The End or Not The End

Week 12

Thursday

Well, I am glad but also sad that this semester is coming to the end. Why? I thought CSC165 was so hard and I was so afraid of it for a long time. But however, I found it very interesting, just like solving math problems. There were so much fun solving and proofing. Generally, I enjoy the time taking this course and I have learnt a lot from it.

Although I know I may not get a good grade for this course after all, I still love it and I would study hard for the final exam. The final exam is on the 25th, which allows me 8 days to study for it since the exam I have before CSC165 is on the 17th.

I would like to take this chance to thank my professor Mr. Heap, my tut TA Ekaterina, and all the TAs from CS Help Centre for helping me in this course. I mean really it helped me a lot when I got a question I couldn't solve. I also made several good friends here. And I would love to take more courses with you guys the future years.

Thanks again,

Thanks for reading and good luck all in the future!!!

Roland Qiyang Liu

Incoming Finals and Assignments

Week 11

Sunday

I was reviewing the previous tutorial problem sets, and I reversed one of them (assume - implement) and disproved the statement.

The original one is proof 5n^4 - 3n^2 + 1∈ O (6n^5 - 4n^3 + 2n)

Therefore, the reverse one is 6n^5 - 4n^3 + 2n ∈/ 5n^4 - 3n^2 + 1

To disproof the statement

∃ c' ∈ R, ∃ B ∈ N, ∀ n ∈ N, n >=  B => 6n^5 - 4n^3 + 2n =< c (5n^4 - 3n^2 + 1)

∀ c' ∈ R, ∀ B ∈ N, ∃ n ∈ N, n >=  B ^ 6n^5 - 4n^3 + 2n > c (5n^4 - 3n^2 + 1)

assume c' ∈ R
   assume B' ∈ N
       let n' = 6, then n ∈ N
       assume n >= B
          then 5n^4 - 3n^2 + 1 < 5n^4 + 1
                                            < 5n^4 + n^4
                                            =< 6n^4
                                            =< n^5
                                            =< 2n^5
                                            =< 6n^5 - 4n^5
                                            =< 6n^5 - 4n^3
                                            =< 6n^5 - 4n^3 + 2n
          then 6n^5 - 4n^3 + 2n > (5n^4 - 3n^2 + 1) 
       then ∃ n ∈ N, n >=  B ^ 6n^5 - 4n^3 + 2n > c (5n^4 - 3n^2 + 1)
   then ∀ B ∈ N, ∃ n ∈ N, n >=  B ^ 6n^5 - 4n^3 + 2n > c (5n^4 - 3n^2 + 1)
then ∀ c' ∈ R, ∀ B ∈ N, ∃ n ∈ N, n >=  B ^ 6n^5 - 4n^3 + 2n > c (5n^4 - 3n^2 + 1)          

So, there is less than a week left for all the lectures. I will sure work slight harder since it's almost the finals. Beside that, I still got the CSC165 assignment 3 due on next Wednesday, CSC148 project II due on Friday. Well, gotta continue get my hands working on them now. MARCH madness is not over yet!!!

Good luck everyone!

Thanks for reading!

Roland Qiyang Liu

The End of Midterms

Week 10

Wednesday

for last week's CSC165 lecture and tutorial,I did not really follow along well. I was still confused while I was trying to remember all the definitions a.nd rules. Substution is also a big part what I am trying to figure out because I was having a hard time to decide when to use a substation or just assume and assign numbers to unknown values.

I did actually pretty well on the second midterm. Although I haven't took my test paper back yet, I checked online and the result was I got perfect for the first one, lost one mark on the last one. Unfortunatly, I completly made a wrong decision on the second question. I knew to disprove the statement, but just like the first midterm, I once again failed on negation: I was not sure about if I should have changed 'equal' to 'not equal' in the implenment part. For that, although I proved part of the negated statement, I did not disprove all of the original statment. Therefore, I guess I need to find more pratices to fix this problem

Thanks for reading!

Roland Qiyang Liu

Double Trouble

Week 9

Sunday

For this week, we had the second 165 midterm test and I also had the 148 term test as well.

There is one question I wasn't sure if I i did correct or not.

For the last question, my solution is that

Assume x ∈ R

             then [x] is the largest integer =< x

             so [x] =< x

             since x + 7 > x + 6

             then [x] + 1 + 6 > x + 6

             then [x] + 1 > x

then ∀ x ∈ R, [x] + 7 > x + 6

I compared this to the sample solution and I found out that mine is really close to it, but not exactly the same. 

And I also saw the solution for question 1 which has the same idea with mine, just not the style. I bet I am gonna lose marks on that. This is really tough since there are so many places to just make a little mistake and lose marks for it.

Thanks you for reading!

Roland Qiyang Liu

Midterms Round 2

Week 8

Sunday

There will be two midterms for me next week: CSC165 and CSC148. And I was too busy to wrote any blog for the past two weeks due to the amount of assignments I had. But in this blog, I want to take chance to talk about Assignment 2 which I had last week.
Overall, the assignment was not that hard and it took me about 2.5 hours to finished it and checked for a second time. However, for question 5 in the assignment:

4. Prove or disprove: for all quadruples of positive real number w, x, y, z, if w / x < y / z, then:

( w / x < ( w + y ) / ( x + z ) ) ^ ( ( w + y ) / ( x + z ) < y / z )

A: Prove/ true

assume ∀ w, x, y, z ∈ R, w > 0, x > 0, y > 0, z > 0

and w / x < y / z

=> ( w / x < ( w + y ) / ( x + z ) ) ^ ( ( w + y ) / ( x + z ) < y / z )

assume ( w / x < ( w + y ) / ( x + z ) ) 

=> ( ( w / x ) * ( x ( x + z ) ) ) < ( ( w + y ) / ( x + z ) * ( x ( x + z ) )

then    = ( x + 2 ) w < x ( w + y )

             = x w + z w < x w + x y

             = z w < x y

             = z w / x < y

             = w / x < y / z

therefore, it is true

assume ( ( w + y ) / ( x + z ) < y / z )

=> ( ( w + y ) / ( x + z ) * z ( x + z ) ) < ( y / z * ( z ( x + z ) ) )

then    = ( w + y ) z < y ( x + z )

             = w z + z y < y x + z y

             = w z < y x

             = w / x < y /z

therefore, it is true

therefore, ∀ w, x, y, z ∈ R, w > 0, x > 0, y > 0, z > 0, w / x < y / z =>

                   ( w / x < ( w + y ) / ( x + z ) ) ^ ( ( w + y ) / ( x + z ) < y / z )

therefore, it is true

The above was my solution. I also checked the sample solution. But it is much different from mine: I separate the two parts and then solved each one of them. And it also seems that I have so much more steps than the sample solution because I thought just in case that I would lose marks for not having enough steps and explain my answer clearly.

Therefore, my question is that does my solution to the question look right? And I also have noticed that my writing style in the problem-solving is not exactly like the sample solutions nor notes, does it matter a whole lot and might causing me to lose marks in an exam?

Thank you very much for your time!

Roland Qiyang Liu

Crazy Busy

Week 4~5

Monday

It's been a long time from my last blog since I was having a super busy time for the past two weeks. I had my ECO midterm, both 148 and 165 midterms last week, plus I had a tons of readings for my Vic seminar. 

Because I'm taking 165 and 148 at the same time, I compare those two courses: 165 is more logic and 145 has more coding and details. Although I'm not doing so hot in 165(e.g. One of my answer for a question on the assignment is complete way different from the simple solution that is given; as well as I did in the midterm test, I didn't understand the simple solution about a question, but I think mine makes more senses; got a 0 from the second lab etc), I still prefer 165 because I found that solving problems in 165 is like figuring out puzzles, like a game. 

Well, it's almost the reading week. For me, I would most likely spend the time to catch up with 165 since I still have a lot of concepts I don't quite understand, and considering maybe how bad I did in the first term test, I'd better start studying ahead and preparing for the next one. 

Thanks for your time!

Roland Liu

Mixed It Up

Week 3

Saturday & Sunday, January 26th, 2013

This is the end of the third week and to be honest, the materials in CSC165 we are being taught and tested are getting slightly harder. For example, I spent three hours straight on thursday with my fully attention (no music, no snacks, no facebook) to focus on the first assignment. But unfortunately, till now, I am close but still haven't finish the entire work, and I am not sure for at least 1/3 of my answers are correct or not. Another example that makes me feel the course is getting tough is the tutorial set: I studied ahead before the tutorial to try the problem sets, but even with the explanations from our lovely & patient TA, I still couldn't understand some of the concepts. Well, I did actually find it interesting when I was trying to figure out and solve the problem in tutorial and on the assignment: those problem are like puzzles and once you've solved it, you feel like you've won a war or gonna get some sweet candies! So I guess I would spend more time if possible to review all my lecture notes and maybe I would also look for some problems from the internet or book to help. Who knows, maybe the weather here is a reason why my brain is not working well: the freezing weather in Toronto is getting pretty annoying, aw, how much I do miss you, Vancouver...

(ECO test next Monday, 165 & 148 afternoon tutorials on Tuesday, 165 assignment dues on Wed, 148 assignment dues on Friday.......)

Thanks for reading!

Roland Qiyang Liu