Books recommendation for Mathematical proofs

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Discussion Overview

The discussion revolves around recommendations for books that focus on techniques for mathematical proofs. Participants express a desire to improve their understanding and mastery of various proof methods, including direct methods, induction, contrapositive, and contradiction.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant requests suggestions for books that teach techniques for mathematical proofs, indicating a familiarity with direct methods and induction but a need to learn indirect methods.
  • Another participant references a previous thread on the same topic, suggesting that there may be additional resources or discussions available.
  • A participant recommends "How to Prove It: A Structured Approach" by D. Vellerman as a suitable resource.
  • Another book mentioned is "The Theory of Sets" by the Bourbaki group, noted for its challenging content but valuable sections on logic and theory construction.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on specific book recommendations, and multiple suggestions are offered without clear agreement on which is the best resource.

Contextual Notes

Some participants may have different levels of familiarity with proof techniques, which could influence their recommendations. The difficulty level of suggested books varies, with some being noted as more challenging than others.

Who May Find This Useful

This discussion may be useful for students or individuals seeking to enhance their skills in mathematical proofs, particularly those looking for structured resources or varying levels of difficulty in learning materials.

JPSartre
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Hi,
I was wondering if you can suggest good books on the techniques for mathematical proofs.

I know this is quite a simple matter but I would be glad if you could suggest me with greats books for teaching proofs.

More often than not I used the direct method and induction to prove problems in abstract algebra let's say. I am not that familiar yet with indirect methods such as contrapositive or by contradiction method. I need to get better at mastering all proof techniques before next fall.

Thanks in advance for your help,
Best
S
 
Physics news on Phys.org
Alright thanks Infinitum!
 
How to Prove it, a Structured Approach - D Vellerman! :biggrin:
You could also check out The Theory of Sets by the Bourbaki group, that book has a section or two on constructing logic and theories. (but this version is a lot harder going than vellermans approach)
 

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