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My nephew is 8 years old and shows great promise as a student. Sadly, as most of you know most programs in secondary education don't offer any foundational courses for higher mathematics. What books/online resources/programs do you recommend?

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    My introduction was *Modern Algebra: An Introduction* which I found very comprehensible (although the last chapter on coding theory isn't very good IMHO). It's at a very basic level and assumes little yet eventually gives the reader some nice machinery, such as Lagrange's theorem, Sylow theorems and basic Galois theory.2012-03-28
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    Enzensberger’s *The Number Devil: A Mathematical Adventure*. Martin Gardner’s various collections, and Ian Stewart’s. Abbott’s classic *Flatland*. Newman’s 4-vol. *The World of Mathematics*. In other words, a wide variety of accessible and engaging topics. Let *him* decide what he wants to get serious about, and when.2012-03-28
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    He hasn't quite been introduced to formal logic, would this cause any sort of problem? @BrianM.Scott thank you!2012-03-28
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    I second Brian M. Scott, but I would also recommend [Proofs from the Book](http://en.wikipedia.org/wiki/Proofs_from_THE_BOOK) which may be a bit too hard, but there are some elementary and **beautiful** proofs. It happened for my friend that he learned a bunch of complex stuff all by himself, just to understand more proofs from the book ;-)2012-03-28
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    @dtldarek I'm afraid that proofs from the book would probably be much too steep to start him off on. My nephew has only been exposed to the much more applied side of mathematics. He does seem to be breezing through it, so I would like to offer him a "fair" challenge so to speak to get him introduced to the beautiful world of abstract thinking.2012-03-28
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    @arete "much more applied side of mathematics" -- then I would go with computer science. It has a nice practical feeling, you **do see** the effects of your work and it involves a decent amount of math. Perhaps you could start with graphics: tillings or fractals which create pretty pictures, also cryptography is a good choice (I was obsessed with it when I was under 10). There are also Markov chain sentence generators (every person I know was just amazed first time seeing those), or FFTs -- transforming your speech into "[Chip 'n' Dale](http://en.wikipedia.org/wiki/Chip_%27n%27_Dale)" talk ;-)2012-03-28
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    K\h oMaL is the Hungarian math journal for young problem solvers that has been given to generations of the best Hungarian mathematicians. Your nephew probably won't be able to solve too many problems at first, but learning to struggle is part of the journey. You can find it in English here: http://www.komal.hu/info/bemutatkozas.e.shtml If it's too difficult, perhaps some other source of competition problems might be a good introduction.2012-03-29
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    @arete: Has your nephew learned any high school algebra? In my case, before I learned some algebra (using library books when I was in the 8th grade; my school didn't offer algebra until 9th grade), what I could usefully read and understand was WAY WAY less than what was the case after I learned some algebra. Also, you say that he's 8 years old but then mention secondary education. In the U.S. that's a gap of 6 to 7 years, which is sufficiently large that the Johns Hopkins program for children extremely gifted in math might be interested.2012-03-29
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    I suggest *The Book of Numbers* by Conway and Guy. Nicely illustrated, very accessible and a lot of fun.2012-03-29
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    The books by Dunham (e.g. "Jouney through genius: The great theorems of mathematics" and "The Mathematical Universe") are readable and motivating. Pólya's "How to solve it" is at times a bit too elementary/simple, but is a must read.2013-02-08

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