Proof Puzzle

One of the main goals of this course is to introduce you to the fundamentals of mathematical proof writing.  

In many ways, writing a mathematical proof is like solving a puzzle.  

How do you solve a jigsaw puzzle?  What strategies do you use?  

At the start, the proof might be clear as mud in your mind.  But after thinking about the claim long enough, you typically have an idea of how the proof should begin and end.  

So it is a good idea to write those down first.  Sometimes, I might share a hint on the "easiest" way to proceed with the proof.   

Next you may see some key features that fit together in the middle, and some tricky parts that you need to examine further before you know how they fit together.

 
The outline  of the pieces are typically stipulated by mathematical axioms, definitions, theorems, and rules of logic.  

Your readings in this course, will help you figure out what the puzzle pieces look like, and how they fit together.  

By the time you are done discovering and writing the proof, you  will be convinced that the pieces fit together logically. 

It will often take several revisions before you have everything in the clearest order possible and each step follows logically from the last, but if you put the time and effort in, you will have solved a puzzle, and you may even want to frame it!