Week in Review #2: Prove it!

We went over the proof outline this week. This outline helps us write good proofs that are clear and organized. I have seen this already in MAT137, but given the similarity between that and CSC165, it came back to me.

First off, a proof is the explanation of why and how a statement is true. To prove something, we have to believe that the statement is true. We start by understanding why it's true. Once we understand why it's true, we then go on to writing it down. However, it does not stop there. Proof writing is not a finite process. Sometimes we may encounter gaps that need to be fixed that require us to start over. The first step, understanding the proof, is where we try and strengthen our weak spots. In MAT137, we call this "scratch work" or "rough work." It is a messy process, but it is necessary that we go through this process to strengthen any given proof. Much like English writing, there is an audience to our proofs: CSC165 students and staff. We have to make sure that our audience can understand our proofs. 

As for style, indentation is required to show scope of assumption. We also begin our sentences with words such as "Assume" and "Then" throughout our proofs. As I learned in MAT137, I could also end a proof with ∎.

This is how a proof would generally look like. We start with "Assume" and end with a concluding statement (starting with "Then" or "Conclude"):

Assume...

      Assume...

      Then...

      .

      .

      .

      Then....

Then...

In addition, I had my third quiz in tutorial on Tuesday. When I went over the exercise with the TA, I had a better understanding of the material. The quiz wasn't so hard either.

I also had my first assignment due yesterday. At first, I did not know how to approach many of the questions. I worked with other people to get help. After many hours, it was finally finished. I felt a sense of accomplishment and relief.