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! :)

What was challenging for me this week?

1)    I was having problems how to translate an english statement to symbolic language? Especially, the first question from this week’s tutorial assignment was pretty challenging for me. I felt like we did not learn how to solve this kind of problems in the lecture since this week we learned about only different laws, scoping, negation and conjunction. I felt very frustrated. I really wished we did some example questions similar to the one in the tutorial assignment during the class! 

      First I tried to use [intersection, empty set, union] and wrote a statement. However, when I checked the Larry Zhang’s slides [I go to Danny’s session, not Zhang’s but wanted to see what he was doing, I thought it might help my understanding and actually which did! yay! :)] 
I noticed that conjunctions V and ^  are used for predicates and ∩ , ∪ are used for sets. This small detail helped me a lot to clarify my understanding of the topic and see why I cannot find the solution. 

2)    2b on the tutorial assignment was challenging for me.

Steps I took: 

     i) I went over the lecture notes again and read the course reading [in which I came to learn that question 2a and 2d are True since they are part of the quantifier distributor law]. However, they didn’t help me much with the b.

     ii) Drew Venn diagram to find the solution. 

Venn diagram helped me to find the solution!

             2b:      ∃x ∊ D, P(x) ∧ Q(x) <=> (∃x ∊ D, P(x)) ∧ (∃x ∊ D, Q(x)) 

                                                              So it’s False!

Problem: as an international student, who are taught math in German, sometimes understanding the English math terms could be challenging, especially when prof is speaking very fast in the class and you cannot write down the word since you don’t know how to spell them. 

Solution: However, last week and this week every day after my class, i went over my lecture slides and make sure I understood every single word on it. Plus the course reading was a great help to me. I found the math terminology [exp: universe, intersection etc] on the course reading and now the course material is more clear to me.

Problem: implications! in the class Danny gave this following example: “if you eat your vegetables, you will get desert” and added that the only and only way this implication is wrong is the time when I eat my vegetables but do not get dessert. Although this makes sense, I was pretty confused why this following statement is not false: I get my desert although i didn’t eat my vegetables. if P is wrong and Q is true then this statement is correct, said Danny. However, i still cannot understand why until I read my course reading. Now I realized that an implication is a one way statement. P => Q. if I eat my vegetables, I get desert. This is the only condition I should focus on the implication. This implication is only correct from left to right, doesn’t work from right to left [one way only]. Saying I got desert although i didn’t have vegetables is not a counter argument for our implication.  this is a different scenario/ statement,  it’s not what we are talking about!

what material challenged me this week?

- translating the problem from a sentence to a venn diagram. I learned about venn diagram when I was at middle school. So first, I had to refresh my memory. Secondly, I needed to practice more. When I read a sentence I can write it done by using symbols. However, it is still challenging for me to draw a diagram and indicate which part of it is empty and which part is full with elements from that set.