Week 5

This week I want to share one of the biggest challenges slash disappointments about UofT [also csc165] in general. I have been keeping up with the course material since the very first week, didn't miss any class, review the material frequently and I spent two full weeks [every day more than 4 hours] to work on my first assignment. By the time I have to do my midterm, I was just too tired and confused [because the longer i think about csc165 material, questions, assignment etc, the more I reach at the point the only thing i know is i don't know anything] and although the midterm was fairly easy, very similar to assignment and previous midterms I got super confused and did very well.. so this is a big challenge for me at UofT in general.. it's really disappointing to get a bad mark after you put so much afford in something.. I guess, I have to teach myself somehow not to be disappointed and keep working more and more..

Anyway.. this week I'd like to blog about question 3 [from the midterm] and question 4 [from the assignment.] This is a funny story!

this was the question:

Although I made it correct on the assignment(!), I got very confused during the midterm [ I guess, time pressure and stress] and answered that S3 is equal to S4 and this question is not solvable! LOL! After I left the midterm I suddenly  realize how to solve it.
So now I'll walk you over how I found the solution:
Assume all x belongs to D
    Then if x is P, then Q must be true   #S3 is true
    Then P and Q intersection must be empty #S4 is false
Then P(x) and Q (x) intersection must be {}

Because if there does not exist any element in P and Q interaction , S4 is false, however, S3 becomes vacuously true!

Folding!

The reason I chose to folding problem to talk about my blog is this was the very first time I 'applied' my learnings about how to solve a problem step by step and it worked! this is a very hard problem and i was able to solve it at the end of the class!
for those of you who doesn't know what's this folding problem is:
 Take a strip of paper and stretch it so that you have one end between your left thumb and index finger and the other between your right thumb and forefinger. Fold the strip so that the left end is on top of the right end. Repeat this several times, each time folding so that the left end is on top if the right end of strip. 

Steps I took to solve this problem:

1) understand the problem [read through many times and say it with my words]

2) devise a plan :

   a) take a piece of paper and fold it as many time as you can [ I was able to fold it max 5 times]

   b) try to find a patter with [after folding it several time, I decided to make a table and write the number of times the fold is toward upward and downwards] => this step was crucial to solve this problem!!

   c) make a table : numbers & patter:

1) D

2)UDU

3)UUDUDD

4)UUDUUDDDUUDDUDD

so after this step I realized this:

                    D
                 UDU
              UUDUDD
UUDUUDDDUUDDUDD

I realized there is always a D in the middle
and it looks like a mirror, the Ds in the middle are reflecting the right hand side to the left. It's like I am taking the whole string and adding it to the right hand side of D in a new string, then negating this same string and adding on the left side of D:
 exp:
                  D
                 UDU
              UUDUDD
UUDUUDDDUUDDUDD

next step is going to be: UUDUUDDDUUDDUDD will be added to the right of D [in the middle]:

                    D
                 UDU
              UUDUDD
UUDUUDDDUUDDUDD
                    DUUDUUDDDUUDDUDD

and now I will right the exact opposite of UUDUUDDDUUDDUDD and at it to the left side of D:

                                        D
                                      UDU
                                   UUDUDD
                       UUDUUDDDUUDDUDD
UUDUUDDUUUDDUDDDUUDUUDDDUUDDUDD


ta-taaaaaa! :)