First Impressions

First entry here we go!

It's been a satisfying month since the start of the course, it's been everything I've been expecting after csc165 last year. It's bringing the challenges that were presented last year except on a higher level. We started off with our old simple/mathematical induction we all knew and grew comfortable with in 165 and dove right into complete induction, well ordering, and structural induction with recursive functions. Upon first learning them, I didn't absorb everything in the lecture and I'm guessing it will take me some time to "master" these new flavours and to apply them efficiently. Practicing writing more and more well thought out and incrementally challenging proofs will set me up to shoot down anything on the midterms or exam, just like in 165.

Looking at the assignment 1, it was a great place to start practicing writing up proofs after doing some from the tutorial problem sets. After writing it up I felt like I was understanding complete induction much better than I had before from the lectures and tutorials because I wrote the proof and didn't toss it away, but instead took another hard look at it and tried poking holes in the proof and evaluating it's structure. It took some time to realize that we weren't being evaluated purely on our ability to solve the proof, but the coherency and elegance of our proof. I recall Heap in one of our lectures mentioning that a good proof is a proof that can be absorbed in "one gulp" - by that he meant keeping proofs to one page. Maximum one page proofs meant we had to consider the audience and assume they can follow our proof if we skipped explaining a few obvious steps and proving nontrivial lemmas we used.

The only thing now I must do is study for the midterm on Wednesday. The structural induction isn't so bad after trying out a few proofs with it, but well ordering is the weird one for me! It's not hard to follow the proof step by step, but in the scope of the entire problem it's a little weird how we have to use proof by contradiction that some number is the least element. I'm starting to read the section in the book, although there doesn't seem to be a lot on it I'll try re-reading the notes and finding some problems to practice on, which helps me out the most.

Still remaining hopeful that I can do just as well as I did in 165, except not learning everything last minute!