Entry #5 - Midterm 2.0

While writing the midterm, I felt fairly confident with my proofs. I knew I had most of the structure correct, and for the actual proving part, I tried to prove everything as explicitly as possible. Where I was unsure of my proof, I made sure to add comments that either explained what I wanted to prove but didn't know how, or further proved something to make it clear.

After receiving my marked midterm, I'm happy to say I did better than I expected. The extra comments I added definitely helped my mark, and I now know that I'll still get a decent amount of marks if I don't know how to prove some element of the proof, but still write out the structure and explain what I want to prove.

And I also found out my partner and I got a 95% on assignment #2, so I guess it's time for the happy dance .gif

Entre #4 - Diagonals

Problem: Find the number of squares that the diagonal line will pass through the interior of.

Plan: 

• Draw examples starting with smallest number of rows/columns
• Try to find a pattern (most obvious ones: m=n & m=1 or n=1)
• Redraw the squares with unknown patterns in a logical order (keep m constant, change n up to 5)
• Try to find a pattern in chart and drawings

Results:
After executing the plan up to 5 m (5 rows), a pattern was found with an even and odd number of m. Exceptions were also found with m = n (square). From this, we wrote out generic formulas for the odd and even number of m. The formulas are as follows:

m is Odd: number of shaded squares = m + n - 1 (as long as m != n)

m is Even: number of shaded squares = m + 2 [[(n-1)/2]] ([[]] is the floor of the function, and as long as m != n)

Looking back:
My partner whom I was working with informed me that she had spoken with Professor Danny who said that a problem occurs with our solution when it comes to multiples. Obviously our solution needs a little more work, and isn't perfected yet. Continuing to graph out more examples and analyzing them would probably help fix any problems that occur.

Entry #3 - Midterm-inator...or not.

Despite the shaky start on the midterm (with the python coding) I was able to grasp most of the questions fairly easily. Walking out of the exam, I thought I did pretty well. Maybe I could've improved my explanations for some of the answers, but all in all I felt good about the test...

That is until...I read over the sample answers for the test that were posted on the course website. Unfortunately, a couple of my answers were wrong for question 1 b), which I thought for sure I had gotten correct. And after reading over the justification for the answers in question 2, I'm not sure my explanations were strong enough.

 Hopefully my mark isn't as low as I'm expecting...but I'm more worried about the answers that I thought were correct but actually weren't. Looks like I may have to go through my midterm and figure out where exactly I went wrong with my thinking.

Entry #2 – Conjunction, Disjunction, Negation, oh my!

In lecture this week we were introduced to conjunction (^) and disjunction (v). Having Python coding experience, I found the concepts of the two easy to follow. (E.g. if one element is False using conjunction, the whole statement is False, while with disjunction the whole statement is True).

However, I did find it a bit confusing keeping track of the way conjunction & disjunction are used in comparison to how we use it in English, which required me to look over the concept a couple of times in my notes.

We were also introduced to Truth Tables, which I find much more useful/easier to understand than the Venn diagrams. I used them frequently while working on the assignment to check whether certain implications were equal to each other as well as convincing myself that the De Morgan’s Law was true (obviously it was…otherwise it wouldn’t be a Law now would it?). 

As for the quiz in tutorial…well my answer wasn’t exactly the same as the one Danny e-mailed us after, so I’m not so sure on the result. 

Things are starting to get a little more complicated in this course, so reviewing my notes is a must from now on. Let's hope I don't get to this point:

Entry #1 - Quantifiers

This week in lecture we focused on quantifiers which usually involved matching statements with functions. To help illustrate these ideas, we were introduced to Venn Diagrams that show whether each of the four regions may be empty or occupied (?), not occupied (X), or occupied (O).

At first, I found the concept of the Venn Diagrams a bit difficult to wrap my head around. In order to understand them further I reviewed my notes and re-did the examples from previous lectures. The concept is fairly clear to me now, and as a visual learner, I feel as though mastering the use of the Venn diagrams will help me further in the course.

Overall I'm finding the idea of quantifiers as claims about sets fairly straight forward. The quiz during the lab went well, so I'd say this .gif does a good job summing up how I'm feeling so far.