Looking for Introduction to Proofs

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    Introduction Proofs
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Discussion Overview

The discussion revolves around recommendations for introductory books on proofs, particularly for someone studying Algebra and Trigonometry. Participants share their experiences and suggest resources that could help ease the transition into understanding proofs and theorems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty with proofs in "Basic Mathematics" by Lang and seeks recommendations for more accessible resources.
  • Another participant suggests "Geometry for Enjoyment and Challenge" as a potential resource that typically covers proof concepts.
  • Some participants endorse "How to Prove It" by Velleman, noting its positive reputation and helpful summary of proof techniques.
  • Another suggestion includes "Book of Proof" by Richard Hammack, which is available online and includes class tests and solutions prepared by the author.
  • One participant mentions Dexter Chua's lecture notes as an alternative, although they caution that it may be too advanced for the original poster.

Areas of Agreement / Disagreement

Participants generally agree on the value of "How to Prove It" and "Book of Proof," but there is no consensus on which resource is definitively the best for beginners. Different perspectives on the appropriateness of other suggested materials indicate a range of opinions.

Contextual Notes

Some participants note that the difficulty with proofs may stem from a lack of prior exposure, and the recommendations vary in terms of accessibility and depth, which may affect their suitability for the original poster.

Who May Find This Useful

This discussion may be useful for students transitioning into proof-based mathematics, particularly those looking for introductory resources to build foundational skills in mathematical reasoning.

hackedagainanda
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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.
 
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Usually this is covered in Geometry, e.g. "Geometry for Enjoyment and Challenge", R. Rhoad et al.
 
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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).
 
"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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