Proofs
Correct, Incorrect, and Humorous

Mathematical Proofs A list of some common proof techniques that are often extremely useful [Humorous].
The Most Common Errors in Undergraduate Mathematics.
Law of the Excluded Middle - A statement is either true or false. There is no third alternative.

Reductio ad absurdum - A proposition is assumed, and then is shown to lead to a contradiction, thereby showing the proposition to be false.

Deductive or Aristotelian Logic.

An interesting view of the relationship between Aristotelian logic and symbolic logic can be found here.

Summary of Types of arguments, deductive vs inductive.

Reference's to Occam's Razor - which says in essence "keep it simple, stupid" or given a choice between to competing explanations, go with the one with the fewest assumptions...

The Scientific Method as a rejection of Aristotelian logic.

"If a man will begin with certainties, he shall end in doubts, but if he will be content to begin with doubts, he shall end in certainties." - Francis Bacon
Visualization of the Proof of the Pythagorean Theorem using a Java Applet [Classic Applet!].

Another proof of the Pythagorean Theorem using HTML and gifs [slideshow].

Using computers to help prove theorems: the famous Four Color Theorem