Tuesday, November 25, 2014

Last 400 metres!

November 25, 2014

Last week, I did not submit a sLog. To be honest, I did not do anything for the course, besides starting on the assignment, so there was nothing to new to note.

To start, Larry gave the class some hints for Assignment 3. These were very helpful, and it alleviated a lot of doubt in my work, and also gave me some hints that I did not occur to me before. With this new knowledge, I will be re-tackling the questions, and hopefully will go a lot smoother than the first run.

I did not as well on Assignment 2. I focused too much on one question, which caused me to miss out on what should have been obvious mistakes. Had I took the time to thoroughly review them, the mistakes could have been easily avoided. Assignment 3 is my time to redeem myself!

Today’s lecture covered countability. The first example was a strange one, and seemed to go against what seems natural to us; size of the set of natural numbers equals the size of the set of even natural number. He explained that because we can map a natural number to a unique even natural number, the two set sizes must be the same (n to 2n). It makes sense, but it is still a foreign thought because we were talking about subsets earlier in the term, and the even numbers are clearly a subset of the natural numbers.

Larry also introduced the idea of countability. However,  I want to know decided that Natural and Integer numbers is “countable”? For every natural or integer number, there is always a higher natural number…so how can you conclude that it is ever “countable”?




And this new material is not in exam. Great. I was not hungry enough to stay awake as well!

And that is the end of the lectures for the term--
Maya.

Thursday, November 13, 2014

O

November 11, 2014.

Lest we forget.






This week we received our term test 2 back. Although there were small mistakes, it was generally a good mark. I am glad I put in some effort to learn the proofs for the assignment. A small mention of the Assignment 3 was made. It is going to be like last time. “Just” need to find the trick.

Lecture continued on about proofs. It started with straightforward questions, but as it progressed, I got lost around the time where he wanted to disprove a statement about Big-O and Omega. He did not quite thoroughly go through each of the last two harder proofs, so I will have to go back and review those. I know when I go to do similar questions, although I have a vague idea now, like everything in this course, I will be scratching my head. I am not quite sure how and why he can arbitrarily let some function equal a certain function, but I will review that in due time….

When I thought lecture was soon to be a wrap, Larry introduced Computability. It is hard to see why it is important. Especially with my mind wandering since the the latter half of the proofs section, I was easily distracted. The individual sentences made sense, but I did not absorbed anything, and I have no idea what the purpose is and the idea behind halting, and non-computability. I will go over it slowly, like every other thing in this course.

Next lecture is final one?
Oh dear.

Toodles,
Maya.

Tuesday, November 4, 2014

Boo boos

November 4, 2014

During this past week, most of the my attention was concentrated on Assignment 2. Deciding whether Claim 1.2, and 1.3 was correct or incorrect was a long battle fought., I was constantly flipping between True and False all week. At the beginning, after working it out logically, I was very very sure that Claim 1.2 was False, although I did not know how to prove it on paper. However, as I was working through the problem to see if I can use math to solve it, it dawned on me that it was probably CORRECT. I started worked on that conclusion, but then I thought about it again, and I decided it had to be INCORRECT. This loop went back and forth many many times.
Looking at the Assignment 2 answers, I was relieved to know that my answer of Claim 1.2 being false, and 1.3 being true. However, because I focused so much on these two parts of the assignment, I did not really think the last 2.1, 2.2 through. The converse should have been false, but I had put as true. Thus is life. I need to make sure the “easier” questions are absolutely correct before I move on…
Today’s lecture was more or less a step by step approach to proving Omega. The steps were fairly structured, so it was easy to follow along. There were stark differences between the examples, which give a general standardized approach depending on the type of equation. Hopefully there will be a decently clear path on future questions.

Maya.

Note: It helps to be not sleepy in class

Double note: My apologies, I forgot that I did not post my sLog for last week until today.

Omega

September 28, 2014

I am starting to wonder what I will do for Assignment 2. Between trying to figure out how to indent in ShareLaTeX (unsuccessful), and trying to figure out the details to the proofs, I have some doubts. I had an opportunity to talk to the professor about the assignment and proofs in general, so I have a better idea of what to do; hopefully it’ll be sufficient to pull me through.

All that aside, this week in lecture, the big O and Omega was covered. Like most materials for the past weeks, although I understand it, but do not understand it. When choosing c/B, the inaccuracy makes me anxious as well: As long as it’s aaaany number greater than X, or annnny natural number greater than Y, etc.. And is O(n^2) Omega(n^2) always going to be compared to (n^2)? I do not know. I was particularly hungry tonight, so my attention span and effort levels are diminishing quite quickly.

As a side note, we watched a slow animation of insertion sort. Twice. WHY!? And as a bonus, the slide had a mini version of the animation on the side.

Soon afterwards, the class participated in an activity: Penniless stacks. I was too tired and hungry so I did not actively try to solve the problem.

No, I will not discontinue to be paranoid.

Maya.

Wednesday, October 22, 2014

Forgotten

October 21, 2014


Larry opened the lecture with an announcement that the assignment has been posted, but to manage our time, because Test 2 will take place the day after. I am glad he mentioned that, because I definitely forgot about it. Earlier, I took a peek at the assignment; it is all proofs (not that I was expecting anything else). I hope I can get comfortable with proofs before the assignment and test comes due…
As the lecture moved on to the next material (more proofs), I still am not sure, how much proof is enough? In PHL245, the tools to prove is limited, making the options limited and straightforward (if you can find the correct path). So far, the proofs in CSC165 could be endless, and less structured. Larry also mentioned there is a lot of practice questions that have been posted. I am planning to attempt those.
The second half of class was about Algorithms. Although the material was straightforward, it was interesting to see all the thoughts that is put into code I passively write for class.
Off to find time to practice,
Maya.

Thursday, October 16, 2014

Proofs

October 14th, 2014

There’s no tutorial this week! I will be able to go home earlier to feed my dog!

In lecture, it was a continuation of proofs. Started with a simple example, which was very easy, and helped me understand the structure of a proof.

However, the professor re-introduced a formula:
>0, >0, x R, | x -2 |<, | x2-4 | <
I had a hard time coming to understand this, and only after the explanation was given, did I have any comprehension of it. Larry said to disregard the complicated-looking formula, and not be intimidated by the greek letters. But this is not about the greek letters! I may have mentioned in a previous sLog, but I am not confident I can solve this proof if something other than this question were to come up.

As we worked through this proof, I may or may not have understood. I can only hope that many many proofs will be done throughout this course, so I can finally say “I GET IT”.


As a side note, I am very impressed with the amount of people who received 100% on their first term test! Too bad I was not one of those, but still very impressed!!


Until next time,
Maya.

Tuesday, October 14, 2014

Tuesday, October 7, 2014

Term tests Augh

October 7, 2014

This week was the day of the first term test. When I was studying for the test, I used previous CSC165 term tests that I could find (2013). These tests had exercises that covered the material evenly. However, I felt there was not enough available exercises to practice with. I was still unsure as to what I did and did not understand 

Larry later sent out an e-mail with the previous term test. This was formatted differently, and covered the material in a different way than I have previously seen. Specifically, question #2 threw me off. There was a symbolized statement, and we had to prove which was correct, the initial statement or its negation. This was to test the understanding of quantifier sequences (e.g. difference between ∀ x, ∃ y versus there ∃ y, ∀ x). Sorting the logic out for this was confusing, so I decided to pop in for office hours. 

On Monday, there was a pleasant number of people who showed up, and proceeded like a mini classroom. Everyone had brought questions, and Larry explained to all of us the details of those answers. It helped me clarify a lot of different topics, and was very productive for me. 

When it came to actually writing the test, it had the same format as the term test Larry had sent out. This was when I was truly grateful I went to office hours. Had I worked on the old test alone, it would have been devastating, as my understanding was only vague. I tried to complete the test quickly, but I got stuck on the last question. It was hard to logically work through it, as the time was slowly running out. Only in the last five minutes I had figured out the answer. I quickly wrote an explanation, and before I can give an example, time had run out. Looking back, I realize, I did not give examples for most questions. I had explained in words; I really hope that is sufficient.

This week’s material followed the test, which was more or less about proofs. The first proof was very straightforward (infinite number of odd numbers), however, when Larry started with the infinite prime numbers proof, it started getting confusing. He was spewing on and on about P and Ks and factors. Ultimately, I was able to understand how the proof followed, however, if I am not confident I can solve a proof yet, if it was given to me to work through. Hopefully by next week, I will have a “Halleluah” moment, or maybe there’s more to proof than I think.

Hasta la vista,
Maya.

Friday, October 3, 2014

Proofs & Problem solving

September 30, 2014

This week’s lecture started with exercises on equivalencies with quantifiers, disjunctions, and conjunctions. Despite having worked on the first assignment this week, I had no idea how to find the answer. The first question was:

P=>Q is equivalent to:
A. ¬P ∨ Q
B. P ∨ ¬Q
C. P ∧ ¬Q
D. P ∧ Q
E. None of the above

I thought of the implication of this quantifier logically, but could not come to a conclusion. As he worked through the answer, it seems like this is less intuitive, and is only clear when the negative of this equation is worked out and compared to the already known equivalency. This exercised reminded me of the brief laws that were mentioned at the end of the previous class. I referenced week 3’s material in the next questions, and was then able to answer the questions. I was at a loss, because Larry had zoomed through the material (despite having a decent amount of time). It seemed like this material was not as important or will be covered in this week’s lecture, so I did not bother looking through these slides.

Looking through some of the theorems, they are very intuitive, but thinking of these formulas in a logical manner every time there was an equivalency question, seemed inefficient. So, I will probably straight off memorize the formulas.

Next thing that came up in class was sort of a fun surprise. Larry introduced it as a “real-life” proof. It was the hanging man paradox. To me, this was totally from left-field. The previous proof was a serious, down-to-Earth math question, but this question was a “neat-test-my-friends’-logic” kind of question. We did not have a lot of time to think this through, but the whole question is very interesting nonetheless, and I just might quiz my friends on it. If I was given the time, I wonder if I would be able to figure it out…

At the end of class, there was a folding exercise. I teamed up with a classmate named Jackie, and tried to work out the problem. Initially, trying to record the up and downs of the paper was very hard, as it kept flopping over, and had to keep the top and bottom consistent as we added more folds. After trying to re-record the folds many times, we started to be more familiar with the patterns. Initially, we looked at the sequences of up and downs. There were no apparent sequences. However, once  I thought of the problem logically (i.e. not in patterns, but focusing on what is actually happening to the paper), I had an “ah-ha!” moment. The paper is getting folded onto itself, and so the creases are happening between the previous crease. In addition, if there is a fold on the one side, there must be another fold on the other side that fits in with the fold. So if we start of with our initial sequence, if we space it out, and as long as we can fill in the inbetween of one side, the other will be simple! I had thought it would simply be one UP fold on the other, while the other was DOWN. Happily satisfied with my answer, I waited for Larry’s real answer.

As you know, there is a slight flaw to my answer, as all the creases on one side do not become just one kind of fold. Almost there, but not quite there. Regardless, the exercise was very engaging and enjoyable.

In this week’s tutorial, Grace very graciously answered my “dur” questions. Thanks again!

Until next time,
Maya.

Sunday, September 28, 2014

Conjunctions, Disjunctions, Negations

September 23, 2014

This week’s lecture outlined conjunctions, disjunctions, and negations.

An interesting point that was brought up in class, was the conjunctions and the use of “and” in the English language. The example that was used, was
“This is a pen and a telephone”

The sets of Pen as P(x) and Telephones as T(x) do not intersect, but this sentence means an x from Pen in addition the Telephone. English is a funny language, and has many complexities that we do not think of day-to-day.

As the class progressed on to negations, the concept, although very simple, seem to conbobulate in my mind. I started to mix up negations to verifying/falsifying statements. On top of that, although the negating of English sentence is straightforward, converting it back into symbols was unintuitive. The difference of when the wedge was used versus → was very hard to distinguish, especially with little examples (beyond simple sentences).

The other topics, conjunctions, disjunctions, I thought I had understood the concepts. However, when I went to do the Tutorial questions, I quickly realized I did not understand at all. The most difficulty was when the sentence had quantifying descriptions (e.g. more than one). Similar examples were not covered in class, so I got creative and tried using the wedge, and putting restrictions on variables. However, I had no idea what I was doing, and was very unsure of my answers going into the tutorial.

At tutorial this week, I was eager to know what the answers were to these questions. When comparing my answers to a fellow classmate (I forgot to ask his name!), I realized my conditions on variables (There exists, For all, etc) were off. I must have been too focused on the meat of the sentence. That was embarrassing.

The most neat answer to me was to the following question:

1) Symbolize the sentence, if C is courses, P(x,y) = x is prerequisite for y
  1. No course has more than two prerequisites

This particular question, I had no answer for. No matter how I scratched my head, I could not get a good enough answer. This utilized three variables (i.e. x, ,y, z) that represented prerequisites. The condition on these variables, was (x=y ∨ y=z ∨ z=x), so if one these were true, then there would be two prerequisites! This made me realize that symbolizing can be a very creative process

Until next time,

Maya.

Saturday, September 20, 2014

Questions, questions, questions

September 16, 2014.

At the start of lecture, Larry had presented a table, where we needed to fill in with the worlds "no", "one", "example", "counter-example". The table was laid out like so:


Universal
Existential
Verify


Falsify



Although I have a pretty good understanding of the concepts taught last class, this table was not intuative. I understood that Verify/Falsify was True/False and Universal/Existential was for All/Some. Perhaps because I had not fully settled into the CSC165 mindset, this all seemed foreign to me. I did not know where to begin. At first, the All/Some True/False was getting mixed up in my brain, but as that came more clear, allocating the words into the table was nonsensical. I had thought each of the words some how correspond to the box. So I formatted my table to look something like this:


Universal
Existential
Verify
counter-example
example
Falsify
one
no

Of course it was entirely wrong. As soon as Larry  had done the first example, my mistakes became very apparent, and I had slapped my forehead, disappointed in my misunderstanding.

As Larry started covering "Evaluating Quantified Claims", and Python syntax were introduced, the for/in/in made it very confusing. The chattering classroom (understandable--people are eager to answer the question!) made it harder to concentrate, to clear the meaning in my head.

At this point, I was feeling down and discouraged, as it seemed to me that I could not keep up with the classroom. I made a mental note to review and practice Python more, so the syntax will be obvious and second-nature to me. This is what I am getting into! The questions were difficult, but I had still made an effort to answer, whether they were erroneous or not. These questions are very good, and got everyone thinking, so please do not misunderstand my frustrations to be negative feedback towards these questions!
The second half of the lecture got more into words/sentences and representing their meanings into symbols. I am currently taking PHL245 (as recommended by the Undergraduate office), and the concepts and questions were oddly familiar. I had already done many similar questions in the PHL course, so these questions were less of a struggle than the initial half. It was good for my confidence, as I was able to answer the questions more promptly. This is not saying there was not any questions that did not get me stumped! The English language can be very complex, and many ways to convey a particular meaning.

One tricky question was when identifying whether a sentence was a statement or not. The specific sentence was: "The sandwich tastes delicious". In my mind, “the sandwich” is a very specific item. When you’re saying this sentence, you are referring to a specific sandwich. However, as Larry later pointed out, there is no context in which the sentence is being spoken, thus losing its quantifying characteristic, not longer making it a statement. Hm!

Finally, the last challenge was to convert the sentence introduced at the beginning of the lecture into symbols. This part was very briefly skimmed over, and not enough time was allocated to work on the question. However, it was very interesting exercise, and I hope it would be done in a similar way in years to come.



September 18, 2014

This was the first week of tutorial, so I thought I might was well briefly review about that as well. The tutorial was brief, and little to no teaching was done. Only the exercises were taken up and quiz completed. Perhaps there was not enough content to cover, but more involved exercises, similar to what was done in class, would have been beneficial. The most confusing topic, implications, will hopefully be covered in next tutorial, with plenty of questions. Although I am taking PHL245 which covers similar topics, it would still benefit me greatly.

Until next week;

Maya.

Monday, September 15, 2014

Hello CSC165

Class: September 11, 2014

The first week of classes. Mostly introduction lectures, and CSC165 was no exception. The class is a 3 hour lecture. Half of the class was dedicated to expectations, assignments, etc. Larry had tried to make it as amusing as he could, which I think he successfully did. The class was laughing, I was laughing. All good times. 

Once the lecture started after a quick break, the first interactive part of the course was discussing the ambiguity of newspaper headlines. My initial thought was the misunderstandings (ambiguity) the article (body) can give rise to. For example, “Death may cause loneliness, feeling of isolation”. If I were to answer the question on my understanding, it would be how the article focused on a very specific group of people, or how it omitted other circumstances, etc. I felt silly when I heard other answers from other students. Whoops. An example of ambiguity and double meaning.

The next section was more problems solving and working through logic. It was very interesting, as it got me involved, trying to solve the problems, instead of a one way interaction (typical classes). However, the Street Car Drama problem, there is a conclusion that I STILL do not agree with. The problem requires you to find the age of the three kids of B. Each line from B concludes a fact about the children, that will be used to find the final answer.

A: Haven’t seen you in ages! How old are your three kids now?
B: The product of their ages (integers in years) is 36.
A: That’s doesn’t really answer my question...
B: Well the sum of their ages is -- [fire engine goes by] A: Hmm... that still doesn’t really tell me how old
they are.
B: Well, the eldest one plays piano.
A: Okay, I see, so their ages are -- [you have to get off the streetcar]

From the 4th line, the conclusion is that the sum of their ages do not produce a unique answer. If you were in that situation, however, it would not be realistic to assume that the sum is not a  unique answer. B is just telling you the sum of their ages, which can be either unique or not unique. I need to remember that this is a LOGIC question, and treat it as such. 


It was an enjoyable class. Still early to know what to expect in the future, but I’m looking forward to it!