students to become experienced problem solvers within a remarkably small number of pages.' David Wells, Penn State University

'Professor Faires has prepared an impressive problem solving primer. The book presents a wide variety of problems and problem solving strategies, and illustrates how the American Mathematics Competitions can be used to develop many important mathematical techniques.' Richard Gibbs, Fort Lewis College

Book Description

This book considers the basic ideas behind the solutions to the majority of the problems from 50 years of the American Mathematics Competitions. Anyone interested in logical problem solving should find the problems and their solutions stimulating, and those preparing for the Mathematical Olympiad will discover many useful ideas.

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Amazon.com: 10 reviews
13 of 14 people found the following review helpful
An excellent source of topical and practice material for students preparing for the AMC exams 26 May 2010
By Charles Ashbacher - Published on Amazon.com
Format: Hardcover
For two years, I was the primary organizer of having the American Mathematics Competition (AMC) exams on campus and found the students taking the tests to be enthusiastic and eager to do well. Mathematics is like any other human skill in that it can and must be practiced if you expect to succeed. The mathematical background used to create the AMC tests is well known and Faires has a great deal of experience with the testing structure.
This book contains a series of chapters of background material for the AMC exams. Each chapter has a brief introduction to a topic with explanations of the basic definitions, theorems and their consequences. This is followed by a small set of worked examples and then exercises with solutions. These exercises are presented in the format of the AMC questions and most of them are from earlier exams.
The chapter topics are:

*) Arithmetic ratios
*) Polynomials and their zeros
*) Exponentials and radicals
*) Defined functions and operations
*) Triangle geometry
*) Circle geometry
*) Polygons
*) Counting
*) Probability
*) Prime decomposition
*) Number theory
*) Sequences and series
*) Statistics
*) Trigonometry
*) Three-dimensional geometry
*) Functions
*) Logarithms
*) Complex numbers

With material taken directly from years of AMC exams, this book is the best place for team coaches to extract study material for their team.
11 of 12 people found the following review helpful
A great buy, it is worth every dollar 30 Oct. 2008
By A. Citizen - Published on Amazon.com
Format: Hardcover
This book is a great book. This book starts at the beginning (in this case proportions) in very easy format to follow and easy to understand. As they come with practice AMC 10 and 12 problems they will hone your understanding of the material. This book is great for beginners a great companionship for those who have Art of Problem Solving by Richard Ruscyzk.

top marks!
16 of 19 people found the following review helpful
What a great book! 30 July 2007
By Farida Akhter - Published on Amazon.com
Format: Hardcover
I read this book just two weeks before the American Mathematics Contests this year as a freshman. I had never heard of these contests, but reading this book gave me everything I need to know! With its help, I qualified for the AIME (though missed the USA math olympiad by 1 question!). If you are into math contests, trust me, this will significantly raise your score.
9 of 11 people found the following review helpful
As it says: First Steps 22 Mar. 2009
By David Jimenez - Published on Amazon.com
Format: Hardcover Verified Purchase
This is a good source to start a serious training for mathematical competitions, but as it says, it gives you the first step. Should be enough for those who just look to improve their AMC scores significantly, but not so useful for those thinking or wanting to participate on IMO, APMO or similar competition.

For the level it has, I feel it is somewhat overpriced, but besides that, it's a good book.
2 of 2 people found the following review helpful
Too Shallow 2 July 2014
By Customer - Published on Amazon.com
Format: Hardcover
This book is disappointing. Mainly, the problems seem more like tests of understanding, than means of applying understanding to genuinely interesting results. Frequently, Olympiad problems are of the latter. As the reader will likely know, Olympiad problems can have their origin in real mathematics; very few of the problems here are of this type. Due to this, I believe there is some deception in the title. The reader will get to see very little of the creativity and ingenuity that is a necessity for doing well in Olympiad settings.

My recommendation would be to start with Paul Zeitz's, tAaCoPS and graduate to one of the books in the Springer "Problem Books in Mathematics" series. If these are too difficult one could start with Polya's Mathematics and Plausible Reasoning, vol. I. Also, there are a number of subject specific texts that are excellent despite the narrowed focus.
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