Catherine Posted October 12, 2008 Share Posted October 12, 2008 He is in tenth grade and ultimately wants to "speed through" calculus so that he can do more "proofy" math. It's my impression that he can do more proofy math starting with algebra, but I need some resources for this. I already have Gelfand's algebra, and we've worked through about 2\3 of the book. Are there any other recommendations for theoretical math? He's finishing up algebra 2, we are starting trigonometry soon. He's done geometry already. Thanks in advance. Quote Link to comment Share on other sites More sharing options...
Jane in NC Posted October 12, 2008 Share Posted October 12, 2008 If you go to the internet bookstore of the American Mathematical Association you will find several series that are geared for students: the Anneli Lax New Library, the Dolciani Mathematical Expositions (not Dolciani texts, but ancilliary problem and challenge books), and some other classroom materials that might strike your son's fancy. Bravo to your son! Quote Link to comment Share on other sites More sharing options...
forty-two Posted October 12, 2008 Share Posted October 12, 2008 The Art of Problem Solving people have some texts that are supposed to be good; there is one on Number Theory and a couple on Probability. I have "The Art of Problem Solving, Vol 1&2", and they seem to have a strong focus on proofs in there from what I've seen, especially in Vol. 2. Also, you might be interested in some of Charon & Myrtle's math rec's, as they are the resident math proof gurus (you can search the boards for their posts - lots of good info there). Their current plan for pre-calc is an OOP, but fairly easy to find, book: "Principles of Mathematics", by Oakley and Allendoerfer (the 1963 edition). Myrtle talks about it on her blog here. I had no trouble picking up a copy of both the text and the teacher's guide in March, though I think I lucked out on the teacher's guide. (I just searched BookFinder.com, and found several cheap 1963 editions.) From my glancing over it, it seems to take much more of a theoretical bent than most other pre-calc texts that I have seen. I know their tentative plans are to go straight from that book to an abstract algebra text, skipping "calculus" entirely (Charon dicusses it here, along with listing their entire planned sequence). No idea how doable that is, and it would undoubtedly require a tutor, but it might be worth considering if your ds really wants to get to "real" math and couldn't care less about calculus. Quote Link to comment Share on other sites More sharing options...
forty-two Posted October 12, 2008 Share Posted October 12, 2008 Regarding the American Mathematical Association books that Jane in NC mentioned, I know that "Introduction to Inequalities", by Beckenbach & Bellman, in particular has been mentioned as good on the board a few times (here, for instance). It is available on Amazon and is also easy to find used. Quote Link to comment Share on other sites More sharing options...
Catherine Posted October 12, 2008 Author Share Posted October 12, 2008 recommended and will look at more in the coming days. It all looks very helpful. Quote Link to comment Share on other sites More sharing options...
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