# Is there a book that teaches proofs from simple to intermediate level?

I am looking for a book that teaches proofs and the book has many exercises from very simple to more difficult? I have noticed with most math books, they seem to leave out pieces too soon before the reader gets a chance to work through lots of examples of a specific level before progressing to the next level. I want more structured approach so that after a couple dozen proofs of class "A", I want to advance to class "B". I cannot overemphasize my need for exercises. BTW, this is in preparation for an analysis course.

• Something like "Problem solving strategies" by Arthur Engels (?) – Imago May 5 '16 at 17:21
• – MathematicianByMistake May 5 '16 at 17:26
• – Michael Burr May 5 '16 at 17:30
• Since you are preparing for an analysis course I would suggest: [amazon.com/… It is not a technically a book about proofs, it is a book about techniques for handling inequalities, something I struggled with early on my math education: It has many challenging problems, and solutions for you to verify. – Luis Vera May 5 '16 at 17:32
• Thanks, I just took a look at that Engles pdf and yes! This is a very good looking book. I need to do some problems to get a full feel. If you know of a couple more along this vein but more focused (ie. proofs in Number theory or whatever topic.) . I have enough books on proof with techniques. I need progressive exercises. I am ready to learn about how to think about the proofs from dead simple to advanced undergrad. Eventually I want to teach so I will have the advantage of being empathetic towards students that don't have a full range of techniques. – MarkoPolo May 5 '16 at 17:40

I recommend

Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni, and Zhang. (link below)

The nice thing is that you can get a taste of the different kinds of mathematical proofs (including the $\epsilon-\delta$ proofs you'll be seeing a lot of in analysis) in a simple, clear, informative setting. I.e., the things that you learn to prove and are proved for you are not that advanced, but the help illuminate what really goes on in a proof.