Studying the masters, not their pupils (budget edition)

October 20, 2013 3:18 PM

I am a frequent buyer of <$5 books on Amazon. Lately I am interested in math treatises but have been unable to find any that aren't way out of my price range. Am I being way too demanding?

Here are some of the books I'm looking for:

*Mécanique analytique, Lagrange
*Mécanique céleste, Laplace
*Introductio in analysin infinitorum, Euler
*Mathematical Principles of Natural Philosophy, Newton
*Cours d'analyse de l'École polytechnique, Jordan
*Disquisitiones Arithmeticae, Gauss

I managed to find Euclid's Elements at my library this week, but none of the others. I have also searched Amazon extensively. Also, I am looking for English editions only.

Thanks in advance! ^_^

posted by myitkyina to Shopping (9 answers total)

Google books has a pdf of the Principia here:

Newton's Principia: The Mathematical Principles of Natural Philosophy
By Sir Isaac Newton, N. W. Chittenden

and there is a commentary here

I'm cheap and poor but my guess is that it's worth finding the best commentaries you can on most of these works and paying for them. If I couldn't do that, I'd find them in a library. You will probably spend enough time slogging through the texts to make it worth it.

Also, while google'ing I stumbled across 17 century maths which seems like it might be helpful to you.
posted by rdr at 4:13 PM on October 20, 2013

I thought, I wonder if this is something you'd find on Aaaaargh dot org, which is basically a filesharing platform for unaffiliated academics. Turns out they have the Newton, and I'd be glad to send it to you though it's absolutely worth it to make an account!
posted by tapir-whorf at 4:16 PM on October 20, 2013

Best answer: Project Gutenberg must always be considered. I found Betrand Russell's Introduction to Mathematical Philosophy there.

Enter "mathematics" in the search page. Explore and enjoy.
posted by megatherium at 4:34 PM on October 20, 2013

Lots of cheap copies of Journey through Genius: The Great Theorems of Mathematics seem to be floating around.
posted by oceanjesse at 4:43 PM on October 20, 2013

Best answer: Dover Publications has a lot of very inexpensive, very good books on mathematics, including some by "primary" authors. Under $5 is probably a bit much to ask.

Set Theory and the Continuum Hypothesis, Paul Cohen

Euclid

The Beauty of Geometry: Twelve Essays, HSM Coxeter

Descartes' Geometry

Newton's Philosophy of Nature

James Clerk Maxwell, Matter & Motion

Newton, Opticks

Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers

Lagrange, lectures on elementary mathematics


There's a bunch.

(Although, you might want to start with some preprocessed analysis before you move on to french, especially if you only want english translations! Carl Boyer's got some good books.)
posted by leahwrenn at 4:51 PM on October 20, 2013 [1 favorite]

Best answer: I came to say Dover as well. However, it's worth noting that reading old math books is not always the most efficient thing to do. I'm not sure if this applies to anything you've listed, but it's not uncommon for something to have become a lot clearer or more precise later. (For example, I've been told that Cauchy was hazy about the difference between continuity and uniform continuity. If you're not clear on that, you probably shouldn't be relying on Cauchy to tell you about it, and so on.)
posted by hoyland at 5:24 PM on October 20, 2013 [2 favorites]

Best answer: At the risk of being irrelevant, what is your purpose with these works? Yes, you will probably find Euclid's Elements in a public library, because an educated layman might conceivably be aware of it, Euclid develops his system straightforwardly, and elementary geometry is an accessible branch of math.

By comparison, you are extremely unlikely to find Newton's Principia. It is impenetrable, inaccessible, highly idiosyncratic, and develops an area of math that an educated layman is not familiar with. I am serious when I say that no one reads the Principia, not even mathematicians.

Do you want these books to decorate your bookshelf or to learn from? Since Newton's days, mathematicians have rebuilt calculus on a rigorous analytical foundation. We have the advantage of centuries of new results, cleaner derivation of results, and much cleaner notation.

In short, while you could, in principle, learn something from Euclid, there is almost no worse book to learn calculus from than Newton's Principia. There is a universe of much better books for a range of student types. And the same can be said about differential equations, and functional analysis, and classical physics, and number theory, and so on.

I would even say that it is very rare to have work in mathematics that both represents an important advance and can work well as a study tool.
posted by Nomyte at 5:24 PM on October 20, 2013 [5 favorites]

Response by poster: I am primarily using modern textbooks, and was planning on using the ones I listed to supplement my studying. I had forgotten about ebooks -- great suggestion.

Thanks everyone!
posted by myitkyina at 5:36 PM on October 20, 2013

Also consider inter-library loan, if your library doesn't have a book, you can probably find one somewhere.
posted by CathyG at 10:16 AM on October 21, 2013