Week 8

Week 8 was an intense week for me, I had CSC165 assignment due on the 3rd of November, CSC165 term test on the 4th of November, CSC108 assignment due on the 4th of November and a MAT137 problem set due on the 3rd of November. So I was pretty much going crazy this week. In the week 8 lecture we started with the formal definition of O(n^2). Then we analysed a sort algorithm, we went through the insertion sort and Professor Larry showed us an animation of how the insertion sort works. We analysed another algorithm known as the maximum slice which is said to be very useful for stockbrokers. In the last hour of the lecture we had a problem solving session called penny piles. The problem said:
 You are sitting in front of two drawers. The left drawer contains 64 pennies, the right drawer contains
nothing. Can you arrange things so that one of the drawers has exactly 48 pennies, using only the following
two operations?
L: If the left drawer has an even number of pennies, transfer half of them to the right drawer (if the left
drawer has an odd number of pennies, operation L is disallowed).
R: If the right drawer has an even number of pennies, transfer half of them to the left drawer (if the right
drawer has an odd number of pennies, operation R is disallowed).
What about arranging things so that one of the drawers contains other numbers in the range [0, 64]? What
about starting with a different number of pennies in the left drawer?

I did it with two of my friends and we pretty much figured out the problem, this session wasn't that hard. I found it quite easy. Today assignment 2 was due. We have the solutions for it already. Now we have a lecture tomorrow and a term test as well. I hope I do well in this one. 

Week 7

So, beginning of week 7, assignment 1 marks were out and the class average was 83 %. Exactly after this we got to know that assignment 2 was due on the 3rd of November. Our next term test is on the 4th of November. This week was full of bad news! Any ways, week 7 we started a new way to prove which is proof by cases. In this we split the argument into difference case and then prove each case. Basically, we cover all possibilities. Using the proof by cases we can also prove the four colour theorem, which I had never heard about before the week 7 lecture. The four colour theorem proof was the world's first computer assisted proof. We also learned about patterns of inference, there were several introduction rules like the negation introduction, conjunction introduction, disjunction introduction etc. We learned some elimination rules as well such as negation elimination, conjunction elimination disjunction elimination and so on. Elimination rules were basically the opposite of the introduction rules. After doing proofs we started with algorithms, we compared two sorting algorithms, bubble sort and merge sort. We observed that bubble sort was slower than merge sort, we did some examples of linear search also.

Week 6

Today in the lecture, we did some more proofs. Today's lecture was even for two hours because the other section missed their class due to the thanksgiving holidays so that was good for us. So, we did some more proofs today, we learned proofs of boolean and non-boolean functions and we also started proving limits. It's good for me that we are proving limits because we already did these in MAT137 and I was kind of confused about the concept. I didn't actually understand much of the concept so by doing them in this course also will sort of help me understand and go over the concept again. We learnt a new thing called a 'floor', I had never heard about this before so for me it was new. Floor is basically the largest integer which is less than or equal to the number. We did a few proofs which involved the concept of floor. Then we also started doing proofs about limits. Prof Larry included some proofs for fun, they were actually funny.This week we have no tutorial! So that is good news! but I'm still looking forward to the next class.

Week 5

Week 5 has been tough, we've been doing proofs! I found proofs really hard. This week, I was down with flu so I wasn't quite able to concentrate in class, due to this I didn't get a clear understanding of the concepts. We also had our term test this week. It wasn't either difficult or easy, it was some what in between. I was expecting an extremely hard test because assignment 1 was really difficult and after doing that I was pretty sure that I wasn't ready for the test and I would fail it, but now that we have our marks, its not that bad!

Well, because of the test, our lecture was for 2 hours and we learned about proving statements by proving that the contrapositive of the statement is false, we learned how to write a backward proof. Writing a proof backwards is a comparatively easy task. We also learned about proving by a contradiction. We did a proof which I found very interesting, it was:

There are 5 boxes in which there are in total 51 balls. Prove that there is box with at least 11 balls in it. 

I really liked this one. Then we did a proof related to prime numbers. This week was nice since we had only 2 hours of lecture but at the same time the week was tough for me too since I had a lot of work to do.

Week 4

In week 4, we have an assignment that is due on the 3rd of October and its quite hard, I've being spending 2 hours since the past two days in the computer science help centre and I've still not been able to complete it. We also have a term test on the 7th and I have no idea how I'm going to pass because it's extremely difficult. This week we learnt some concepts such as bi-implication, transitivity and mixed quantifiers. We learnt the negation of bi-implications. I didn't really understand the concept of bi-implication actually. This week's class wasn't good for me since I hardly understood what we were being taught. After learning those 3 things we were finally done with the language of Mathematics. After all that we started proofs, so it's getting even more challenging. The professor told us a trick for proving and the trick is that we prove backwards. This is extremely helpful. Then we did a problem solving session, we had to fold the paper 4 times and then judge what the sequence of the ups and downs for the foldings would be. This session was fun, I was actually involved in the trying to figure it out. This was the only fun thing that happened in this week up till now since this has been a hectic week for me.