Number theory and its history

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1. generationPJul 2020
   Concrete Mathematics by Knuth and Patashnik (already mentioned for u/pmiller2) if the kid likes numbers. That's perhaps the guiding thread of the book -- it's about the beautiful (yet usually very elementary and natural) things you can do with numbers.

   Geometry Revisited by Coxeter and Greitzer and/or Episodes in Nineteenth and Twentieth Century Euclidean Geometry by Honsberger if the kid is into plane geometry. It's an idyllic subject, great for independent exploration, and the books shouldn't take long to read. Not very deep, though (at least Honsberger).

   Anything by Tom Körner, just because of the writing. Seriously, he can make the axiomatic construction of the real number system read like a novel; open https://web.archive.org/web/20190813160507/https://www.dpmms... on any page and you will see.

   Proofs from the BOOK by Aigner and Ziegler is a cross-section of some of the nicest proofs in reasonably elementary (read: undergrad-comprehensible) maths. Might be a bit too advanced, though (the writing is terse and a lot of ground is covered).

   Problems from the BOOK by Andreescu and Dospinescu (a play on the previous title, which itself is a play on an Erdös quote) is an olympiad problem book; it might be one of the best in its genre.

   Oystein Ore has some nice introductory books on number theory (Number Theory and its History) and on graphs (Graphs and their uses); they should be cheap now due to their age, but haven't gotten any less readable.

   Kvant Selecta by Serge Tabachnikov is a 3(?)-volume series of articles from the Kvant journal translated into English. These are short expositions of elementary mathematical topics written for talented (and experienced) high-schoolers.

   I wouldn't do Princeton Companion; it's a panorama shot from high orbit, not a book you can really read and learn from.

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2. mike00632Oct 2019
   "Number Theory and its History" (1948) by Øystein Ore is considered a classic.

   https://www.amazon.com/Number-Theory-History-Dover-Mathemati...

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3. thejteamOct 2013
   If you are looking for an accessible book on Measure Theory, I like "Lebesgue Integration on Euclidean Space" by Frank Jones. A good undergraduate level textbook, problems integrated into the text instead of at the end of the chapter. I wish I hadn't given my copy away now.

   For number theory I liked "Number Theory and its History" by Oystein Ore. Best part is it is cheap. Good intro to number theory, it was accessible to me in high school (I was advanced, but no genius) and I learned things that I never even encountered in college as a math major.

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