SLOG Week 11

So after 11 long weeks of SLOGing, I have finally finished learning all the concepts that this course has to offer. To be honest, I will really miss taking this course since it introduced me to many new ways of thinking which will help me out in the long run on my journey to get a specialist in computer science.

During this last week of classes, we wrapped up everything on computability and we were also introduced to the concept of induction. After listening to the lectures, my previous understanding of induction from MAT 137 was strengthened quite a bit however, the way to go about doing induction was slightly different. Instead of starting with a base case, we do the inductive hypothesis first and only after that do we prove the base cases which are the cases that are not covered by the inductive hypothesis.


As I was going through some other Slogs, I came across a slog that definitely helped me.

Through reading Abhinav's blog, it reminded me greatly about how complex proofs can be and how one simple step to make all calculations much easier. I will definitely keep this method of thinking with me as I go into my exam for this course.

http://ace165.blogspot.ca/2014/10/proof-can-be-tricky.html?showComment=1417660930106#c6828251752445604463

SLOG Week 10

Sort of late with this entry this week since I completely forgot about SLOG. I should probably manage my time better next time to get this in on time, although I think this is sort of the last SLOG seeing as how there is only like one week left of class.

This week we only had two classes due to reading week and so we didn't cover much. In these two lectures, we moved on from Big-Oh to halting and computability. Turns out it is impossible to determine whether a function halts or not using a halt function because it means it will half only if it doesn't halt which is a contradiction.

Also, something I found interesting was the problem that could not be solved for 70 years even by the professor. It showed that something that looked like it could be proved very easily actually turned out to be super complicated. Maybe one day I'll be able to solve it and become a millionaire.

SLOG Week 9

There's only about two weeks of classes left and I can't believe I've made it this far. This week has been less hectic for me since I finished all my tests and assignments and I even get some time to relax since we have no class Monday.

This week we learned about Big-Omega and Big-Theta. Big-Omega is roughly the same as Big-Oh except that its definition has the equality sign flipped at the end of the consequent whereas Big-Theta is basically when something is bounded both above and below by the same function. I found this weeks lecture to be easier since we didn't have to count any steps to prove any of the statements which is something I still need to work on. Also I particularly enjoyed proving general statements because the structure of the proof flowed very linearly (didn't require going backwards) and made a lot of sense logically.

On another note, I'm planning to start reading the other sections lecture slides in order to enhance my understanding of the material since they provide some different examples that I could try out and then check whether I'm right or wrong.


I especially liked Albert's blog which showed that there are people who struggle with proofs like me and despite that, can still keep a very positive attitude as demonstrated by his very interesting blogs.
http://99bugsbutaglitchaintone.blogspot.ca/2014/11/week-9-more-on-big-oh.html?showComment=1417660757626#c5659481090157877391

SLOG Week 8

This week we had our second term test. Oh how gruesome it was :(. I discovered that I write way too slowly with a pen since I try not to make any mistakes as pens aren't erasable. I ended up probably spending 3/4 of the test writing while only using the rest of the time to think about how to do the questions. Hopefully I won't do this again on the exam since that would be pretty brutal on my mark. Also this week I found out a neat trick about proof structures that was pretty obvious but I somehow ended up missing it; that is you don't have to write out the entire statement at the end as you can just use some sort of indication to show that it follows from the rest of the statements.

We also continued with Big-Oh this week. I'm having a hard time coming up with the equations through counting steps despite having programming experience and I'm trying to resolve this issue by constantly reviewing the notes everyday. However, when they give me the polynomial to work with, I'm having little to no trouble which I suppose is a good thing. Hopefully I'll have everything cleared up before our third and final test.

SLOG Week 7

Through each topic we cover, I initially find it extremely challenging and then by the end, I find that it becomes second nature to me. With the introduction of big-Oh  and bounds however, I'm a bit sceptical that this pattern will continue. The amount of thought needed to be put into the proof of different cases is just mind blowing and I don't see how I'll ever get used to it.

On another note, I've just finished assignment 2 and found that I learned quite a bit more about how to conduct proofs, such as indentation and how linear proofs are. However, this wasn't without cost as I just spent literally 18 hours without sleep trying to figure out what value to take for an existential proof.


After reading Quinn's slog, I feel more comfortable that other people are in the same situation as me for counting steps in order to successfully do big-Oh proofs. I will indeed do my very best in order to make sure that I fully understand this concept by the time of exams through studying and practising many problems everyday.
http://quinn165.blogspot.ca/2014/10/week-7.html?showComment=1417661682781#c8808796752548769768