Week 4

This week, we're back to the old stuff from last year, but more indepth. Danny taught us about how we can prove recursive functions using induction. This part isn't too difficult to understand because we practiced recursion a lot in 148 last year. I believe most of us understand how it works. Then, there's time complexity and unwinding. Coming up with a function that calculates the time complexity of a recursive function wasn't too hard after learning how to unwind. All it takes to learn how to unwind are just basic math concepts.

-Assignment 1-
Assignment 1... I'd say it's more difficult than last year. I invited my friend over one day to discuss it. After looking through it, we just sat there staring into empty space. I knew how to do question 1 because I've done something very similar many times in high school. The other three were just horrible. Question 2 took me an hour to start off... I had no clue of how to do question 3. I couldn't even understand what question 4 was talking about. So, we decided to go on discussion board. Thank god! Question 4 is postponed to the next assignment. We've also found some hints that Danny and other classmates gave us. However, we still had little idea of how to solve the questions. Therefore, we went to the computer science help center. It was extremely helpful. The TAs tries hard and they don't just tell you the answer, which is great. I will only end up in bad condition for tests and exams if they just tell me the answer. I think understanding the material is more important than getting 100% without knowing what's going on. For question 2, the TAs told me different ways to design the technique. Afterwards, I just proved it by using induction. For question 3, I just had them explaining to me what Danny's hint meant. Then, I immediately knew how to do it. I am expecting a decent grade for this assignment. =D

Week 3

This week, Danny went into details of Principle of Well-Ordering. He showed us how to use it and how to prove the cycle of implication between Complete induction, Simple induction and Principle of Well-Ordering. I actually have no idea of how Danny proved the cycle. The only thing that I understands is what is Principle of Well-Ordering and how to use it. I figured that's probably the most important thing for now. As for the prove, lots of reading is required for me. I feel like csc236 is laughing at me now...

-Problem set 2-
We had our second problem set due this week. There was only one question about complete induction. It was the very famous stamp question in week 2 lecture slides, but with different numbers. It felt great to actually solve it youself. I didn't have a hard time proving it.

Week 2

Danny finally taught us something new this week! Another type of induction was taught, which is called Complete Induction. It is interesting to see how different it is from Simple induction. It proves P(0) to P(n - 1) hold, then use that to prove P(n) also holds. After understanding the basic concept of it, I still don't know when to use which induction. It seems like I will have to do lots of exercises and read the textbook for more details... I really like the stamp and chocolate examples. Without them, I couldn't have understood how complete induction works. Principle of Well-Ordering was also rougly introduced.

-Problem set 1-
Finally, our first course work of the year. It is based on simple induction, which was taught last week. I think Danny is kind enough to give us two questions that are so similar to the examples mentioned in week 1 lecture slides. Question 1 is basically the same, but just with a different base. So, I think problem set 1 is free marks. Thanks Danny =D

Week 1

Another exciting year in Danny's class! Last year was great fun, it certainly was interesting to learn about proofs. Now at least when I see those forall or exists symbols, I won't get tangled up. This week is mostly introduction of the course and some revision from last year. It's good to know that the great grading system is still here. I don't know if it's Danny who decided it, or the faculty. The system is great! It makes all of our lives much easier. There will be no tutorials this year, instead, we are going to have 6 problem sets. I think having an adequate amount of course work such as problem sets is great. It forces lazy people like me to keep up with what's going on and allows us to understand course materials better. There are still assignments. I am expecting them to be as challenging as last year.
To conclude, nothing much went on this week. There were no problem sets or assignments. As for the slides on Simple induction, this is simply revision from last year.