CaptainMac wrote:
I'm another one who obsesses over math. I'm specifically interested in numbers and their origins, their meanings, etc. I currently work as a part time math tutor for elementary kids and am asking for two books on number theory for Christmas. Additionally, I have a large box of math manipulatives (which I have an excuse to use since I am a tutor) and a collection of calculators...two graphers, a scientific, a ton of four functions, a "Little Professor", and a good old fashioned slide rule. I also managed to snag a few math textbooks whenever the local schools dumped them or have bought them online (I have four Algebra books, one geometry, a calculus book, a stats book with a CD, a few books on basic math, one on math history, and a ton of elementary-grade books including a really nice hardcover third grade book from the 80s; not to mention a book on descriptive geometry, one on fractals, a complete book on Judy Clocks, a few volumes on teaching math, a few workbooks that go with textbooks, and a physics book, which is close enough to math that I'll include it-----basically a whole shelf in my room is devoted to math books). I also have a ton of math software including multiple copies of Math Blaster (and some old computers to run them on for students).
Hah, nice list, CaptainMac. I probably would have wished for something similar for x-mas, had my family the necessary finances for that. But nowadays, I would not wish for such things if I was your age, due to the internet. Now you have wikipedia, google,
MIT Open Courseware (free course materials from MIT), and
wolfram's Math world. You can get very far with that.
If you buy any books, just stick to the most popular textbooks used in schools appropriate to your math competency level. You sort of asked for that above, but a few standard textbooks and the internet will have you set for years. I am not sure what your level is, but I will take a guess anyways and give you a list of subjects to search for textbooks on:
- College Algebra: Assuming you can do basic arithmetic, then you need a solid foundation in algebra to proceed further.
- Trigonometry/Precalulus: Depending on the algebra book you choose, you might be able to get enough trigonometry in a pre-calculus book. Or you may need to go with a highschool geometry book. This topic will be a prerequisite for complex analysis and calculus.
- Modern algebra: This covers group theory, set theory, rings, and fields. A field is basically a set of "numbers" which can be added, subtracted, multiplied, or divided. So there is the field of real numbers, rational numbers, integers, complex numbers, quaternions (a non-commutative field with three "imaginary numbers", i,j, and k, such that, i^2=j^2=k^2=ijk=-1), onctonions (non-commutative and non-associative field, where there is a 4th "imaginary number", L, and the product relations involving iL, jL, and kL.).
- Real analysis: Real analysis actually overlaps everything on this list that deals with real numbers, except it is done in a mathematically rigorous fashion.
- Complex analysis: Similar to real analysis, except with complex numbers. This is where you will learn the math behind the mandelbrot and julia sets, though there will be no focus on them.
- Number theory: This goes beyond modern algebra and real analysis and examines stuff like prime numbers and stuff.
- Calculus: The bread and butter of every physicists. You only need algebra and trigonometry/precalculus for this.