Week 3 - More Principle of Well-Ordering Equivalence of Induciton Flavours Traps and Tricks

This week's lecture started off with the comparison and connection between Principle of Simple Induction, Principle of Complete Induction, and Pricinple of Well-Ordering. It could be seen from the proofs that there was a cycle of implication between these three principles- if you believe one, you must believe the other two. Before the lecture, I didn't know how PWO was connected with the other two, but now I clearly see a connection between them. It was nice to note these connections, as now we could refer to all three principles when doing proofs. The next topic, bases larger than zero, I didn't have any trouble with. It was similar to the material from the previous two weeks except that the base case could be changed to any number. The induction step still remained the same.


PROBLEM SET #2

This week's problem set is bit harder than last week's, but still manageable. The lecture slides weren't a big help this time, but the textbook was. There was a similiar example on the textbook, and after consulting the book, the problem didn't take me long to solve. It just took me a while to realize that we are supposed to substitute in a specific number for N before proving it. The try and error part of this problem to find N took me the longest time.

Week 2 - More Induction Flavours

Complete induction is very similiar to simple induction, except that for simple induction, we assume p(n) is true to show p(n+1) is true; whereas in complete induction, we assume p(0)... p(n-1) is true to show that p(n) is true. However, I find complete induction more challenging than simple induction, this might be due to the fact that I was exposed to simple induction more and complete induction is still a new concept. The theory behind the two method is the same, they both require base cases and an induction step. I guess one other challenge at this step right now is trying to figure out which method to use (either complete or simple). To get used to it, I will look more into complete induction, read the textbook pages for this topic, and do some exercises on both methods to see in which case should use what.


PROBLEM SET #1

I find the first problem set not that challenging to solve. Both questions are similiar to the examples given in class. After reading over the lecture slides, it didn't take me long to crack the problems. I think I'm getting more comfortable at simple inductions now. Just hope I can always pick up the materials of the course this fast.

Week 1 - woohoo~

Here comes another exciting school year with computer science. woohoo~! As the course code gets larger, the course is got to be harder as well. But I'm glad to have Danny as my prof again, he makes everything so much easier to understand. =)

Looks like this course is a continuation of 165, it's mostly about writing proofs. First week's lecture is not too deep yet, it's more like a review of last year's materials on simple induction. Instead that this time around, we don't have to follow that annoying format anymore. This is such a big relief for me, I remember last year, I spent so long writing everything following the strictly defined structure.