I am not sure quite how to explain what I am looking for. I am trying to reteach myself mathmatics and am having a hard time finding good books for it. Too many books I find do not tell you the why, they only tell you the how. This is especially true for arithmatic. I need a book that covers everything, preferebly up to calculus. something that explains it in the same depth of understanding that you would need if you were designing a calculator. I guess that I am sort of looking for something akin to the Feynman lectures, but for math. The closest I have found so far is Mathematics for the Nonmathematician by Morris Kline, but even this does not go into the depth that I would like.
I like Sideways Math From Wayside School which had the best story problems I’ve ever seen. May be out of print–but shouldn’t be.
I think I understand what you’re looking for. It may not exist. (I could be wrong.) At least not in one place, under one cover.
If no one comes up with a suitable title, I’d suggest the following …
You’re going to have to tackle each topic yourself. Get a three-ring binder. As you go through each topic, whatever it is, get your specific “why?” questions answered, somehow, somewhere, by someone. Don’t quit until you’re satisfied, and then write out your understanding of it, in complete sentences, and then put that into your binder.
Put your questions to different sources. There’s this board; there’s a mathforums on the net somewhere, which has a lot, and has experts manning it (I just checked - http://mathforum.org/ - but they’ve changed it around since I was last there); there’s whatever texts you have; Britannica can be good for some things, too.
You sound like you have the drive and determination for this. It may take a while, but it will work. If you put in the time, and attention, you will get there.
The Kline book isn’t bad as an overview. It does start from basic axioms and moves through the major topics in math. Another good book is Ian Stewart’s '95 book. I’ve always liked his writing style. My suggestion is to use these books as part of a study outline. Then augment the material by digging into the many references (and the references from the references!) that you will find in the books. It’d be very helpful if you can have ready access to some experts in what you’ll be studying. Sometimes a five-minute conversation can clear up a fuzzy issue that would ordinarily take hours of book research.
Edmund Landau’s “Foundations of Analysis” is exactly what you’re looking for, but it’s not really written for a lay audience. You really do need some experience with the how before you can get to the why, IMO.
Just curious. Could you give us some examples of the “why’s” that you need explained? It might help us help you.
Like, you may know how to add 438 and 53, including lining up the numbers right, but do you know why you have to line up the numbers? And why you do the whole carrying-the-one business?
Because if those are the sorts of questions you’re asking, that’s the sort of thing I’d teach using poker chips (and place value), instead of a book.
Things like why do the different methods of finding roots work, why does the Euclidian algorithim work, why does “casting out nines” work, proofs for the commutative, associative and distributive laws etc.
Hm. I don’t really have any textbook recommendations. Maybe someone else does.
In the meantime, there’s the internet, and mathforums.
casting out nines - http://www.jimloy.com/number/nines.htm
The trick will be to get an explanation that you understand, or that you understand enough of to make sense of whatever it is.