Bounds, Well-ordering, and A1

We're already a month into the semester! They say time flies by when... actually time flies by all the time. Before I know it, I will be a broken down old man. But for now, I will continue to distract myself from my mortality by doing things like going to school, and learning about computers.Which swiftly bring me to the topic at hand: my favorite course of all time, CSC236!!

I was perhaps ten minutes into the first CSC236 lecture of the year, when I high-fived myself out of pure joy. I was really glad that I had taken MAT137 over MAT135 ("Calculus!" not "Calculus") last year. When I told my friend about my experience of extensively using induction last year in relation to limits, behaviours of functions, bounds on series, and a lot of other stuff, the response that I got was a blank stare. So while a few of my friends struggled for the first few classes to wrap their minds around the concept of induction itself, and why it is valid at all, I certainly felt like I had a head-start in the course.

By the time "Well Ordering" had arrived, the course was beginning to get a tiny bit more challenging. Even though I had used the same principle in the aforementioned math course in relation to bounds and sequences, the "round-robin tournament" proof done in class by Prof. Heap threw me off. While I understood the logic of the proof, it still felt invalid to me. So I went home, read over the annotated slides (by the way, THE GREATEST IDEA OF ALL TIME), and I still felt that the proof was invalid. So I did what any scholar in this day and age does: I loaded up Wikipedia. More specifically, the "round-robin tournament" page. It turned out that I had a false understanding of what a round-robin tournament was to begin with. My understanding was that the tournament is a elimination-style one-match-at-a-time tournament, while that is not the case at all. Either I had a lapse of concentration in the lecture and the concept was explained, or that everyone knows what a round-robin tournament is and I just had a gaping hole in my knowledge. In any case, everything was back to normal.

I felt like I was ready for the final exam right then and there... but then Assignment 1 happened. Three straightforward questions which collectively took 45 minutes, and then a monster in the form of question 4. Binary strings. Occurrences of 10s and 01s. I must have written 3 or 4 separate proofs for that question, but none of them felt completely valid to me. It was Friday, the assignment was due that night, and I was stuck. I didn't know what to do. It was actually Prof. Heap's hint in class about starting out with a stronger claim that gave me the idea. So like any geniuses I've seen in the movies who get a great idea in the middle of a class, I got up and left and knocked over everyone's papers and almost tripped on someone's bag, walked to the closest window and took out a marker and started writing on the glass. OK, none of that happened, but I finished my proof after class, and just to make sure that my approach was valid, I went to the extra office-hours on Friday, and indirectly, and without getting into too much detail, explained my approach, and Prof. Heap indirectly, and without getting into too much detail, replied that it sounded valid.

I must apologize for having such a long post, and I feel for Prof. Heap and the TAs who have to read several hundred of poorly written, very similar posts about students doing proofs. But hey, that is what you get when you shut down the alternative "Student Tweets" assignment, which would've made life easier for all parties involved.

Stay tuned for a preview from next week's episode of SIAMAK'S CSC236 SLOG:

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Mid-term exam!!! Was it a success or failure? Find out if this student aced the test, or if he was dealt a tough hand! Next week on SIAMAK'S CSC236 SLOG.