Intro to Proof Class: Velleman's How to Prove It

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Velleman's "How to Prove It" is a valuable resource for those taking an introductory proofs class. The book features a variety of exercises that range from easy to challenging, with some examples containing errors. It emphasizes the importance of using logic effectively in proofs, guiding readers on when to use direct proof, proof by exhaustion, or proof by contradiction. Although proof by induction is covered later in the book, many students may not encounter it early in their coursework. A helpful strategy for tackling difficult proofs is to translate them into symbolic logic and persist in finding a solution; seeking help after an hour of struggle is advisable. To self-check a proof, reading it critically to ensure it is convincing is recommended.
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I'm taking an intro to proof's class this semester. What are your thoughts on Velleman's How to prove it book? Are the exercises easy or hard to do?
 
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The book has great examples (though some haves errors). The proofs can be really easy or take 30-60 minutes to do. The key point of the book is to use logic to carry out a proof the right way. It helps you decide to prove directly, by exhaustion, or by contradiction. The book goes into proof by induction much later but I haven't gone over it in class.

Tip: If you get stuck on proving a theorem, try to translate it to symbolic logic and keep trying to finish the proof. If an hour has gone by, you can go get help. This helps you try out more approaches to the problem.

Finally, one way to self check a proof is to read it and be convinced.
 

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