Brushing up


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Brushing up

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Aug 12, 2006, 10:15pm

First a bit of background: I took math up to calculus my senior year of high school, but since then it has gathered dust on the back shelves of my mind (I'm an English major). And I miss it.

Since it's never too late, I want to brush up on what I once knew so that I can start learning about all the cool stuff I never got to (linear algebra, multivariable calculus, etc.). I'm not quite sure what the best way is to go about it, though -- work through textbooks? I'm not averse to doing that, of course; if that's the best way, any recommended textbooks? If it's not, any ideas on what to use instead?
(I just ordered Jan Gullberg's Mathematics: From the Birth of Numbers on Amazon, based on Stevey's mention of it, for what that's worth)

Thanks! :)

2ccc3579 First Message
Aug 13, 2006, 9:02pm

Try Clifford A Pickover's Calculus and Pizza for a refresher on Calculus.

Aug 31, 2006, 3:15pm

I highly recommend Berlinski's A tour of the Calculus as well as The Advent of the Algorithm by the same author. Moreover, his remarkable erudition, facility with language and a unique writing style are a bonus for an english major! Check it out!! Cheerio...

Sep 20, 2006, 11:30am

This message has been deleted by its author.

Sep 20, 2006, 11:33am

Hmm interesting. What do you like about Calculus and Pizza, ccc3579?

Dec 14, 2006, 4:57pm

It is not exactly what you asked for (it is not exactly a textbook) but I highly recommend the book What is Mathematics? by Richard Courant. As Albert Einstein has written, it is "a lucid representation of the fundamental concepts and methods of the whole field of mathematics....Easily understandable".

As a more textbook-like work, I would recommend Apostol's Calculus, volume 1 and 2. In them you will find both one- and multi-variable calculus, and also linear algebra. I like these books much better than the more modern calculus books.

Dec 14, 2006, 6:06pm

Message removed.

Dec 24, 2006, 1:44am

I really encourage you to try to take a course if you can. You could do calculus, or for a different flavor, you could take an intro to proof-writing course. The intro to proofs course is often a course on set theory or linear algebra, though the actual content varies from school to school and isn't as important as the fact that it teaches proof writing. And some schools don't have a single course for such a thing.

Dec 24, 2006, 6:00pm

Just to add to 8: An Accompaniment to Higher Mathematics is a nice book to keep on hand while you're studying mathematics. It teaches proof writing and reading, and also how to spot clues in theorems and problems to help relate seemingly different mathematical concepts. If you patiently work through it as it suggests, it will teach you how to think like a mathematician.

Jan 12, 2007, 11:28pm

Re: Berlinski's A Tour of the Calculus... Ugh! I got about halfway through it during a vacation before putting it down in disgust. About a third of what he writes is *really* good, so I understand why some folks rave about it, but not worth reading the other two thirds... He's too in love with his own literary voice to be a good writer; doubly-so when it comes to writing about math...

rljacobson's advice about taking a proof-writing course of some kind is probably quite good. I recently started on a second bachelor's degree in math, and at my school the first course majors in math and comp sci take is called "Discrete Structures". It covers logic, set theory, proofs, relations & functions, and counting--a smorgasboard of tools you'd use in advanced courses. Most schools seem to have a similar course. I linked the MIT versions of this course at

11jmricker First Message
Edited: Jan 13, 2007, 9:48am

Calculus Made Easy was the book I found that really opened the doors for me and helped me understand Calculus. I struggled through my first class until I read that book and had this fantastic ah-ha moment and understood what my calculus book and professor was trying to tell me. If only they explained it as clearly as Silvanus P. Thompson does in the book.

Edited: Jan 18, 2007, 11:41pm

I read Calculus Made Easy back when I first took calc and I remember liking it, too. IIRC, it emphasized the "how to do it" part rather than the "why it works" part, though.