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.