LAST sLOG ENTRY

...And time's up! 12 weeks of the year down and I've gone through a lot of new experiences this semester, especially in this course. This course was way more abstract than I anticipated. I assumed that this course would be another computational math course, but I was very off. On the other hand, the course has helped me develop my creative thinking and logical reasoning skills

Now, I haven't been on here for a while and a lot of things were covered. The last thing I talked about was covering Big-O and Big-Omega, and the final assignment. For the last two weeks, we covered more Big-O and Big-Omega proofs with limit techniques, which I was really excited about because I am confident with doing limits, and Big-O and Big-Omega of general statements, which was easy as well. After discussing Big-O and Big-Omega, we were introduced to the halting problem. This topic was a very interesting topic. The fact that NO ONE can determine an algorithm to predict that a function will halt is crazy. In conjunction with the halting problem, we learned about reduction and proving a function is not computable. This type of proof was confusing at first since my Python skills are not that advanced. Danny used methods like "hash", which I am not sure what it means, but by the end of it, I understood that he was showing that this function was non-computable. Lastly, we talked about countability, diagonalization, and induction. To be honest, I sort of dozed off during this section, so I am not entirely sure what it is about - I've been loaded with assignments and test for the past couple of weeks. If you wish to know about these last topics, I recommend visiting Celina's posts (http://celinasopiniononcsc165.blogspot.ca/). So that ends all the material needed to be covered in this course!

For anyone taking CSC165 and reading this sLOG, I recommend reading Albert's last post (http://99bugsbutaglitchaintone.blogspot.ca/) as it will prepare you for the course. I would just like to add to his list some things to keep in mind which I gathered from my mistakes and experiences:

- Be on top of the material, Make sure you understand what is being done because there is a lot of abstract math involved in this course.
- If you do not understand something, either a step that was done on a question or an entire chapter, go to office hours - not just for assignments.
- Finally, do not fall asleep during lecture - and this goes for all courses. You will miss key concepts that will come up on your assignments and tests.

In the end, this course was really challenging, but interesting, I highly recommend it for people who like problem-solving and/or like puzzles and riddles as this course will really develop your thinking skills. now all that is left is the final exam. May the odds be ever in our favour!


Commented on:
http://99bugsbutaglitchaintone.blogspot.ca/

PROBLEM SOLVING: FOLDING

Folding Problem: If you fold a strip of paper, by folding the left side on top of the right, over and over again, can you predict the up/down creases after each fold?

Understand the Problem:
- After each fold, there will be a crease that will either point up or down after unfolding the strip.
- The number of creases increase after each fold.

Devise a Plan:
- Fold a strip of paper 4 times while recording the up/down sequence after each fold.

Carry Out the Plan:

Number of Folds (n)	Up/Down Sequence (U = up, D = down)
1	D
2	UDD
3	UUDDUDD
4	UUDUUDDDUUDDUDD

Look Back:

- At first, I found that the number of creases for the successive fold would be ((2^n - 2^(n-1)) + the number of creases previously)

- Then I noticed that this equation related to the sequence: the sequence of one fold was always at the end of the next fold

- To get the overall sequence, however, I noticed that if you started from the left of the sequence with a U, then alternate D/U in between each crease of the original sequence, you would get the next sequence

- e.g. (Bold = crease from original sequence)

         Fold 1 = D = D

         Fold 2 = U + D + D = UDD

         Fold 3 = U + U + D + D + U + D + D = UUDDUDD

Acknowledging Conflicts:

- When trying to find a pattern after each fold, my expectations were always crushed. After 2 folds, I thought a pattern would have been established (ie UDDUDD after 3 folds)

- After I found the equation for the number of creases and realizing the ends of each sequence, I thought I would be able to find the entire sequence, but I only got the last sections

- I knew that there was a pattern involved, so I assumed that if I found an equation, I would be able to guess the next sequence. So, I spent the majority of the time trying to find an equation when I realized that equations only apply to numerical patterns, not directions.

        

WEEK 10

Nearing the end of the semester, things are getting a bit hectic. Assignments are piling up in addition with all the studying we have to do for our other courses. As a result, I haven't been able to focus on this course as much as I hoped. Regarding the material, however, I feel like I am starting to understand Big-O and Big-Omega. The proofs we worked on in class seem to be getting simpler, but I will probably still need a lot of practice. We also got our test results back and I was extremely disappointed when I saw my mark. I truly thought that I did well on this test. I have yet to pick up my test to see what went wrong, but I intend to look at it very, very carefully to ensure I won't make those mistakes again on the final exam. Lastly, we are expected to get our third and final assignment in this course. I intend to get all my assignments for my other courses done and to strictly concentrate on this final assignment. I probably will not be on here for the next week due to studying, but I hope to make time for my final post. Until then, wish me luck! (Like, a lot of luck)

WEEK 9

9 down, 3 to go. Not only this course, but the entire semester has been moving by so quickly. This week felt pretty quick as well. We had our second Term Test and overall, it was straightforward. I feel like I did better on this test than I did the previous test. I had trouble proving the second claim. It involved using the definition of the floor of a function and disproving a conjunction. I knew that when disproving a claim, you have to negate it. Since it was a conjunction, De Morgan's Law had to be used, which resulted in a disjunction. With disjunctions, proof by cases had to be used. This was all I was able to come up with, so I was only able to write the structure. I'm hoping that I get a better mark than last time.

This week was also the due date for our second assignment. I felt fairly confident handing in the assignment, but when the solutions were posted, I realized that I had proved 2 false statements and falsified 1 statement. I'm truly hoping that I get part marks for my reasoning. As for the material covered, we just covered more Big O functions. I am getting a little more comfortable with Big O and Big Omega, but like proofs, I still need more practice. I think like all the material covered so far, the assignment will provide me with some clarification on certain aspects. Wish me luck for the next 3 weeks!

WEEK 8

With midterm week over, I was able to catch up on my sleep and actually stayed up during my lecture. This week, we covered the amount of time / number of steps taken for linear search and insertion sort, and the worst case scenarios of insertion sort - both upper and lower bound. Counting the number of steps for linear search was simple. When it came to looking at the upper and lower bound of insertion sort, things became much more confusing. However, as we went through it, the steps of proving each bound made sense. I realized that all of the steps would require creative and logical thinking, which I lack. Overall, the material was reasonable but I will need to look at it quite often.

In addition to this week's lecture, I have been working on the assignment. This assignment was a bit more challenging than the first, but it provided me with a lot of practice with proofs. Some of the claims, particularly Claim 1.2 and 1.3, were difficult to prove. These claims involved the formal definition of a limit. I'm not in MAT137 so I'm not that familiar with it. However, with the help of Prof. Heap and Prof. Zhang, I was able to prove each claim - at least I think I did. Hopefully I will do well on this assignment.

WEEK 6

(Apparently I forgot to publish this post.....so here it is! LOL)

Like I said last week, this week went by quickly. There was no lecture on Monday due to Thanksgiving, so we only had two lectures this week. This week we proved more expressions. The expression we're proving in lecture seem fairly simple to understand, but then again, I'm going to need more practice with proofs for the next test. We also got our tests results. To be honest, I thought I could have done way better. I made a lot of small and stupid mistakes that could have been caught if I looked it over more carefully. All of these mistakes added up and caused for my low grade. Next test, I am going to study even more and to look over my answers much more carefully. I am hoping that for the next test, I will do much better.

WEEK 7

To be honest, there were times during lecture where I have fell asleep because of all the work I have done. I've had two midterms this week and I have been working on multiple assignments simultaneously. As a result, my focus on this week's material has been on and off, so I am not entirely sure on what we covered.It appears, however, that we've begun to look a sorting. I have some background with sorting algorithms from high school, but then again, my knowledge in Computer Science from high school is extremely basic. To fully understand what we did, I visited http://firstweekoflogic.blogspot.ca/2014/12/week-7.html and from the looks of their post, I seem to understand it, which is a good sign!

We also got our second assignment this week. I looked over it as well. There are only two parts to it but there is some substantial work that has to be done and a great emphasis on logical reasoning. This assignment will be difficult and time consuming. However, I think that I will be able to complete all the questions and it will provide some practice for me. With all my midterms done, I plan to catch up on all the sleep that I have missed and to get my mind back into this course.