SLOG #9

This will be my last SLOG for the course. Although I was very afraid that I wasn't going to enjoy this course at the beginning, I can say that I have gained a lot of knowledge about a topic I was previous unfamiliar with. Danny did a great job teaching the material and Maria was thoroughly able to explain and clarify concepts during the tutorials. Overall, this course has been enjoyable. Lectures are officially over and now it's time to start preparing for exams. Good luck to everyone!

SLOG #8

Problem Solving Episode: Diagonals

Understanding the problem:
There is a rectangular grid with m rows and n columns. A diagonal line is drawn from the upper left corner to the lower right corner and it passes through certain number of grid squares. How many grid squares will the diagonal line cross through? This means to determine a formula for the number of squares using m and n.

Devise a plan:
Start small, and draw grids with different column lengths and rows to find a pattern between m and n, to figure out the number of diagonal squares by recording the number of squares the diagonal crossed through in a line. This was done by increasing the column lengths and rows by 1 and separating the odd, even, and mixed results.

Carry out the plan:
After drawing several grids, I was able to come up with the equation that the number of squares, x, is equal to the sum of the number of rows and the number of columns subtracted by the difference of the greatest common divisor of m and n. Algebraically, x = m + n - gcd(m,n). I determined this by observing the pattern for odd values of m and n, even values of m and n, and mixed values.
The calculations I used to determine the formula was:
d = m + n - s, where d was the missing difference.
Then I observed the values for d and realized that it was the gcd of m and n that resulted in the value of d.

Look back:
Although my plan wasn't the most efficient or organized, I was able to reach the final result after doing a few calculations using m and n.
 

SLOG #7

Unfortunately due to certain circumstances at home, I haven't been able to post as regularly as I'd like to. I have been reading other students' SLOGs and have come across some very interesting ones. I found the following blog very humorous but insightful at the same time: http://1d10terror.blogspot.ca/. I really enjoy how you can gain a sense of progress in the course through reading his SLOGs. As Michael said in his blog, I should have done the problem solving episode much earlier on, but I will complete it before the end of this week. Similarly, Assignment 3 isn't too challenging but manipulating the inequalities is what was taking a little bit of time. At first, using the proof of a limit that approaches zero was confusing me but gladly it was covered in the tutorial. Now I have completed the first four questions and the last one is the one that still confuses me, even after the quiz, which I know I did poorly on. I understand the structure and the proof by contradiction, but I'm still having a tough time coming up with the actual halt function itself. It seems to make sense when Maria explained it during the tutorial but when I attempt the problem myself, I can't seem to figure it out. I am going to review the tutorial exercises and the course notes until it becomes clearer. Another SLOG that interested me was the following: http://chargaslog.blogspot.ca/. It seems as if Charga and I tend to have the same problems in common, such as feeling off track, which is what makes it interesting to see that I am not the only one who feels this way.

SLOG #6

It turns out that I performed extremely well on the mid-term. It was reassuring that a lot of the questions resembled ones we had gone over previously with some minor differences. Also, I was able to score well on the quiz in last week's tutorial, so my results on both evaluations were definitely a confidence booster. The material for the big O is not overly complicated, but the proofs for upper and lower bounds are somewhat confusing because I'm not entirely sure how to prove it correctly since it appears that you can prove them in more than one way. Hopefully this will be clarified in next week's tutorial.

SLOG #5

I am beginning to understand the concept of proofs a lot more after completing the assignment. After looking at the assignment solutions, I was able to determine where exactly I went wrong so that I know not to repeat the same mistake on the midterm. However, the current material we are learning regarding worst-case complexity and O notation is confusing to me. In tutorial, we counted each step in a line of code, where as in the lectures, we counted each line as a single step of code. I found this really confusing at first but now that I am aware of the difference, it is slightly more clear. Hopefully reading over the course notes and lecture notes again will clear out some of these confusions. Currently, I am polishing my knowledge of proofs so that I can perform well on this mid-term.

SLOG #4

Despite the snow storm, the midterm for CSC165 did not go terribly, but it wasn't as well as I had expected. Although I felt confident on certain questions, my answers turned out to be incorrect. However, once I looked at the solutions, it made much more sense to me in terms of my misconceptions and where exactly I went wrong. This motivates me to work that much harder so that I am entirely clear on all the ideas that are being taught in this course.

SLOG #3

This week has been more challenging in comparison to the previous weeks of the course. Although I am finally beginning to understand how to translate logical symbols into sentences, I am having a difficult time translating a sentence in English to logical symbols. This is because I always feel like my translation is sufficient and then I discover that there is another part I am missing to make the translation complete, resulting in my answer being wrong. Although I felt confident about my tutorial quiz dealing with proofs, I am certainly nervous about the midterm which will encompass much harder types of proofs. Another thing I am struggling with is implications, in terms of deciding which statement implies which. On the assignment, I spent a lot of time trying to figure this out. I am aware that truth tables makes it somewhat easier to determine the implication but I am still having a tough time with it. My goal for the upcoming week is to keep attempting various types of questions until I am able to produce answers that are correct so that I am able to perform well on the midterm.