Ebook 105 Algebra Problems from the AwesomeMath Summer Program, by Titu Andreescu
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105 Algebra Problems from the AwesomeMath Summer Program, by Titu Andreescu
Ebook 105 Algebra Problems from the AwesomeMath Summer Program, by Titu Andreescu
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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.
- Sales Rank: #150142 in Books
- Published on: 2013-07-15
- Original language: English
- Dimensions: 10.00" h x 7.00" w x .75" l, .0 pounds
- Binding: Hardcover
- 200 pages
About the Author
Titu Andreescu, University of Texas at Dallas, Richardson, TX, USA
Most helpful customer reviews
6 of 6 people found the following review helpful.
A place to start problem solving
By Yair Mulian
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.
This book consists of 16 sections:
1. Preface
2. Completing the square and quadratic equations
3. Factorizations and algebraic identities
4. Factoring expressions involving a - b, b - c, c - a
5. Factoring a^3 + b^3 + c^3 - 3abc
6. AM-GM and Holder's inequality
7. Lagrange's identity and the Cauchy-Schwarz inequality
8. Making linear combinations
9. Fixed points and monotonicity
10. The floor function
11. Taking advantage of symmetry
12. Introductory problems
13. Advanced problems
14. Solutions to introductory problems
15. Solutions to advanced problems
16. Other books from XYZ Press
These "tools" are often needed in problem solving but are rarely included in the standard high school syllabus. These problems were gained after long teaching experience of problem solving at the author's school Awesomemath and demonstrate the way to master the techniques in the easiest way. There are much more than just 105 problems in this book - each of the 13 first chapters contains ~20 solved problems which are not included in this counting.
The book ends with a 105 problems which left for the reader (though a full solution is included) - 52 in the introductory section while 53 in the advanced section.
3 of 3 people found the following review helpful.
Nice problem book
By Blake Thornton
This is a nice problem book suitable for advanced students. The AwesomeMath program is well known as one of the premier summer mathematics programs. If you are considering this book you should definitely look up this program: [...]
Approximately half of the book is solved algebraic problems. The second half is the 105 problems (half "introductory" and half "advanced") and solutions to these problems. These are, of course algebraic problems and I don't think any of the problems are easy. Here's a random example from near the beginning: Prove that 3(x+y+1)^2 + 1 >= 3xy for all real numbers x and y. These are difficult problems, but accessible to good students who want to learn.
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 book's are all top notch and this is no exception.
1 of 1 people found the following review helpful.
This book is perfect for enhancing your algebraic intuition
By Josef Tkadlec
This book is perfect for enhancing your algebraic intuition. The theoretical chapters provide important theorems (often with more proofs) and show many useful techniques. And I genuinely love the magic with numbers and expressions that happens all the time -- for example in one of the introductory problems one is given that two random-looking expressions are bounded from above by 47 and 52, respectively, and is aked to prove that some other expression is bounded by 17. The funny thing is that equality can occur...
Two (hopefuly useful) facts.
1) Even though this book is called 105 Algebra Problems, it contains more than 250 of them -- there are about 150 more problems (also with solutions) in the theoretical chapters, which illustrate the concepts presented there.
2) The chapter Making linear combinations is devoted to systems of equations and the chapter Taking advantage of symmetry focuses on symmetric polynomials.
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