Customer Reviews

Problem Solving Through Problems

5 star:		(7)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

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.

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!

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.

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.

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.

This really is a great mathematics book. Before reading this, I read How to Solve It: A New Aspect of Mathematical Method by George Polya, another classic in math literature. This book takes the method of Polya's heuristics one step further by providing a wealth of examples in various disciplines including geometry, calculus, and abstract algebra. For anyone interested in developing problem solving skills, this book is a MUST!

The only downside: no hints and solutions.

Awesome book!!!!!

i nearly owned all the books on problem solving because i just love it.
i rarely write book reviews but only for the excellent ones.
this book is a true gem, mathematical olympiad challenges is goos as well.
have fun.

I dive inside the book. The organization by strategies is fine and ease the reading, the problems are challenging enough. If you are interessed in mathematics, student or not, buy it. You will not regret it.