Week 12 : Tackling Assignment 3 + More about computability

In the end of the semester, this assignment helps me to summarize the concepts of how to apply limit techniques and familiar about asymptotic proofs. This is the first time I found that Piazza so helpful, since people always ask the questions about something I'm confused as well. I like the atmosphere of discussing same topic through computers.:)
Anyways, I feel I know better about limits technique during proving, rather than just memorize the definitions and try to squeeze them out. Well, the metaphor is bizarre but you know what I mean...Now I'm more familiar with the usage, or the whole idea of proving a big-Oh, a big-Omega and a big-Theta. However, I'm still little confused about halting problems. While doing the assignment, I did not understand how reductions help prove whether a function is un-computable or not. Luckily, there was some guy sharing his confusion about halting problems on Piazza. The part of Larry's answer helped:

These sentences really helped to clarify my thoughts.:) Now I feel that my thoughts become more "logical" while proving.

This final week we only introduced two new concepts: countability and induction. Since I took linear algebra last semester, the concepts of mapping, one-to-one and onto are no strangers to me.

Here is an example of proving |X|=|Y| where X={natural numbers}and Y={even natural numbers}.
The key of tacking that would be showing f is well-defined, 1-1, onto step by step.
(Remember to check indention)


However, the Truth-Table of showing fx() cannot be programmed confused me a great deal.I'm plannig to go to the office hour.


Also, I learnt induction while doing math proofs on Calculus class. The main structure is to first assume a base case and then start the inductive steps(n => n+1).

Additionally, I really appreciate "Review for final" part Larry summarized for us.It tells us that which parts of course materials are more likely to be tested, like a list high-lighting all the important concepts of the course.

Last, I thanked Yahui and Timothy by commenting on their last post. http://timothylock.me/sLOG/2014/11/30/week-11-halting/#comment-8

http://yahuiliuslog165.blogspot.ca/2014/12/week-12.html?showComment=1417621909149#c5547709964358051958

While browsing their Week 12 slogs, I found there were other students commenting "Thanks" as well, so my sense of picking slogs is seemingly pretty good~

Well, finally the semester ended. I would say I really enjoyed this course and loved the creative teaching style of my instructor, Prof Larry Zhang. Definitely, I would recommend csc165 to my friends. Now it's time to say: good luck to the final!