Week 3 of CSC236

Perhaps it was because I'm late almost every class now , but I start off the class being a little confused about the problem thats being taken up.Luckily Prof. Heap writes his solutions in a very understandable way so that when he starts to write the actual proof I understand the problem right away. It was very interesting to see induction proof's using the Principle of Well Ordering.I find it easier to not write base cases since its obviously less writing.Using the Principle of Well Ordering you do don't have to write the base case explicitly, but its still there because you are using the fact that there is a smallest number for which the problem is true for.

Although the 3 proofs of induction we use are similar , I did not know that they implied one another. After seeing the proof , you can see that for example proving something by complete induction , you can conclude something about the smallest element in the principle of well ordering for another fact. It would be very interesting to see a cross over of the induction proofs , maybe we'll see them later on.

I was wondering if you could prove something even though the proposition is false , and today i got to see that. It was interesting to see that even by adding 1 word like "full" with binary tree could make a difference between a correct and a wrong proof, or even how adding 1 to a constant can be used to correct a false proof. Looking forward to completing the assignment this weekend , hopefully the last question won't give me problems.

I was happy to see that the problem set 2 was quite easy , the only "difficult" part was to find out the number N for which the postage could be made. Also it was nice to see I did well in problem set 1 , hopefully I can use the problem sets to boost my mark , even if it'll be by a small factor. Looking forward to completing the assignment this weekend , hopefully the last question won't give me problems.

I found this pretty amusing.

Week 2 of CSC236

Now onto the second week. Breathing a sigh of relief after finishing the first problem set. But another problem set awaited me after my long journey home. Hopefully it won't be harder than PS 1. To me it was the perfect difficulty for a problem set as it reinforced the material covered during the previous week. Week 2 material seemed a tad weird in the beginning. But after the second lecture of week 2 I really liked the complete induction proofs , they are more or less the same as simple induction , especially the antecedent that's used for both. The consequent part is quite simple , especially if I can make a connection between the current n case to any of the previously assumed cases. The only question that gave me some trouble was the full binary tree example. Most likely because I was late for class , but during the actual proof I could see how using each embedded tree in the left and right node trees can create odd number of nodes.

The stamp problem was nothing new since we did it in CSC165 last year. But using strong induction it seemed a lot easier, the only part that gave me trouble was why we had to start induction after the 11 cent postage , but after attempting problem set 2 and reading the book it became very clear. The book although good for examples , to me doesn't compare to the lectures , because to me it's a lot easier to understand Prof. Heap explain the different cases , and why the base cases are 12 for example in the postage problem.
For the new problem set and assignment i really need to push myself to start early since I'm already swamped with assignments and already a bit behind. Hopefully my assignment proofs will be adequate.

I'll be adding random and weird pictures sometimes to keep you entertained. Hope you enjoy them!

Week 1 of CSC236

First week of this theory course seemed very familiar to the CSC165 theory course from first year. So far its been fairly easy since the induction proofs have been very simple and straight forward. Its been quite easy so far especially the new form of the proofs. Last year's proofs were quite methodical and had to be written in a certain form. Although they weren't hard , the proofs layout this year is quite easy , suitable to my lazy self. Also the new tablet projector way of teaching is quite clear, Danny can write however small or big and i can see it perfectly even from the back of the class, although the climate in the class room is almost like back home in the good old humid days.

Looking forward to working on the first assignment, although I still have two weeks ,I think it'll be best if I started sooner rather than last year when I procrastinated to the end. The problem set doesn't seem to be too difficult , I've already started working on it and am half way through it, although the second question seems to be giving me some migraines.But I have lots of time to figure it out and I'm sure I can finish it easily.

So far its been quite an interesting first week , in all my courses. Looking forward to the rest of the year hopefully I wont fall off the bandwagon. 0 or 1 , only two choices. Although I did have a nightmare where I saw a 2 , but we all know theres no such thing as 2.