Theoretical Math vs Pure Math...and books??

[mjr]

Does anyone know if there's any real distinction between Theoretical Mathematics and Pure Mathematics?

I ask because my kiddo (age 11) has begun to show interest in things like the Googolplexian, BIG FOOT, Hilbert's Hotel and other large numbers. He also seems to be at least a little curious about things like Set Theory and Number Theory, and things WAY over our head, like Aleph Null, the "omega" used in math (see the first two bullet points under "Mathematics" there), the Banach-Tarski Paradox and things like that.

I also bought Euclid's "Elements" recently (thick ass book!).

But does anyone have any good recommendations or suggestions for websites and/or books on these topics and other theoretical/pure math books for him?

[Chromatix]

If there is such a distinction, I would make it between "pure" maths which is all about abstract concepts and obscure number theory, and "applied" maths which is always related to some real-world concept.

Note that it is entirely normal for things to move out of "pure" into "applied" categories when a real-world application is found for them, such as in cryptography which often makes use of Galois field theory and some specific number theories.

[TheSHAD0W]

"Pure" math isn't quite as pure as you might think. "Hilbert's Hotel", for example, was mentioned earlier, and the methods devised for it do have applications in computing; for instance, managing an arbitrarily-sized swarm of peers using a finite number of commands. (Think peer-to-peer over the internet, perhaps; or between cores in a supercomputer.)

[Seshat]

Personally, I'd recommend just letting him have free rein in your local library, and when that starts to run out (it will, if this is his interest), doing your best to get him access to university-level math.

Fortunately that's a lot easier these days than it used to be!

[Crai]

Get him some books by Stephen Hawkings, best I can come up with lol.

[Kaylyn]

MIT has a free open-courseware site that has access to many of the school's courses, including math, complete with video lectures and homework and exams (all for your own benefit; the courses aren't graded). If you go by their "prerequisites" it seems everything requires a basic understanding of calculus first, but for that there's Khan Academy.

I'm currently refreshing my algebra and working up towards trig and calculus through Khan Academy's site...I was only ever required to take up through college algebra and statistics in college, and advanced math which is a combo of some trig and some pre-calc in high school, and I've always wanted to learn calculus. I'll probably attempt some of the MIT stuff once I grasp calculus and maybe tackle some finite math.

[mathnerd]

The terms "pure" and "theoretical" math really boil down to a distinction without a difference. One could argue some subtitles, but there's really nothing there to differentiate the two.

As for your child, there's really nothing out there (published) that breaks down abstract math for kids. The lesson plans I wrote for such a thing are on a computer that's dead and I haven't tried to recover the files from, and I'm quite positive I'm not the only teacher on the planet that's done the same thing. Actually, I know for a fact there's one more, because I helped him write the lessons. The trouble with finding resources like this is pretty much everything assumes a minimum foundation through at least single variable calculus, and often times through multivariable calculus and linear algebra. You're almost going to have to find somebody like me* that's local to you who's able to break these concepts down for a person without the assumed foundation in the higher levels of computational mathematics.

*I did a 6 week unit with my 7th graders that covered the basics of logic, set theory and group theory (abstract algebra).

[mjr]

He actually found a video on the Banach-Tarski Paradox, and got me to watch a few minutes of it with him.

It was quite interesting, though. Last weekend we also bought him some math manga books on more advanced math (above his age level, anyway).

I also managed to pick up a copy of "The Elements". All 13 volumes in 1 book. It's friggin' thick!

[Chromatix]

When I was younger, I had a book which covered some mathematical curiosities through the medium of 8-bit computing. That sort of thing would probably be interesting, and computer programming is itself a very deep branch of (applied) mathematics. If you can get him to understand - *really* understand - pointers and recursion, he's got a bright career ready-made for him.

The actual programs in that book were written in BBC BASIC, and with a little tweaking will run on a Raspberry Pi with RiscOS loaded. The trick of course is knowing exactly what to tweak, ie. what the relevant differences between a BBC Micro and a Raspberry Pi are.