# Want to Learn How to Write Proofs? Get This Book!

Alright, so you signed up for discrete math or linear algebra and figured “how different can this be from calculus?” right? It even started out that way – mostly calculations and definitions. Then *BOOM* they hit you with this:

Suppose that A,B, and C are nonempty sets. Prove that $A \subseteq B$ and $B \subseteq C \Rightarrow A \subseteq C$.

This isn’t a calculation. This isn’t a “if you see this – do this” type of situation like some math. While you CAN make a set of rules to write many of the basic proofs you will need, true proof writing is an art and there are many correct ways to go about it. It’s likely your book won’t help you too much on setting up the logic and the right kind of thinking for proof writing. It is completely different from the thinking that you would use to “find the derivative” or “solve this linear equation” for instance!

This is why I recommend “How to Prove It – A Structured Approach” to all of my students. The author, Velleman carefully develops logic and technique for writing proofs while introducing mathematical ideas like sets and relations that you will need to understand anyway. There is an ENTIRE CHAPTER on proof techniques and great practice problems.

I truly can’t recommend this book enough. In fact, this is the book that was used in my “intro to proofs’ class in college – that’s how thorough it is (If only all colleges had such a course!). If you want to do well in your advanced math courses, you will be glad you bought this.

NOTES: The link above is NOT an affiliate link. I live in Illinois, so it isn’t possible anyway :). Also, the image is from a pretty funny blog..