First 5 weeks of CSC236

As of now, we are almost half of the way from CSC236 final for fall term and I have to be very appreciative to Danny Heap. Danny Heap has struck me greatly( in a positive way) and I feel very fortunate to face it early in my university career.

From my perspective, in fact most of you will also think the same way, I think that CSC165(Mathematical Expression and Reasoning for Computer Science) was to help us think completely different from high school math, and helping students to think more logically and elegantly when they are faced with some rigorous math questions. For example, when I was first introduced with Epsilon and Delta proof from MAT137, which I had never came across in high school,  at first I felt like it was the hardest mathematical concept that I had ever faced in my life. In fact, it was the hardest concept to me at the time; however, I was taking CSC165 concurrently with MAT137 in fall term, and  I was introduced with Epsilon and Delta also from CSC165. Learning Epsilon and Delta from CSC165 has helped me a lot to understand the topic. It was then, that I have became little be more mature with mathematics,  and logical thinking have helped me to be more immune to other very rigorous mathematical concept. After finishing MAT137 and CSC165, I thought I was a very good logical/analytical thinker. That arrogant belief has disappeared, just after first few weeks of CSC236.

As I mentioned earlier, Danny has struck me with a very alerting wake up call.  When I was first introduced with Induction Proof in CSC236, I felt like it was going to be somewhat easy, since I had already learned it from MAT137. In fact, I was very used to mathematical induction and I was able to see the pattern really quickly with almost any mathematical induction questions. Actually, I have to say that I merely memorized/followed the template. Going into 2nd or 3rd week of CSC236, I was introduced with another type of induction, Complete Induction, and that was the moment where my maturity with mathematic has took another step. If I remember correctly, I was at Danny's office hour to ask if my solution for one of the assigned question  (It was a question regarding number of squares that can be cut from a chocolate or something) from lecture was correct. And I felt very embarrassed of myself. When I was working on the question, just like any other induction proof questions, I merely followed the template and I thought I came up with a right answer. However, it took me almost an half hour to come up with the right answer when I was at Danny's office hour, because I went completely different path when I was solving the question. The question was to be proved by using Complete Induction, but since I was more comfortable of using Mathematical Induction, I resisted to use Complete Induction. And Danny knew it right at the moment and he told me something that I will always and have to keep in mind in the future when I am solving a math question; in fact with any questions.

My mentality when I am faced with a particular math question, I tend to find a short-cut or try to find an easy way of solving it. However, now I know that there really isn't a short cut or an easy way ( or more preferable way) of solving a question. Danny told me that I must be comfortable of using all the possible ways/methods to solve a question, and in fact it is true. By trying to just use a method which I prefer, I will never able to go to the next level to be more logical/analytical thinker. And I am very lucky to realize it early and want to thank Danny.