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Looking for Introduction to Proofs

  • #1

Main Question or Discussion Point

Hey, PF! I am currently studying Algebra and Trig, and was wondering what's a good book to use to get eased into the process of proving statements and theorems. I'm planning to use Basic Mathematics by Lang but the proofs in it have been a real hindrance to my progress. Even just simple proofs like the irrationality of the square root of 2 are a struggle right now.
I currently have How to Prove It by Velleman, but was wondering if anyone has any experience with it or other introductory books on proofs.

My knowledge of Proofs is non-existent. Thanks for your time.
 

Answers and Replies

  • #2
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Usually this is covered in Geometry, e.g. "Geometry for Enjoyment and Challenge", R. Rhoad et al.
 
  • #3
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I think Velleman's book is highly regarded, you should try it. Another suggestion would be "Book of proof" by Richard Hammack. It is freely available online here, and the author, being a teacher, had prepared tests for a class he taught which you can find here (with solutions).
 
  • #4
"How to Prove It" is good. It has a nice summary of proof techniques at the end.

An alternative could be Dexter Chua's lecture notes. They're short, but they might also be too advanced for now. After all, it's from Cambridge University. But it's worth trying to explore that territory.

https://dec41.user.srcf.net/notes/IA_M/numbers_and_sets_trim.pdf
 

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