Customer Reviews

Problems for Mathematicians, Young and Old (Dolciani Mathematical Expositions)

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I should preface my review by saying this is the first item I've ever reviewed on Amazon, and I've been buying from Amazon for 10 years. I felt I had to write this review as a counterpoint to an earlier negative review given to this book.

Not only are the problems in this book very interesting to work on, they also illustrate key points in algebra, calculus, set theory, etc. I would say that successfully completing the problems in this book would give you mathematical expertise comparable to that of a first year math graduate student.

When people ask me for math book recommendations, this is the book I suggest. Everyone I've suggested this book to has liked it.

For reference, I have a PhD in EECS (I minored in math) and have taught engineering for the past 12 years.

I would put this book above the puzzle books by Martin Gardner. The problems range in prerequisite knowledge from none required (brain teasers and logic puzzles) to undergraduate degree in mathematics (topology, calculus). I especially recommend it for someone who likes good brain teasers (like the three light switches puzzle) but also knows some complicated math.

Apparently, after a long career as a mathematician, Halmos sat down, gathered together the problems he had been accumulating for years in various forms and assembled them into this book. The result is an interesting and peripatetic piece of work -- well-edited, well-composed, and fun. Some of this stuff requires the facility which only comes via an advanced degree and math. Other problems can be tackled by high school students.

There are no attributions nor (inexcusably) any references so
that one is simply led down many dead ends. Rather than
originality we have here simply a selection taken from much
better collections e.g. Engel, Olympiad Problem Book, plus
countless others.