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Problem-Solving Through Problems (Problem Books in Mathematics) Paperback – January 1, 1983

ISBN-13: 978-0387961712 ISBN-10: 0387961712 Edition: 1st

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Problem-Solving Through Problems (Problem Books in Mathematics) + Problem-Solving Strategies (Problem Books in Mathematics) + The Art and Craft of Problem Solving
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Product Details

  • Series: Problem Books in Mathematics
  • Paperback: 352 pages
  • Publisher: Springer; 1st edition (1983)
  • Language: English
  • ISBN-10: 0387961712
  • ISBN-13: 978-0387961712
  • Product Dimensions: 0.7 x 6.5 x 9.5 inches
  • Shipping Weight: 1.1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #171,902 in Books (See Top 100 in Books)

Editorial Reviews

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"This is a very welcome addition. The main message of the book is that the only way to learn to solve problems is to solve problems! I found this book very helpful. I am quite sure the book will be in constant use and I have no hesitation in recommending it." (The Mathematical Gazette)


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35 of 36 people found the following review helpful By David E. Molnar on May 5, 2002
Format: Paperback
I would like to suggest that the audience for this book is somewhat broader than just the "all-star" math students. I will indeed use this book to help students preparing to take the Putnam exam this fall - it is the best book I have seen for this purpose.
But in just the first two chapters, Larson presents strategies such as working backwards, modifying the problem, mathematical induction, and the pigeonhole principle, in a way which all math majors can benefit from. A graduating senior reported that once he started participating in math contests, his performance in ALL of his math classes improved. Problem solving unifies mathematical understanding. This student took the Putnam last fall (which, if you've got this far without knowing, is a six-hour national undergraduate mathematics competition taken by 3000 students in the US and Canada each year, approximately half of whom score zero) just to see what he could do, to gauge his improvement in mathematics. There isn't much more of a compliment a student could give me, intentional or otherwise.
That can't all be attributed to this book, but it is that good. The presentation is unique; the organization - by strategy, rather than by year or whatever you see in other problem books - is illuminating by itself, and has improved my pedagogy; and he just makes hard problems look easy.
Any student past the level of Linear Algebra who is up for a challenge will benefit from this book.
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18 of 19 people found the following review helpful By A Customer on September 24, 1998
Format: Paperback
An excellent resource for anyone interested in mathematical problem solving at the undergraduate level. Comes with many interesting problems taken from various mathematics contests. Additionally, the writing is clear and user-friendly. The only thing lacking is a companion workbook/solution guide. If you know anyone taking the AIME, USAMO, IMO, or Putnam exam, do them a favor and buy them this book! It's well worth it!
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7 of 7 people found the following review helpful By A Customer on June 3, 2001
Format: Paperback Verified Purchase
This book would be especially helpful for someone planning to compete in the Putnam Exam. Lots of example covering many topics in upper undergraduate maths and of course the classic "folklore" techniques, strategies, and tools of problem solving(e.g., pigeonhole, invariants, coloring proofs, etc.). This is more of an advanced book as compared to others aimed at Olympiad contestants. Nonetheless, it is an invaluable source for anyone interested in non-routine mathematics.
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14 of 17 people found the following review helpful By Nihal Mehta on January 6, 2003
Format: Paperback Verified Purchase
Finally, a book that develops problem solving techniques in a structured way for the Putnam. However, the techniques can be generally applicable to solve problems in many different areas.
The power of using "first principles" to solve problems that at first sight seem almost impossible is brought out clearly. (Example, show that any sequence of consecutive integers is divisible by n!. Where does even start to solve such problems? The book shows you how.)
You can read the book from the beginning to end, but a better way is to read it at random. Read the first chapter, though. It does a marvellous job of enumerating the different types of techniques.
Enjoy this book. You'll be amazed at how simple ideas can lead to difficult problems.
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1 of 1 people found the following review helpful By Enrique Trevino VINE VOICE on April 17, 2010
Format: Paperback
I have been teaching for the Math Olympiad for seven years and this book is one of my favorite resources. It covers a lot of great techniques for problem solving, specially the first chapter. The first chapter is a great introduction to problem solving. The chapters covers several techniques which the author calls heuristics, which are the basics. This chapter is kind of like learning the basic moves of a new dance. To do learn any other aspects of the dance, you need to master the basics and this book really honed in on the basics. Mastering the first chapter is, in my opinion, a crucial step in preparing for mathematical competitions, like the Mathematical Olympiad or the Putnam.

I highly recommend this book.
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