WEEK 11&12
Since brief fall break in week
11, therefore, we did not have lecture last week, which gave me a period of
time to recall and to summary what we have learnt before.
What I Learnt
This week we mainly covered
computability, countablility and induction.
Computability
Computability
problem was the most difficult part I felt in CSC165. In order to overcome it,
I went to both Denny and Larry’s lectures about this part. I have to say,
different ways in teaching this part really inspired me a lot. After class, I
reviewed the slides and added the notes I wrote myself. In addition, I also
communicated with classmates about how they understood computability and saw
their slogs on the website. I found the course notes that Yahui Liu posted is
really a helpful supplement to the slides and also improved my understanding to
this part. (http://yahuiliuslog165.blogspot.ca/2014/11/week-11.html).
Summery:
We use reduction to decide whether it is computable or not
f reduces to g
g computable implies f computable
f non-computable implies g non-computable
a)
Want to prove a function computable: show this
function reduces to a function g that is computable.
b)
Want to prove a function non-computable: show
that a non-computable function f reduces this function.
This is a typical example:
Interesting Part: Countablility and Induction
I was so surprised that there were
so many parts overlapped with other math courses. In countablility, the
definitions of 1-1 and onto I have learnt in MAT223. Besides, the proof
technique--induction was also an important content in MAT137. I felt happy and interesting
because all the knowledge is relevant and interact each other.
Achievement about Assignment 2
I was so exciting
because I got 100 in A2, which was unbelievable. It was my first full mark and
would be a milestone in my campus life. My effort was rewarded, which, in a
large extent, encouraged me to do better in the final exam and further study.
