[thetallstick]

Apostol Calculus Vol 1

The introduction gives a history lesson, a great description of the method of exhaustion with descriptive drawings, and some very straightforward proofs on finding the area under the curve for parabolic segments via some basic infinite sums (no limits), all in 10 pages in a conversational style. And it just gets better from there.

My dad gave me his book he used in the 70s and I read it in high school in parallel to the textbook the school issued. Everyone thought I was some genius because I thought calculus was so obvious and I could explain it so well but I was just parroting the text and proofs from this book, basically verbatum. I told the other kids to use it as well but no one did.

[tpdly]

+1 for Apostol V1! I also read it in high school, ended up testing out of Calc 1 in Uni, having learned plenty from reading that on my own. As you say, it really is so conversational and easy to follow. Starting with integration works really well, you build lots of sums and then use a supremum/infimum as opposed to a limit. I think the mental imagery for that is a lot more manageable than limits, especially if its your first time watching infinities disappear.

[tzs]

> My dad gave me his book he used in the 70s

That would probably be the second edition, published in 1967. The first edition was in 1961.

If you have a kid and they go to a college that uses Apostol you can give them your 2nd edition without worrying that it will be too far off from the current edition because the second edition is the current edition.

Same with volume 2. The 1969 second edition is the current edition. The first edition was in 1962.

Anyone happen to know of a list somewhere that lists subjects and for each gives you information on how well it can be learned from old books?

For undergraduate calculus for example a 50 year old textbook is fine. At worst some of the example and exercises might be outdated or maybe mildly sexist by today's standards.

On the other hand, that 20 year old book on learning Java with Symmantec Visual Cafe sitting on one of my bookshelves is probably nearly completely useless.

In between would be books where parts of them are still relevant and accurate and parts of them have been superseded and would at best only be worth reading for historical purposes.

[tlavoie]

"On the other hand, that 20 year old book on learning Java with Symmantec Visual Cafe sitting on one of my bookshelves is probably nearly completely useless."

Hah. I think I learned Java with that book as well, and used Visual Cafe starting out. I think one thing I did pick up (relatively) early was that books written to have a short shelf life were probably poor investments. Some "Word 6.0 for Dummies"-type book is probably meant to get someone up to speed that had pirated the program, and not a more general mind-expander that is going to lead you to thinking about how to implement some idea in whatever you're using today.

[Breza]

Dover Publications has a whole catalog of old math textbooks. It's amazing how good many of them still are.