Problem Solving Through Problems [Paperback]

Loren C. Larson (Author)

Book Description

Publication Date: 1983 | ISBN-10: 0387961712 | ISBN-13: 978-0387961712 | Edition: 1st

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

Editorial Reviews

Review

From the reviews: "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)

Product Details

• Paperback: 363 pages
• Publisher: Springer; 1st edition (1983)
• Language: English
• ISBN-10: 0387961712
• ISBN-13: 978-0387961712
• Product Dimensions: 9.2 x 6.1 x 0.7 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.9 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #386,308 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

34 of 35 people found the following review helpful:

5.0 out of 5 stars How can I have not given this 5 stars yet?, May 5, 2002

By 

David E. Molnar (MN) - See all my reviews
(REAL NAME)   

This review is from: Problem Solving Through Problems (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.

17 of 18 people found the following review helpful:

4.0 out of 5 stars Lives up to the title, September 24, 1998

By A Customer

This review is from: Problem Solving Through Problems (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!

7 of 7 people found the following review helpful:

5.0 out of 5 stars Excellent source for problems and problem solving techniques, June 3, 2001

By A Customer

This review is from: Problem Solving Through Problems (Paperback)

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.