# 105 Algebra Problems from the AwesomeMath Summer Program

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*Titu Andreescu*

A publication of XYZ Press

The main purpose of this book is to provide an introduction to central
topics in elementary algebra from a problem-solving point of view. While
working with students who were preparing for various mathematics competitions
or exams, the author observed that fundamental algebraic techniques were not
part of their mathematical repertoire. Since algebraic skills are not only
critical to algebra itself but also to numerous other mathematical fields, a
lack of such knowledge can drastically hinder a student's performance. Taking
the above observations into account, the author has put together this
introductory book using both simple and challenging examples which shed light
upon essential algebraic strategies and techniques, as well as their
application in diverse meaningful problems. This work is the first volume in a
series of such books.

The featured topics from elementary and classical algebra include
factorizations, algebraic identities, inequalities, algebraic equations and
systems of equations. More advanced concepts such as complex numbers, exponents
and logarithms, as well as other topics, are generally avoided. Nevertheless,
some problems are constructed using properties of complex numbers which
challenge and expose the reader to a broader spectrum of mathematics. Each
chapter focuses on specific methods or strategies and provides an ample
collection of accompanying problems that graduate in difficulty and complexity.
In order to assist the reader with verifying mastery of the theoretical
component, 105 problems are included in the last sections of the book, of which
52 are introductory and 53 are advanced.

All problems come together with solutions, many employing several approaches
and providing the motivation behind the solutions offered.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

#### Readership

Middle and high school students interested in mathematics competition preparation.

#### Reviews & Endorsements

In case you are thinking about participating in a mathematical contest in the future and need a good place to start this might be one of the best choices for you. ...

-- Yair Mulian

... This book is clearly meant for students who enjoy working on such problems and learning new tricks to solve problems. I strongly recommend this book for such a student. Andresscu's books are all top notch and this is no exception.

-- Blake Thornton

This is an excellent collection of problems, solutions, and narrative that would be great as self-study for motivated high school students, or for a math circle leader to use as a resource for a problem solving class. I'm very glad that I worked through the material. Content-wise, this book is top-notch! ...

-- Japheth Wood