HALT?!

    This past week we only had 2 lectures because of the fall break! We started looking at halting problems and computability of functions.

    All of this stuff makes no sense to me whatsoever... I have no idea what's going on so I think I should really look at the course notes on halting and computability and go over the lecture slides as well. And if I still don't understand it by then I should probably go to office hours to clear things up before the exam! I should probably start on assignment 3 as well... Hopefully I won't have that much trouble with assignment 3 as I did with assignment 2 when I just just starting to understand proofs.

Edit: So after reading a few SLOGS from other students, I found a SLOG that was able help me with understanding the basic concept of halt using a small diagram: click here to understand halt!

Problem Solving (Folding)

Earlier in the course we were presented with a problem. We had to take a strip of paper and fold it in half several times. We then had to unfold it to determine the sequence of the crease points (either up or down). We then had to predict the sequence for any number of folds.

We started by folding the strip of paper in half and unfolding it back to the original strip. We then recorded the crease point into a table. This was repeated 4 more times until we had the strip folded 5 times.

When we had the pattern recorded in a table like this, we started to see how the pattern of the creases repeats itself. We then decided to align the pattern so that all the middle creases line up.

After the alignment we saw how the pattern was symmetrical but the creases were flipped depending on which side they were on.

We also saw how the middle crease was always a down crease. We also saw that everything to the right of the middle crease was the previous pattern and everything to the left of the crease was the previous pattern but flipped (D turned into U and U turned into D).

We also observed how the number of creases increase with a pattern. The number of creases can be determined by taking the number of creases from the previous pattern/number of folds multiplying it by two and adding one. So, if the function C(p) gives us the number of creases based on the pattern, we can determine the number of creases of the next pattern by using this equation: 2 * C(p) + 1. This means that we don't even have to know the current pattern to determine the number of creases, we just need the previous pattern!

So with that being said, we can determine the number of creases if the strip of paper was folded 6 times.

# of creases with 6 folds = 2 * (31) + 1
                                        = 63 creases

And with some extra time on our hands, we can also determine the pattern for 6 folds based on our analysis.

UUDUUDDUUUDDUDDUUUDUUDDDUUDDUDDDUUDUUDDUUUDDUDDDUUDUUDDDUUDDUDD

Another student solved this problem and was able to determine the pattern for the first 10 folds using some code that he typed up in python! TAKE A LOOK AND SEE FOR YOURSELF!

Week 6-9

    Over these few weeks we continued with proofs. I found the proofs on assignment 2 to be quite challenging but it did help me with getting a better understanding of proofs and coming up with the 'body' for different proofs. Shortly before the second term test we started to learn about counting steps by determining the amount of iterations of loops or lines in the given code. We also starting to learn about Big O and Big Omega. And with that we can determine the upperbound and lowerbound of an algorithm's run-time in the worst case scenario.

Week 5

   This week we continued with proofs and we also had our term-test. I feel like I did pretty decently on the term-test because I had a good understanding of the course material after working on assignment 1 and going over the old term-test. Even though I had an aid-sheet with me I barely had to use it and it made me very happy because it meant that I was confident in my answers and course material!

    On Friday we started doing proofs by contradiction which is pretty much proving that the contrapositive is false. At first I didn't really understand what was going on but after going back and reading about how we do proofs cleared everything up for me. Even though I sometimes still have trouble coming up with the "body" of the proof, I still really enjoy learning/doing proofs.

Week 4

    After reading another students SLOG I felt like I had a better understanding of antecedents and consequents of implications and how to determine which is which and how the how the statement can mean completely different things if you have them swapped!!
 
    The main thing we learned this week was proofs and I am slightly confused by it... I understand the layout of the proof and how we're supposed to indent but I'm having difficulty coming up with the steps in between to show the proof.

    Assignment 1 was due yesterday and I can say that I've spent quite a fair amount of time working on it this week and trying to understand everything to prepare myself for our first term-test, which I am extremely nervous about. I guess it's a good thing that we have the option to bring in a aid-sheet to help us out!

Week 3

    This week we learned about conjunction (∧), disjunction (∨) and negation (¬). Conjunction and disjunction were very straight forward and easy to understand but I found myself having a bit of difficulty trying to wrap my head around the whole negation thing when I'm trying to "work" the negation as far into the statement as possible instead of just having it in front of the entire statement. We also went over drawing and tabulating truth. Another interesting thing we covered was De Morgan's Law where we showed with a Venn diagram how ¬ (P ∨ Q) ⇔ ¬ P ∧ ¬ Q.

    I have also been spending quite a fair amount of time working on assignment 1 this week. I have been spending a lot of time on it because I am still having quite a fair amount of difficulty understanding implication. I have found myself constantly struggling to determine what the antecedent and the consequent is in the statement. I feel like I should try to get help with this before it's too late! Maybe I should go to the help centre as much as I can to get help on understanding implications?

    We ended this week off with the "Folding" exercise where we had to fold a strip of paper multiple times and use different problem solving techniques to predict the sequince of ups and downs when we look at the creases in the paper. In the end, we were given hints to think recursively and symmetrically to try to find the solution to this problem and predict when the next sequence will be.

Week 1-2

    It's almost been 2 weeks into the course and I already feel like I need to spend more time reading the course notes and going over the annotated slides in order to keep up with what we're learning. I also find it kind of difficult trying to understand these new concepts.

    The one thing that I found confusing was the Venn diagrams. I think I only found them confusing because most of the time I wasn't sure on where to put the 'O' or the 'X' and some times I wasn't sure if they were even needed! However, after doing the tutorial exercise and going over it during the tutorial session, I now feel like I have a good understanding of the material.

    As of now, we are learning about implications. I find it very interesting but I'm a bit frustrated because I am having some difficulty trying to understand contrapositives and converses and what kind of information they provide about claims. 

    Hopefully, by the end of the weekend, I can go over the course notes and annotated slides about contrapositives and converses and try to get a good understanding of them. If not, I think I should seek some assistance as soon as possible!