Virtual Week: Endgame

Virtual Week signifies the end of our semester. This semester has been quite the learning experience. First, I would like to thank Danny. You are an amazing professor; one of the best I've had yet! Listening to you in lecture made concepts clear and really understandable. I think the greatest characteristic you possess is that you know what it is like to be a student. You try to help us do well in this course, with your very helpful and ever-shifting grading scheme. I think your generosity will help out a lot of students when it comes to their final marks.

I think doing well in this course requires us to build a strong foundation out of the fundamentals in this course. I wish I had discovered this earlier in the term. I'm sure reading the course notes on a regular basis would have given me a great deal of help. By having the fundamentals in check, I'm sure any problem is not too far a stretch for our minds.

Looking back on this SLOG, I realize I actually really like the concept. Believe it or not, I actually enjoyed Slogging every week; I didn't see it as a nuisance or a chore. Doing my SLOG on a weekly basis helped me express my emotions, from venting out my frustrations to celebrating on seemingly small achievements. Even if nobody from our course was reading, the facade of having someone out there to talk to was comforting, After reading several other SLOGs by different student, I realized that I wasn't alone in many cases.

Throughout the course, I have made great strides as a student. As some earlier readers may notice, I overcame my self-diagnosed chronic-procrastination with hard work and determination. After thinking of every course as a hurdle towards a degree, I took viewed every course as an obstacle. I wouldn't spend anytime trying to "stop and smell the roses" so to speak. However, looking back at the subject of Formal Languages and DFSAs, I actually enjoyed what we learned. I actually took what we learning as a way to be enlightened. I actually took the time to "stop and smell the roses". The sense of euphoria, which I had temporarily lost, has started to come back slowly. I am no longer a drone programmed to complete my task.

I feel confident going into examinations. I will pass this course and take my experiences with me. Hopefully I will take the optimism I gained from the last few weeks in this course, and apply to everything I do in my university career from now on. Devoting time to do more readings and finding ways to expand my thinking, will help me greatly in the near future.

Slogging has given me the impression of writing an open diary; I am able to express my emotions, as well as recapping the week that was in the course. At the same time, it was able to give me a window to my previous mindsets and goals. I am able to look back in this magical mirror, known as my SLOG, and see how I was before. I'm glad that I kept with Slogging and I think it is a really great idea. This is the last SLOG entry I will do, and surely I will miss Slogging. So for the last time everyone good luck with your exams and future endeavors, and wish me good luck as well!

Problem Solving Tutorial: Space Slicing

Problem:

I can divide a sheet of paper into two regions with a single straight line. With two straight lines, I can divide a sheet into four regions, and with three straight lines I can divide it into seven regions.

If n is some positive whole number, what is the maximum number of regions I can divide a sheet of paper into with n straight lines?

So, first I'll write down the information that is given and denote the number of cuts by the letter n:

Number of cuts (n): 1
Number of sections : 2

Number of cuts (n): 2
Number of sections: 4

Number of cuts (n): 3
Number of sections: 7

I started of looking for a pattern and I quickly realized there was a potential pattern when looking at the number of sections created. If you look at the number of sections created, it increases from 2 to 4 to 7 sections. When the number of cuts is equal to 2 there are 4 sections, which is 2 more sections than there was only 1 cut. Similarly, when the number of cuts is equal to 3 there are 4 sections, which is 3 more than there was only 2 cuts.

So,

(n = 2) - (n = 1)
= 4 sections - 2 sections
= 2 sections

(n = 3) - (n = 2)
= 7 sections - 4 sections
= 3 sections

As you can see, the difference in the number of sections increased by 1 (from 2 sections to 3 sections in difference).

So following this potential pattern I would get:

(n = 4) - (n = 3) = 4 sections
(n=4) - (7 sections) = 4 sections
(n=4) = 4 sections + 7 sections
(n = 4) = 11 sections

By isolating for when there are n= 4 cuts, we see that there should be 11 sections. We can confirm this pattern by visually seeing the number of cuts and the number of sections which result.

 Since the result when the number of cuts is either 1 or 2 is obvious, I'll skip to when there are three cuts and four cuts. This will be really helpful in visualizing what we are working with.

When n = 3, number of sections = 7 :

 When n = 4, number of sections = 11 :

So now it is safe to say that what I identified earlier is indeed a pattern. The updated information is now:

Number of cuts (n): 1
Number of sections : 2

Number of cuts (n): 2
Number of sections: 4

Number of cuts (n): 3
Number of sections: 7

Number of cuts (n): 4
Number of sections: 11

This problem deals with recursion. We can say that:

T(n) = { 2                          , if n = 1
           { T(n-1) + n            , if n > 1

You need to unwind this formula:
T(n) = T(n-1) + n

After unwinding, you can find the closed-form for it.  Using the "golden ratio" where α = (1 + √5)/2 and β = (1 - √5)/2 . You can prove that the closed for holds for when n = 1, and for where n > 1. By doing so you are able to prove the recurrence and therefore solve the problem I am unable to unwind the recurrence, so it seems that I am stuck here.

Week Twelve: Circles, Arrows and Assignment Three

So this week we continued our journey through the extravagant journey of dealing with DFSAs and Languages. This stuff really never ceases to amuse me. As I said before, this topic is definitely one of my favourites in the whole course. I think I really like the logic of how everything works together. Although we did work with a Regular Expression for one DFSA that turned out to be horrendous to write down. Danny even stating that the Regular Expression would probably not even fit on his slide! Hopefully there will be a question on DFSAs on the final and hopefully I can eat it right up! The morning section still has one tutorial left and we are pretty much done the course! Like the cliche says, time really does fly. I will probably make a summary SLOG entry before the deadline to share my overall experiences with this course, as well as my farewell to my SLOG. However, before I get carried away I still have to complete a problem solving tutorial to do! So look forward to at least two more SLOG entries before the deadline.

Assignment Three was due not to long ago. I seem to be on Pacific Standard Time, so do not get confused with this being posted before the midnight deadline! Anyways, there were four questions to be completed, just like for Assignment One. There were some DFSA and Regular Expression questions, which I was able to complete to some extent. If I were to say I had trouble in something, it would probably be the overall structure of the proof. I am not sure if what I did was suffice, but I did what I could. I`ll have to look over the course notes and annotated slides to get a better idea of that. The correctness proofs caught me off-guard. It felt like forever since we have done those, even though in reality it has only a couple of weeks. My excitement for the latest section made me forget that we did these types of proofs. I will admit to being rusty in the section, but I was able to persevere. This was in large part to our fabulous TA Lila. I probably would not have completed the assignment to such an extent without her help. She was amazing! Four hours of students asking questions and she handled with such ease! If you are reading this Lila, I just have to say thank you! I am not sure how well I will be graded on the assignment. Only time will tell if I put enough detail into my work.

As I said earlier in this post. I will most likely have two more SLOG entries before December 5th, so look forward to that. As always everyone, have an awesome day!
 

Week Eleven: Creating Machines and Languages

When I heard that we were creating machines to except languages we made, I had a totally different picture in my mind. This was probably the result of watching far too many Saturday morning cartoons when I was younger! I like this topic a lot more than what we have been doing recently. For me, this topic is one of the most interesting topics in this entire course. I am very intrigued by the concept as a whole. The concept seems refreshing from all the work we've done with induction in this course. Even if there is induction to follow with this topic, I don't mind at all. I don't know why, but I feel as though this concept is easier to grasp, as well as more concrete. Some of the more mathematical and abstract ideas in the course required a lot of intuition to do. However, the concept with machines, and their accepting and non-accepting states, seems to allow me to visualize on what the problem is and what destination we need to reach to solve the problem.

Some of the regular expressions are review from what we've been doing in CSC207, while some of them are not. Although, I think we will be exploring deeper into the area of regular expressions in this course. I am still a bit shaky on the concept of some expressions like concatenations and what they exactly mean. I think the wording on what concatenation means has to be drilled into my head. For example, when Danny explains what it means in non-technical English terms, the concepts seem to flow better. For now I will read the course notes to get a better grasp on this whole new concept and prepare for the quiz accordingly. I'm really looking forward to the last few weeks of this course! Good luck to everyone in their adventures in this course and wish me luck!

Week Ten: Chapter Seven and Formal Languages

A shortened week didn't deter learning this week. The contents of this week are kind of confusing; which seems like a bad trend for me lately. I just haven't had the time to focus fully on this course. I wasn't able to go to class on Wednesday, so today's work was somewhat hard to digest. There isn't much for me to comment on this week. As per usual, I will try my hardest to do the tutorial problems for this week and reread what I missed in the annotated notes.

We got our tests back today and I wasn't surprised with my mark, or how poorly our class did in comparison to the night class. Apparently our marks will get bumped up by 3.5 marks; which is very generous of our professor! That is nearly a 20% bump, which pushed me up enough to pass the second test! It is time for me to celebrate this achievement by ending my SLOG entry early this week. So a shortened week has resulted in a shortened SLOG entry for this week. All the best!

Week Nine: Correctness and a Break

After the second test, I was hoping we would start onto a new topic. However, it seems as if we are still in chapter two for a while! More correctness showed up on our Wednesday and Friday lectures, and to be honest, it seems a little dry. Trying to prove whether an algorithm is correct may be important, but it really doesn't do it for me. This is something I have to get used to, since it will be on the final exam! The concepts seem pretty straight forward with, very little few twists and turns. I think with more exposure to the topic, I will be able to grasp the concepts in no time! There are a few bumps along this road of algorithmic correctness, but with the "study long-weekend" around the corner, I hope to get some CSC236 done.

Speaking of the study break, I think it is a great chance to catch my breath! I will be able to get some studying for all the courses I am taking. The one negative I see about this break is that we are going to miss a tutorial, yet again. We haven't had a tutorial dealing with algorithmic correctness yet, and I was hoping to get some more practice in it. The night section still has the tutorial, so I will attempt to do the tutorial exercise which is meant for them. I also think that the Wednesday, after the break, would have been a much more suitable time for our second test. It would have mimicked the same format as the first test (which followed the Thanksgiving weekend). This way we would have been able to salvage one tutorial and there would be less people complaining about the "advantage" the night class had. Regardless, not everything can be planned as I said; only Danny knows the difficulty of setting-up material to be covered for the test. All in all, I enjoy the break and hopefully I manage to make some progress on algorithmic correctness at home. Everyone enjoy your break and wish me luck!

Test Two: A Disaster and a Half

So, I wrote the second term test on Monday and it was an utter disaster; it was horrific! I had thought that it would be prepared for the task, but clearly I wasn't prepared at all; I undoubtedly failed. I will limit the specifics, because there is still the night section that needs to write the test. I should start of by saying I really messed up on unwinding! There was a similar example done in class, but I choked under pressure. I was able to muster-up some what of an outline through my incomplete unwinding; I don't expect many marks from that question. The rest of the test, I had no idea how to do. I don't think there were examples like that done before, but I can be wrong. I had no idea how to approach it or even set up a base case for it! I had to settle for an "I don't know how to answer this question", because it was truly that; I had no idea where to start! I think this test required us to have a better handle on the fundamentals rather than depending on specifics to appear on this test; that is where I probably went wrong in my studying. This can be contributed to comparing to the first test, where all the questions were complete in class one way or another. I do also have specific issues about this test.

One gripe I have with this test, is the morning class had to write it on the Monday, while the evening class gets to write the test four nights later! If people from the morning section were to inform the evening section about the type of questions, or even the difficulty of the test, the evening section will be much more prepared to write the test. I understand there are limitations on the tutorial times, but I still think it could have been better carried out. Also, I did not like the time constraint the assignment had on us preparing for the test. We did have the weekend, but we also have four other courses to manage as well. If I were to solely take this class, I would have done fine with studying through the weekend, but sadly that is not the case. Another issue I had with the test was the upload of the past term test. Helpful or not, I was hoping the past test would be uploaded BEFORE the day of the test. It would have given us a better idea of how the test would have been. My final issue with test would be the questions. I wish the questions could have been shorter and maybe one or more questions on the test. Why? Well, there were a lot of topics covered up to this midterm. I spent a lot of time trying to grasp all the other concepts we had covered, but on the test we had a very limited range of questions asked to us. Either that should have been the case, or maybe Danny should have told us specific areas to cover. Since Danny told us that all of chapter three and a bit of chapter two were "fair-game" I expected the test to represent that notion. Those were the complaints I had about the test and I think I vented enough to get rid of that built up negativity.

Now don't get me wrong, I want to emphasize that I could have prepared better for this test. There are ways I could have avoided this "disaster and a half" and I'm sure I would have done much better. I definitely could have approached the test more efficiently. However, I do feel discussing in a bit more detail could have save me from all this despair. Danny, if you're reading this then I'd like to say you're still an awesome professor. I'm truly sorry if I ruined your mood, but the test ruined my day.