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I'm learning about proofs in school, quite a few different sorts (but not geometry ones), but the teacher is teaching by slides mainly, not books. The main ones are proof by direct/indirect/contraposition/etc. and proof by mathematical induction, and also proof of inequalities with and without absolute values. I sort of understand it in theory, but when it comes to examples I get them wrong a lot of the time or just don't know how to start/where to go.

I was hoping with more practice I'd get better at it but I can't find examples (with answers) that I can try out. I need the answers both to make sure I'm doing it correctly and to help me out when I get stuck. I can learn from them quite well; what mistakes I'm making and how to do something, how to get out of a problem and continue on when I get stuck, etc.

Does anyone have or know of any good material or resources they can recommend for beginners in this? Something with both examples for me to practice on and the answers so I can check them? I've got tests coming up, and I'd be so very grateful for any help. Thanks!

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I highly recommend this online course: https://www.coursera.org/course/maththink

It is starting again in the next few days, and I found it very helpful in getting to understand the concept of a proof, and what the various types of common proof are.

I'm not sure if the course will end in time for you, but fingers crossed it does.

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