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Title: Mathematical Olympiad Challenges by Titu Andreescu, Razvan Gelca ISBN: 0-8176-4155-6 Publisher: Birkhauser Boston Pub. Date: 26 April, 2000 Format: Paperback Volumes: 1 List Price(USD): $29.95 |
Average Customer Rating: 5 (5 reviews)
Rating: 5
Summary: This book is amazing!
Comment: I remember the first time I touched this book, i fell so in love with it that it was very hard for me to remember how many other things I had to do during my day. It really illustrated how every problem you solve (or at least try really hard) can be an entire lesson you can use later on.
It is very well organized, even the problems in each section are set in a way that each one helps with the previous one in case a more creative solution doesn't show up...
I love this book, and I really recommend it for any student studying for any math contest around the world. It really helped me, and I'm sure it will do the exact same thing to anyone with the desire to spend countless hours solving beautiful math problems. Good luck, God bless you all :)
Pura vida.
Rating: 5
Summary: Fantastic Book!
Comment: This is a marvelous book for lovers of mathematical problems. Scattered about are wonderful problems in Geometry, Trig, Algebra and Analysis, Invariants, and Number Theory. A truly delightful read that will have you working on some problems for hours. Each section introduces the reader to the concept or technique needed to solve the problems in each section. The problem sets start off with a few "warm-up" problems that quickly build up to some that require keen (some brilliant!) insight. A true gem among most problem books since this book is not merely a book of problems, but also contains clear presentations and introductions to various concepts in mathematics. The solutions are a true delight, the ingenuity and beauty of mathematical problem solving is captured exquisitely in this fabulous book. Highly Recommended. A++
Rating: 5
Summary: Review for Mathematical Olympiad Challenges.
Comment: The book, Mathematical Olympiad Challenges", is a delightful book on problem solving written by two of the leaders of the craft. Mathematical problem solving is a skill that can be honed like any other and this book is an ideal tool for the job. Problem solving usually involves elementary mathematics; this does not mean "easy mathematics". An elementary mathematical problem is one that is easily stated and can be understood by anyone who has had basic training in the subject (up to calculus). The solution, though, may be quite hard and may require a great deal of ingenuity and thought.
It should be noted that being an exceptional problem solver does not necessarily make one a good mathematician, but it helps. This is certainly true of the second author who is also a renowned mathematician in the field of knot theory and three dimensional topology.
As mentioned the two authors have a sterling record in the arena of problem solving and in coaching would be problem solvers. I am more familiar with Razvan Gelca who led the University of Michigan team to a top five finish in the highly competitive and extremely challenging Putnam exam. This exam is administered yearly and is open to all college students in North America; usually around 430 universities and colleges send teams to compete in the Putnam. The exam has been offered since the thirties and finishing at the top carries a great deal of prestige. Razvan's superior abilities led to the spectacular success of the Michigan team which was no mean feat.
My own experience with the book has been one of revelation with each passing page. I used the book to teach the problem solving course at the University of Michigan, Ann Arbor, and it helped me immensely. The book possesses a variety of topics in elementary mathematics, ranging from algebra to geometry to trigonometry to number theory. Each chapter is divided into sections and each section has a theme. In keeping with the theme, the authors mention some useful formulae and/or facts that may be used in that section. This is followed by a demonstration of some dazzling problem solving techniques applied to a couple of problems. This is then followed by a list of challenging problems of varying levels of difficulty, all related to the theme of the section. There are roughly 18 such sections and many, many problems to think about. The rest of the book, which is the bulk of it, is dedicated to providing elegant solutions to every problem posed in the first part. Occasionally a problem merits more than one solution and sometimes the way is pointed to some interesting mathematics. The authors also acknowledge the source of many of the problems in the book which is a good indicator of the pedigree of the problem. Almost every solution is a gem and each problem demands its own style of solution. As noted earlier, problem solving is a skill and the authors try and succeed in conveying that idea in the problems and solutions they present.
Here is a sample problem from the book; if you can't do it and want to know how, check out the book:
"Show that any cube can be divided into 'n' cubes for any integer 'n' bigger than 54."
In summary if you are interested in figuring out puzzles, if you are a problem solver of elementary mathematical problems, or if you are just plain curious how a large fraction of mathematicians got hooked on mathematics, I would highly recommend you give this book a try. You may learn something and may even enjoy yourself in the process.
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