Lecture notes and other nice math writing

Various notes on computation

A must read in every first-year applied math course: "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later" by Cleve Moler and Charles Van Loan (journal link).

"An Introduction to the Conjugate Gradient Method Without the Agonizing Pain" by Jonathan Shewchuk, who has written several nice introductions.

Worked examples and completed thoughts

Keith Conrad has a fantastic collection of mathematical "blurbs".

Ever wondered when exactly you can differentiate under the integral sign?
Would you like to see eleven proofs of the Gaussian integral formula?