What is the Best Book for Learning Proofs?

In summary, the conversation is about a person seeking recommendations for books to improve their understanding of proofs before taking a proof-based course on linear algebra and vector calculus. The suggestion given is to read Velleman's book along with their linear algebra text to avoid getting bored.
  • #1
SMG75
23
0
Hey all,

I have a pretty solid background in what would be best described as applied or engineering math. However, I have had a very limited exposure to proofs. This fall, I will be taking a course covering linear algebra and vector calculus in an entirely proof-based manner. I'm looking for recommendations on books to read to get up to speed on the art of proofs. Any help would be appreciated.

Thanks!
 
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  • #2
Velleman's book is pretty good. However, I suggest you read it together with your linear algebra text. Reading a proof book can get quite boring if that's all your doing.
 

1. What makes a book the best for learning proofs?

A good book for learning proofs should have clear explanations, a variety of examples, and exercises for practice. It should also cover a range of proof techniques and provide helpful tips and strategies for approaching proofs.

2. Do I need to have a strong math background to use the best book for learning proofs?

While some familiarity with basic math concepts and notation is helpful, a good book for learning proofs should be accessible to readers with varying levels of math knowledge. It should also provide a review of relevant concepts as needed.

3. Can I use the best book for learning proofs for self-study?

Yes, a good book for learning proofs should be suitable for self-study. It should have clear and comprehensive explanations and examples, as well as exercises with answers or solutions provided for self-assessment.

4. Are there different books for learning different types of proofs?

Yes, there are books that focus on specific types of proofs, such as geometric proofs or algebraic proofs. However, a good book for learning proofs should cover a variety of proof techniques and be applicable to different areas of mathematics.

5. How do I know if a book is the best for learning proofs?

You can research reviews and recommendations from other mathematicians or students who have used the book. You can also look for books that have been used in reputable universities or recommended by experienced math professors.

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