Mathematical Olympiad Challenges [Paperback]

Titu Andreescu (Author), Razvan Gelca (Author), Mark Saul (Foreword)

Book Description

ISBN-10: 0817641556 | ISBN-13: 978-0817641559 | Publication Date: January 10, 2001

This significantly revised and expanded second edition of "Mathematical Olympiad Challenges" is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory from numerous mathematical competitions and journals have been selected and updated. The problems are clustered by topic into self-contained sections with solutions provided separately. Historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on creative solutions to open-ended problems.New to the second edition are: completely rewritten discussions precede each of the 30 units, adopting a more user-friendly style with more accessible and inviting examples; many new or expanded examples, problems, and solutions; and additional references and reader suggestions have been incorporated. Featuring enhanced motivation for advanced high school and beginning college students, as well as instructors and Olympiad coaches, this text can be used for creative problem-solving courses, professional teacher development seminars and workshops, self-study, or as a training resource for mathematical competitions.'This [book] is much more than just another collection of interesting, challenging problems, but is instead organized specifically for learning. The book expertly weaves together related problems, so that insights gradually become techniques, tricks slowly become methods, and methods eventually evolve into mastery. The book is aimed at motivated high school and beginning college students and instructors...I strongly recommend this book for anyone interested in creative problem-solving in mathematics. It has already taken up a prized position in my personal library, and is bound to provide me with many hours of intellectual pleasure' - "The Mathematical Gazette" (Review of the First Edition).

Editorial Reviews

Review

"The authors are experienced problem solvers and coaches of mathematic teams. This expertise shows through and the result is a volume that would be a welcome addition to any mathematician's bookshelf." MAA Online

Book Description

2nd edition, soft cover --This text refers to an alternate Paperback edition.

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Product Details

• Paperback: 260 pages
• Publisher: Birkhäuser Boston (January 10, 2001)
• Language: English
• ISBN-10: 0817641556
• ISBN-13: 978-0817641559
• Product Dimensions: 9.2 x 6.2 x 0.5 inches
• Shipping Weight: 10.4 ounces
• Average Customer Review: 5.0 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #648,050 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

37 of 39 people found the following review helpful:

5.0 out of 5 stars Review for Mathematical Olympiad Challenges., April 4, 2001

By 

Krishnan Shankar (Ann Arbor, Michigan, USA.) - See all my reviews

This review is from: Mathematical Olympiad Challenges (Paperback)

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.

15 of 15 people found the following review helpful:

5.0 out of 5 stars Fantastic Book!, August 5, 2001

By A Customer

This review is from: Mathematical Olympiad Challenges (Paperback)

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++

19 of 20 people found the following review helpful:

5.0 out of 5 stars Pure delight!, February 9, 2001

By 

marian deaconescu (Kuwait) - See all my reviews

This review is from: Mathematical Olympiad Challenges (Paperback)

I have spent many entertaining hours going through the book only to realize how rusty I became in these last 25 years that passed since I was faighting a hopeless battle in the Romanian solvers' contest against the first author.

The book is centered around a number of tools, tricks, techniques, as you want to name them, which are then used to solve a number of problems depending on them.

The problems are carefully arranged in increasing order of difficulty (maybe that's the reason I was able to solve some of the first entries!), so that the reader is not immediately discouraged by problems too hard to solve.

The actual selection of the problems clearly reflects the taste of the authors. Not a bad taste, I would say, if one notices that Titu Andreescu was the man behind the brilliant success of the USA olimpic team in 1994 (all whose members got then the maximum possible number of points).

I was one of the coaches of an olimpic team myself and I know how fast one goes through a list, I would say through *any* list of problems with these gifted guys. From this point of view, the book is an essential instrument for all who contemplate being involved in problem solving training.

But the book is a good teaching tool for high school teachers who wish to challenge their best students with more interesting problems. As another potential pool of customers, I would say that those old sea wolfs as myself, who get bored from time to time of the technicalities of professional maths will find this book a nice companion.

Yes, I like this book and I warmly recommend it to all lovers of problem solving.