Assignment 2

With Assignment 2 being due this Friday, I had the goal of finishing it this weekend. Unfortunately, this does not look like it’s going to end up happening. I did however spend a lot of time this weekend looking over the lecture slides from the past few weeks (ever since we started the topic of time complexity).  Even though I was mentioning last week that the tutorials and lectures have been very helpful and that I understand the topic much more, I still did not get much of a chance during the week to practice. On Saturday, I sat down and started working through the problems for Assignment 2. For the second question, since it’s similar to questions we have done in class and tutorial, I forced myself to not look at those examples and try it out on my own. Once I did, I looked at the examples and noticed that for the most part, I was on the right track. This is a huge improvement from last week were I didn’t have even the slightest idea of how to do any problems of this type. Question one was where the problems arose. To figure out a recursive definition, I decided to just start listing all of the odd maximal contiguous ones free strings in the set of binary strings of various lengths. Then I started looking to see what happens as the length increases to see if I could find a pattern. I came up with a formula but I have no idea how to get to a closed form. For the most part though, the weekend was quite productive. Getting more practice doing problems has definitely been a big help.

Lecture and Tutorial

Hey!

So, with three midterms last week, I was really worried about the tutorial quiz for this class. I didn’t have much time to look over the slides from last week’s lecture and did not understand how to do the tutorial problems. On Thursday, before class, I went in not understanding anything and was very stressed out. Fortunately, I found both the lecture and tutorial to be very informative. In fact, I found that after, I felt a lot more comfortable with the topic of time complexity. I think I simply need more practice. After tutorial, I understood how to do all three questions on the tutorial handout and therefore understood how to do the question on the tutorial quiz. Looking at Assignment 2, I feel like I now have a general idea of what I need to do. Unlike with Assignment 1, I plan to give myself plenty of time before the due date to start and work through each question.

I hope everyone had a great week!

First Test and the Coming Week.

Hi again!

I am so stressed right now! I have three midterms this coming week and I feel like I am not prepared for any of them. Also, it seems like the more I study, the more stressed I become. On the plus side, I felt that the midterm for this class went well. I thought the difficulty and length were just right and I was able to finish all three questions with enough time left over to check my solutions. Before the test, I was having a lot of trouble with the well-ordering principle, which was worrying me. After looking online and doing some extra reading, I discovered how it was related to mathematical induction and complete induction and things became much clearer. Looking back at all the proofs we had done in class, I was able to see how what we have proved using mathematical or complete induction, could also be proved using the principle of well-ordering. Now, I am looking forward to our next topic of time complexity.

Anyway, I hope everyone is having a good weekend. I cannot wait until the next one when I will be done with tests for a while. 

Favourite Proof and First Test

Hi everyone!

I am really excited to be posting my very first blog! I hope everyone has been having a good Thanksgiving long weekend. Mine so far has been fairly uneventful. I have however, now that Assignment 1 is done, started to study for our first test. Looking back at the past lecture slides, I came across a proof that I really enjoyed. Although we did not finish it in class, I had a fun time struggling to come up with a solution. Which one? It was the chocolate bar proof where you had to determine how many breaks any m x n chocolate bar can be broken up with. I think one of the reasons I particularly enjoyed this proof is that before, I didn’t quite understand complete induction. Working through the problem showed me how useful complete induction really was. Also, I found it quite interesting that no matter how you broke up the chocolate bar, it would always require the same amount of breaks.

Anyway, now that I have gotten a better grasp of complete induction (hopefully), I have moved on to another concept I can’t quite understand: the principle of well-ordering. I have been looking online to see how well-ordering and mathematical induction imply one another but have so far not gained much more insight. Hopefully by Thursday things will all be clear!