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I have limited time to spend on the resource (3-6 hours) and never done any proofs and I need to be able to apply deductive, inductive and other proof techniques to some relatively easy propositions (basic number theory, trees etc.).

Please recommend a resource (website, or short book) that will meet these objectives.

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Not exacxtly "quick and dirty", but the best resource for learning to prove stuff is Polya's How To –  user22805 Sep 2 '12 at 4:38
    
This is a strange request. What is limiting your time? –  Snowball Sep 2 '12 at 4:50
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@Snowball: My work schedule is pretty busy and I am getting my CPA. Maybe I can accommodate more time, but it will be hard to invest too much into it. The purpose of my request is for an online/distance learning class I am enrolled in (algorithms) that has proofs in homework problems. –  Wuschelbeutel Kartoffelhuhn Sep 2 '12 at 4:56
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Learning how to prove things is a skill you learn yourself through practice...there is no book that will make you create your own proofs of things. This is not just a "topic of maths" that can be learned in a few hours but the basis of all mathematical thought! –  fretty Sep 2 '12 at 9:04
    
This skill takes a little time to cultivate, but you should be able to make rapid progress if you are determined! You can probably get helpful feedback on your proof-work here, too. –  rschwieb Sep 2 '12 at 13:20

2 Answers 2

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The following books will be of use for you:

  1. How to solve it, as David Wallace mentioned.
  2. (geared towards contestual math) The Art and Craft of Problem Solving
  3. How to Prove It (this could be used by anyone in highschool or a bit before)

For basic number theory stuff you have several options depending upon your background:

If you don't have any abstract algebra, then I would reccomend Elementry Number theory by Strayer. It does use some algebra, but very little. There is also the Rosen book, which is widely used. Rosen is supposed to be simple and straight forward.

For graph theory stuff, any introductory discrete math book would be fine, enless you want to learn a lot about the subject. In the case that you do want to learn a fair amount about it, then I would reccomend Graphs and Digraphs by Chartrand, Lesinak, and Zhang. The 2nd option is much more involved. You can also find plenty of free introductory number theory books online, by googling "free number theory." Apperently, number theory is stuck in jail.

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thank you very much for the recommendations. however, it would be overkill to get a book for each type of problem i am trying to solve (they are relatively elementary - its more about the introductory application of proof techniques, rather than the mathematical domain of the problems). i am at the college level and the types of problems i want to be able to solve are "show directly that this tree has n-1 nodes", "show that this expression(x) is larger than that expression(x) via induction" –  Wuschelbeutel Kartoffelhuhn Sep 2 '12 at 5:01
    
In all honestly, I think that if you're just looking for one source, you're better off getting a general discrete math book. These books always cover some number theory and graph theory. Just search "discrete math" on amazon or w/e and find a book that appeals to you. These books usually have an intro proof section too. –  Chris Dugale Sep 4 '12 at 5:13

I'm kind of amazed that no one's pointed out the tricki yet. Also if you search for the type of question you're thinking of you should be able to find great examples of simple proof techniques (induction, telescopy, etc.) on this very site. And if you know the names of techniques I think google will be your friend: searching explain proof by induction turns up some useful results and nice examples.

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thanks for those tips. i checked out tricki but im specifically looking for a nice and easy intro/overview, and the proofs there seem to be more advanced (analysis etc). i will keep in mind to search for simple proofs on the web and on this site. –  Wuschelbeutel Kartoffelhuhn Sep 2 '12 at 21:01

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