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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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closed as primarily opinion-based by Lord_Farin, sandwich, Fixed Point, M. Vinay, Claude Leibovici May 24 at 5:50

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.If this question can be reworded to fit the rules in the help center, please edit the question.

    
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. – Alex Becker Mar 28 '12 at 22:26
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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. – Brian M. Scott Mar 28 '12 at 22:51
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I second Brian M. Scott, but I would also recommend 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 ;-) – dtldarek Mar 28 '12 at 23:29
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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: komal.hu/info/bemutatkozas.e.shtml If it's too difficult, perhaps some other source of competition problems might be a good introduction. – Brett Frankel Mar 29 '12 at 2:01
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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. – Dave L. Renfro Mar 29 '12 at 14:40