I don't think I was gifted per se, but a curious kid. My mom was a fan of Asimov, who had written books on a huge array of topics, and there may be a few math titles in there. But at the same time, introducing a kid with math talent to science isn't such a bad thing either.
I was like that as a child, but after enough years of wider academic exposure as a student, decided I liked applying mathematical ability towards electronics, business, and chemicals better than average compared to becoming a real mathematician.
Science-fiction can be stimulating in that regard, someone who likes science in addition to math might be the one to turn some of it into science-reality someday :)
Eventually I came to the conclusion that the better math textbooks had more than just math. One of the most enlightening math books I had was a late 19th century antique text "Progressive Higher Arithmetic" which was never in one of my courses, but was given to me when I was an old teenager and it could be an interesting reference in any century. Not only the differences in the way teaching has been done in the past, but a nice leather-bound volume with numerous blank pages among those adjacent to the front & back covers, covered with poetry written by the original owner. With a pen and common inkwell, in beautiful handwriting there is one that I can not forget:
I wish I remembered the series of math books that my school system used. It was during the "new math" movement. We learned about sets in first grade. Proofs were introduced fairly early. There were problems for which "no answer" was the correct answer.
If you could find a collection of the Mathematical Games articles from Scientific American, those were entertaining and required little background knowledge, but conveyed the fun of math.
Geometry is a good subject because it doesn't have very many prerequisites other than basic arithmetic, and the older textbooks were mostly about proofs. (Note I'm biased, proofs are what made math come alive for me).
Honestly, I think you might be missing something here. "Azimov on Numbers" was maybe the most real math book I read as a kid. I don't know of any other book aimed at a kid's reading level that covers aleph-null and Cantor sets.
Comments
I don't think I was gifted per se, but a curious kid. My mom was a fan of Asimov, who had written books on a huge array of topics, and there may be a few math titles in there. But at the same time, introducing a kid with math talent to science isn't such a bad thing either.
I was thinking more of a real math book.
I was like that as a child, but after enough years of wider academic exposure as a student, decided I liked applying mathematical ability towards electronics, business, and chemicals better than average compared to becoming a real mathematician.
Science-fiction can be stimulating in that regard, someone who likes science in addition to math might be the one to turn some of it into science-reality someday :)
Eventually I came to the conclusion that the better math textbooks had more than just math. One of the most enlightening math books I had was a late 19th century antique text "Progressive Higher Arithmetic" which was never in one of my courses, but was given to me when I was an old teenager and it could be an interesting reference in any century. Not only the differences in the way teaching has been done in the past, but a nice leather-bound volume with numerous blank pages among those adjacent to the front & back covers, covered with poetry written by the original owner. With a pen and common inkwell, in beautiful handwriting there is one that I can not forget:
Remember me when death shall close
My eyelids in the last repose
And evening breezes gently wave
The grass above your school-mates grave.
I wish I remembered the series of math books that my school system used. It was during the "new math" movement. We learned about sets in first grade. Proofs were introduced fairly early. There were problems for which "no answer" was the correct answer.
If you could find a collection of the Mathematical Games articles from Scientific American, those were entertaining and required little background knowledge, but conveyed the fun of math.
Geometry is a good subject because it doesn't have very many prerequisites other than basic arithmetic, and the older textbooks were mostly about proofs. (Note I'm biased, proofs are what made math come alive for me).
Honestly, I think you might be missing something here. "Azimov on Numbers" was maybe the most real math book I read as a kid. I don't know of any other book aimed at a kid's reading level that covers aleph-null and Cantor sets.