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When I took discrete math as an adult I realized that this was a subject I would have enjoyed and done well at much earlier in life, even in my early teens.

Does anyone know if there are good books, particularly on combinatorics, aimed at people in middle or high school? I'm thinking particularly of one enthusiastic young programmer of my acquaintance.

(Note: I have moved this question from its original posting on StackOverflow. Before it was removed from there, someone suggested Concrete Mathematics and Bryant's Aspects of Combinatorics, both of which are even harder than the various books by Grimaldi, Epps, Rosen, and Roberts, which I used in college-level courses. Someone else suggested Martin Gardner's books. But actually, I'm looking for something more systematic than math games yet aimed at a less mature reader than a college-level textbook.)

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I don't know of any, but there should be. – Michael Lugo Apr 8 '11 at 2:39
up vote 3 down vote accepted

For a younger reader who's not yet ready for Rosen, I would definitely recommend Discrete Mathematics DeMYSTiFied. It's a really good introductory/self-study guide.

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Thanks very much. – brannerchinese Apr 8 '11 at 1:44

How about Ross Honsberger's Mathematical Gems and Mathematical Morsels? The math in those books should be accessible to a motivated middle school student. These books have a pretty diverse collection of topics and there is a lot of discrete math in them, so they seem to satisfy your conditions.

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I was a middleschool student when I read the Morsels. It was really challenging for me, and almost impossible for my peers. But despite that, I recommend that book. – picakhu Apr 7 '11 at 23:50
Thanks. This looks good. The sole Amazon reader review of Mathematical Gems III says, "For Martin Gardner fans in search of something a little more highly engineered, Gems II and III will prove to be a sound investment." I'll be glad to hear other suggestions, too, though. – brannerchinese Apr 8 '11 at 0:06
For the record, the book in question is here. Honsberger is the author of a whole series of Mathematical Plums, Mathematical Delights, Mathematical Chestnuts, Mathematical Diamonds, etc. etc. – brannerchinese Apr 8 '11 at 0:14
@texmad - I should have mentioned that Honsberger had many more similarly themed books. Your middle school student would have enough to keep him occupied to high school and beyond. – svenkatr Apr 8 '11 at 2:48

You might look into the Art of Problem Solving books; these are specifically for younger people since they're for people who want to compete in middle and high school competitions. I haven't read them, though.

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I was going to suggest these as well. The series is specifically designed for better math students in grades 6-12 and goes from algebra to calculus but includes 3 or 4 books on discrete math that most students wouldn't see. They teach everything a student needs to know, i.e., you learn the same stuff you would if you were just taking some class in high school. But, there is also the emphasis on problem solving. – Graphth Apr 8 '11 at 2:09
That sounds very good. In high school, I always felt there was a tactical aspect to problem solving that I was too impatient to look for, and as I got older I got better at finding them. I'd like to think that young people are getting actual training in how to attack problems methodically. – brannerchinese Apr 8 '11 at 2:59

Though these are not primarily discrete math, and you've already discounted one of them:

  • Martin Gardner's Scientific American articles and books produced from them

  • Richard Smullyan's puzzle books. Mostly logic oriented, but still lots of discrete thinking.

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Thanks! I do think there's definitely a place for puzzle books in a young person's development, in spite of the comparative lack of structure. – brannerchinese Apr 8 '11 at 1:45

Try this one:

It's extremely readable even for young people. Cheers :D

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Thank you very much. – brannerchinese Apr 9 '11 at 14:36
I'm rather in shock over the price, though. I guess this is officially a 'textbook'. There's a paperback version listed, but it turns out to be merely the student solutions manual. – brannerchinese Apr 24 '11 at 10:23

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