Another idea along the lines of "pure math"

[Myrtle]

A month or two ago I ordered a copy of Serge Lang's "Basic Mathematics."

 

Serge Lang was a member of the Bourbaki (Wiki entry on Lang) and went on to write this book on "everything you should have learned in high school about math." He says in so many words in the preface, but much more diplomatically than I'm paraphrasing, that students are showing up to college incompetent and that this book should be used to brush up on whatever it is that you might have missed out on.

 

I finally got around to looking at it again, because at the time I ordered it I was wondering how good of a high school text it would make, (not very good since there aren't enough problems in it for the average student.) However, I started thinking that since a lot of folks might be rusty in some topics that this might be a good book for mom to brush up on quadratics or polar coordinates or whatever. The problem I had when relearning forgotten math, the first time I did this a couple of years ago, was that I didn't want or even need to really, rework a billion problems in a book, and so abbreviated problem sets might actually be useful in cases such as mine.

 

But the really neat thing about this book is that it has a ton of proofs in it. Serge Lang proves everything. And so, at any rate, if you aren't inclined to track down out of print Dolciani's, this book is still in print and has all those proofs in it. Because I'm sure that deep inside the burning question of "Why is the multiplicative inverse unique?" has been keeping someone up late at night and this it, baby, the lofty weight of this existential angst will be lifted from your mind as you explore its contents.

 

It is expensive though, at $50 a pop you might want to try interlibrary loan. The used ones I could find at alibris and bookfinder.com started at $24 and rapidly went up from there.

 

And even better, it looks like a bunch of pages are previewable in Google books so you can decide for yourself if this along the lines of something you can use.

[Nan in Mass]

Well, the multiplicativ inverse's uniqueness hasn't been bothering me, but I actually have been worried in the middle of the night remembering that polar coordinates exist and I have absolutely no memory of how to do them. I can only vaguely remember thinking that they were important and rather fun. Sigh.

[Storm Bay]

And all this time I thought it was being premenopausal that was keeping me up! Thanks for the suggestion, and I'll look this up, even though we ordered a 1965 Dolciani (was just mailed from the seller today, so as long as USPS gets it here, we're golden.) More because I am rusty and would like to see all those proofs.