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Problems From the Book, by Titu Andreescu, Gabriel Dospinescu
Download PDF Problems From the Book, by Titu Andreescu, Gabriel Dospinescu
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The authors provide a combination of enthusiasm and experience which will delight any reader. In this volume they present innumerable beautiful results, intriguing problems, and ingenious solutions. The problems range from elementary gems to deep truths. A trully delightful and highly instructive book, this will prepare the engaged reader not only for any mathematics competition they may enter but also for a life time of mathematical enjoyment. A must for the bookshelves of both aspiring and seasoned mathematicians.
- Sales Rank: #756694 in Books
- Published on: 2010-08-31
- Original language: English
- Dimensions: 8.50" h x 6.75" w x 1.50" l, 2.22 pounds
- Binding: Hardcover
- 571 pages
- A series of articles paired with collections of problems, designed for students preparing for high-level high school contests such as national olymipads.
- 554 pages.
Review
This is an exceptionally well-written book. The material is arranged in small chapters, with brief theory in the beginning of each chapter followed by a set of exceptionally difficult problems with solutions. These solutions are elegant, innovative and beautiful. You learn a lot from the solutions. In every page, you will discover one or more clever steps/tricks that will make you wonder "How come I could not think of that?". If you are preparing for Mathematics Olympiads, working through this book will boost your confidence 100 fold. If you are a math enthusiast, you will enjoy the material - most of it is "Mathematical poetry". Grab it before it gets sold out! --Dr S Muralidharan
Problems from the Book is rife with elegant mathematical pursuits that are well worth the effort of exploring and solving. For high schoolers up through University students, the book's problems will illustrate important concepts and provide hours of fun at every sitting. --David Cordeiro
This book is a treasure of the mathematical gems: many many very nice problems and results, historic notes and useful comments. Readers will also find many very interesting original problems from the authors of the book and from others. If you want to develop your mathematical skills in problem solving and your knowledge in diverse mathematical branches, you will definitely find many instructive topics throughout this book. Many thanks to Prof. Andreescu and his colleagues for their invaluable books and problems. I do highly recommend this book and all other books by Prof. Andreescu to all mathematics lovers: from the pupils preparing to participate in mathematical contests to people searching excitement in mathematics. The book contains the following 23 chapters, in addition to preface, bibliography and index: 1. Some Useful Substitutions 2. Always Cauchy-Schwarz ... 3. Look at the Exponent 4. Primes and Squares 5. T2's Lemma 6. Some Classical Problems in Extremal Graph theory 7. Complex Combinatorics 8. Formal Series Revisited 9. A Brief Introduction to Algebraic Number Theory 10. Arithmetic Properties of Polynomials 11. Lagrange Interpolation Formula 12. Higher Algebra in Combinatorics 13. Geometry and Numbers 14. The Smaller, The Better 15. Density and Regular Distribution 16. The Digit Sum of Positive Integer 17. At the Border of Analysis and Number Theory 18. Quadratic Reciprocity 19. Solving Elementary Inequalities Using Integrals 20. Pigeonhole Principle Revisited 21. Some Useful Irreducibility Criteria 22. Cycles, Paths and Other Ways 23. Some Special Applications of Polynomials --H. A. Shah Ali
About the Author
Dr. Titu Andreescu is an associate professor of mathematics in the Science and Mathematics Education department at the University of Texas at Dallas (UTD). Much of his career has been devoted to competition math, an efficient medium for teaching creative problem-solving for a wide-range of math topics. With over 30 years of experience teaching, coaching, and mentoring the brightest mathematical minds of our age, Dr. Andreescu's books are essential for every math enthusiast's library. Here are just a few highlights from his distinguished career: -Authored, co-authored, and edited more than 40 math books and publications -Head coach and leader of the USA International Mathematical Olympiad (IMO) for 8 years -Director of the Mathematical Association of American (MAA) American Mathematics -Competitions for 5 years -Has contributed hundreds of problems to various math competitions including up to and including the IMO, -Co-founder of the Purple Comet! Math Meet, the first international team based math competition, -Founder and Director of AwesomeMath, an organization that provides enriching experiences in mathematics to intellectually curious learners.
Most helpful customer reviews
9 of 9 people found the following review helpful.
A valuable resource... for the right reader
By Daniel Finkel
When a math book uses the phrase "from the book," in the title, you know they're being ambitious. The reference is to Erdos's description of wanting to experience the mathematics in "God's Book," of all time beautiful problems. And in large part, the authors live up to their ambitions. This book is a collection of excellent, deep problems, along with how to attack them.
Be warned, though, that the barrier to entry is extremely high. A remarkably bright math student I know said that this was the first book recommended to him when he became interested in math contests... at the age of 10. The experience of trying to read it proved very discouraging for him. I can imagine no 10-year-old, no matter how brilliant, who would benefit from reading this book. The appropriate audience is probably 1 in a million high school juniors or seniors, and 1 in 50 college mathematics majors. Basically, if you can get a problem right on the Putnam and you want to take it to the next level, then this book may be for you. I'd say that a Masters level mathematics education is the right background.
For those who have the experience, the interest, and the capacity to handle the technicalities (and there are many), this is a book that pays back the effort you put into it. There is a wealth of problems, many quite beautiful, and while some of the strategies for dealing with them have a "trick" quality to them, others are wonderful. I'd recommend this book especially to mathematics graduate students looking for ideas to pursue during the summers or other time off.
3 of 3 people found the following review helpful.
A Treasure of the Mathematical Gems
By H. A. Shah Ali
This book is a treasure of the mathematical gems: many many very nice problems
and results, historic notes and useful comments.
Readers will also find many very interesting original problems from the authors
of the book and from others. If you want to develop your mathematical skills in problem solving
and your knowledge in diverse mathematical branches, you will definitely find
many instructive topics throughout this book. Many thanks to Prof. Andreescu and
his colleagues for their invaluable books and problems. I do highly recommend
this book and all other books by Prof. Andreescu to all mathematics lovers:
from the pupils preparing to participate in mathematical contests to people
searching excitement in mathematics.
The book contains the following 23 chapters, in addition to preface, bibliography and index:
1. Some Useful Substitutions
2. Always Cauchy-Schwarz ...
3. Look at the Exponent
4. Primes and Squares
5. T2's Lemma
6. Some Classical Problems in Extremal Graph theory
7. Complex Combinatorics
8. Formal Series Revisited
9. A Brief Introduction to Algebraic Number Theory
10. Arithmetic Properties of Polynomials
11. Lagrange Interpolation Formula
12. Higher Algebra in Combinatorics
13. Geometry and Numbers
14. The Smaller, The Better
15. Density and Regular Distribution
16. The Digit Sum of Positive Integer
17. At the Border of Analysis and Number Theory
18. Quadratic Reciprocity
19. Solving Elementary Inequalities Using Integrals
20. Pigeonhole Principle Revisited
21. Some Useful Irreducibility Criteria
22. Cycles, Paths and Other Ways
23. Some Special Applications of Polynomials
3 of 3 people found the following review helpful.
An amazing value...
By Eudaimonia Dad
Problems from the Book is rife with elegant mathematical pursuits that are well worth the effort of exploring and solving. For highs schoolers up through University students, the book's problems will illustrate important concepts and provide hours of fun at every sitting.
Each of the 23 chapters has two parts, a "theory and examples" section that presents the main theoretical results of the topic plus example problems (many have intriguing tricks you can use to solve them), and a "problems for training" section. This book will guide you towards deeper understanding about how problems are designed and how to best approach them - a necessary book for every true math competitor!
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