- Paperback: 236 pages
- Publisher: The Mathematical Association of America; illustrated edition edition (27 Feb 2003)
- Language English
- ISBN-10: 088385645X
- ISBN-13: 978-0883856451
- Product Dimensions: 22.6 x 15.2 x 1.5 cm
- Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
- Amazon Bestsellers Rank: 1,512,103 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Product Description
Product Description
Rather than simply a collection of problems, this book can be thought of as both a tool chest of mathematical techniques and an anthology of mathematical verse. The authors have grouped problems so as to illustrate and highlight a number of important techniques and have provided enlightening solutions in all cases. As well as this there are essays on topics that are not only beautiful but also useful. The essays are diverse and enlivened by fresh, non-standard ideas. This book not only teaches techniques but gives a flavour of their past, present and possible future implications. It is a collection of miniature mathematical works in the fullest sense.
Book Description
The authors have grouped problems to illustrate a number of important techniques, and provided enlightening solutions in all cases. There are numerous essays on diverse topics that are enlivened by fresh ideas. This book not only teaches techniques but gives a flavour of their past, present and possible future implications.
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Here we consider a sum of the form where f is a numerical function. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Back Cover
Here we consider a sum of the form where f is a numerical function. Read the first page
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Customer Reviews
Most Helpful Customer Reviews
1 of 1 people found the following review helpful
Format:Paperback
The authors of this excellent book met in 1993 at an International Mathematics Olympiad, where they swiftly conceived the idea for this project, as a collection of fresh and non-standard problem-solving techniques that would be aesthetically pleasing at the same time. The result, clearly a labour of love, is arranged into groups of five short chapters, each bringing together three or four problems under a common theme. You will find here offbeat circle theorems, unusual inequalities, quirky logic puzzles and much more besides. Often there is some interesting historical footnote to the central problem, and often too there is humour in the way the problem has been posed. The chapters appear in groups of five interspersed with Coffee Breaks, that consist of a few simpler stand-alone problems. The questions themselves come from Olympiads and journals for the most part, excellent preparation for a student soon to enter an Olympiad, or for an able Further Mathematician who would like a challenge. The analogy with a rich mathematical tool chest is tempting: if you are looking for a new chisel or rasp then this book is a good place to look. But the authors prefer, "an anthology of mathematical verse," and there is certainly a strong sense of the poetry of good mathematics here.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
3 reviews
14 of 14 people found the following review helpful
Please write volume 2, 3, 4....
8 April 2003
Format:Paperback|Amazon Verified Purchase
This book is a co-work of two world-known Mathematics Olympiad Masters, Svetoslav Savchev from Bulgaria and Titu Andreescu from USA. Both are trainer/leader/problem committe member of the national/IMO team for many years, and are really excellent and famous in the olympiad field.
Reader may ask that what this thin book will give in an age with numerous contest problems and with new training books appearing every year. The answer is "the Insight". It is divided into 50 sections(topics), each section is a essay containing the analyzing several(3 to 6) related problems, usuall from easier to harder. These problems are carefully selected from the huge collection of problems in numerous mathematics magazines and contests.
This is the FIRST book in english to teach olympiad readers that how the problems are relating with each other, how a simple idea grows into a hard and beautiful problem, how to think in a higher point of view. However, the style of this book is rather relax and warm.
This is not a textbook nor a problem book, neither suitable for training owing to its form. It's for reading, appreciating, and for those teachers/students who have been familiar enough with the standard problems and tired of training sessions. If you want to know what a mathematical olympiad is, what a beautiful cute problem is, this book is for you.
This book is a pearl indeed. I really hope the authors will publish the volume 2,3,...
7 of 7 people found the following review helpful
Mathematical Miniatures
27 Jan 2004
Format:Paperback
Mathematical Miniatures is a wonderful book, with a new approach to an old favorite topic: problem solving.
The book is comprised of 50 chapters, each one telling a mathematical story. The majority of the problems come from math Olympiads and the most clever solutions and applications are always accompanied by the name of the problem solver. One cannot help but be in awe at amazing insights in solving tremendously complicated problems, performed by high school students under the constrictive time frame of the Olympiad tests.
The topics of the problems are reflective of the Math Olympiads topics, and will particularly appeal to the pure mathematician. But the beauty of the ingenious, albeit elementary mathematics will grab any passionate mathematician's attention. The sequence of 50 chapters - 50 mathematical topics is broken by nine "coffee breaks", and preceded by a warm up set. Each of the breaks proposes to the reader a handful of problems - some easy, some quite hard - all of them teasing and inviting. This is to say to the reader: don't just read about how others have cleverly solved problems, try your hand at some! I have to confess to falling for this trap several times and going through the house mumbling to myself "hmm... I used to get this in 5 minutes when I was in high school". Luckily all these problems come with solutions as well.
Overall, a delightful book, recommended not only for one's mathematical reading pleasure, but also for math clubs in either high school or college.
7 of 22 people found the following review helpful
For the professional mathematician
23 April 2003
Format:Paperback|Amazon Verified Purchase
A bit too over my head. Really a book for the professional, not the amateur. I love math, as explained in a college textbook, but this book was a bit too Poincaire-brief and condensed for me. I need a more verbose, baby-steps book.
So that's why I'm giving it two stars. Of course, once you are a master, then less is more.
I did give it away to a professional mathematician, who liked it.
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