Talk:Mathematical Proof
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[edit] Call/Vote for Reorganization and Various Fixes
The reorganization issue I have is that "Methods of Proof" (which come from prepositional logic: contructive/direct, contrapositive, contradiction, and counterexample) should be separated from what I will call the "Tools of Proof" (higher level proof methods such as proof by induction, exhaustion, pigeonhole -though it's not here right now-, etc.). I don't feel I quite have the right to do this myself if the book is still alive in any way. Also, there is at least one proof that I would like to fix, but don't know how to use the system well enough to patch it (so that the only fix I can do right now would be to remove it). This is in "counterexamples", where the author tries to make a bijection but misses one case (that is, that any terminating decimal is equivalent to a nonterminating decimal). I'll try to look into the syntax of this system and maybe fix it myself, but like I said, the only way I can fix it right now is by removal. Mo Anabre 16:54, 1 May 2007 (UTC)
I've fixed the proof I referred to above... I'm still looking into perhaps revamping various parts. If anyone is especially adamant against my doing so, speak now. Otherwise, after school gets out in a few weeks, I'll start running through it. Mo Anabre 23:29, 1 May 2007 (UTC)
[edit] Add interest by adding puzzles
Why not start the book with a nice example? How about the puzzle about the checkerboard and the dominoes? Take a checkerboard and cut off the two opposite black corner squares. Now try to place 31 dominoes on the remaining squares. Is it possible? (The answer is no - the reason is that each domino is on one red and one black square. The truncated checkboard has 32 red squares and 30 black squares. If there was a solution, at least one of the dominoes would have to be on two red squares.) Solving this puzzle is similar to constructing a proof. Maybe it's the same thing. You can work this example through the whole introduction, or maybe a set of puzzles could work their way through the whole book. 12.47.208.50 16:53, 24 April 2006 (UTC)
[edit] Velleman's Proof Designer
Daniel J. Velleman has a program that goes along with his book "How To Prove It. Second Edition". It provides proof checker and builder that uses a concise syntax that could be used as a standard format for all proofs in the book? Comments, Questions, Concerns?
[edit] Geometry?
Why is this book under the Geometry section? Geometric proofs are only a limited part of Mathematical Proof.
[edit] Good Ideas
You've got great ideas. Please change anything you think needs to be. It won't hurt my feelings. I'm just an undergrad--I only started the book because the topic interests me. Go ahead and add puzzles and I'll try to standardize the method of proof and everything. Thanks for the input. -Gandalf 03:23, 4 August 2006 (UTC)
[edit] Getting basics out of the way?
From what I've read of deadtree proof books, it may be a good thing to focus a little more on background first, like maybe moving Basic Set Theory into its own page, talking a little bit about the properties of arithmetic, and maybe flushing out Boolean reasoning a bit more. I mean, what's there is good, but there isn't a dedicated section for De Morgan's Laws, and I'm not sure where they'd best fit.
Of course, adding too much background material up front could make the book overly dense, so maybe there should be some very simple proofs early. The contrapositive identity would make a good candidate in my opinion, but I'd like to hear if anyone else has any ideas. --cgranade (talk) 15:24, 24 July 2008 (UTC)
