A guide on Mathematical Proofs

Project description: Quick tips on how to make the most out of your time in your first trial of proving things. This was written to help the students I TAed while in my Masters at ITAM. If you have any suggestions, please send me an email! It is not a paternalistic set of advices, but a gathering of useful ideas that helped myself when needed.

1. Have a handy collection of definitions and (maybe) the most important theorems. When facing a question that you don’t know how to start, start simply by stating the definitions and theorems.

2. Divide by cases! It works a lot!

3. Use proof by contradiction. It is really easy to use! (But some people don’t like it since it does not shed light on any specific thing about knowing the stuff)

4. Do not be hasty. The ability to prove things is nurtured proportional to the effort you put into it and it may come over time.

5. You can use (and abuse) of symbols such as ∀,∃… but on the other hand, it is nice to translate it back to words, or vice-versa.