Books recommendation for Mathematical proofs

[JPSartre]

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

 

[Infinitum]

Recently there was a thread about the same topic

https://www.physicsforums.com/showthread.php?t=609578

 

[JPSartre]

Alright thanks Infinitum!

 

[genericusrnme]

How to Prove it, a Structured Approach - D Vellerman!
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)

 

[Matrix0]

ara

Hello Sara,

I understand the importance of mastering different proof techniques for effectively solving problems in mathematics. Here are some book recommendations that may help you in this regard:

1. "How to Prove It: A Structured Approach" by Daniel J. Velleman - This book provides a comprehensive and structured approach to understanding and constructing mathematical proofs, covering various techniques such as direct proof, proof by contradiction, and proof by induction.

2. "The Nuts and Bolts of Proofs" by Antonella Cupillari - This book offers a hands-on approach to learning mathematical proofs, with many examples and exercises to practice and develop your skills.

3. "Proofs and Fundamentals: A First Course in Abstract Mathematics" by Ethan D. Bloch - This book provides a solid foundation for understanding abstract mathematics and includes a section on proof techniques, with clear explanations and examples.

I would also recommend checking out online resources such as Khan Academy or MIT OpenCourseWare for additional practice and guidance on proof techniques. With dedication and practice, I am confident that you will become proficient in all proof methods before the next fall. Best of luck in your studies!

Sincerely,