WEEK 5

Like last week, this week went by pretty fast. It was also a pretty hectic and stressful week as we had our first test of the course, and it was also my first test of the semester. The test was not as bad as I originally thought it was going to be. The process of making an aid sheet really helped me understand the material and clarified any confusions I had. The sample test that was posted was also a very big help since it was relatively similar in format and question type as the real term test. I am really eager to see what I got on the test and to see my mistakes. Overall, I think I did well. As for the topics discussed in lecture, that too was fairly straightforward. We looked at more proofs and just started to look at contradictions. With the test this week, we did not cover a lot of material, and with Thanksgiving on Monday, I expect the following week to the same as last week.

WEEK 4

Week 4 went by pretty fast. I guess it was because the material was understandable and working on the assignment made time go fast (I'll talk about the assignment later). This week, we looked at transitivity - the process of moving the negation through a series of quantifiers and predicates. This topic was easy to grasp. We then talked about double quantifiers. Again, this was an easy concept to learn. Lastly, we started to look at proofs. Proving statements was not my strong suit in high school. For instance, proving trigonometric identities was difficult for me to answer. I have a feeling I will need tons of practice with proofs in order to just get a basic sense of what I'm doing. Hopefully it will come to me. The example we did in class was clear, but then again, that was a simple proof.

Besides the lectures, the very first assignment was due. Had to spend a lot of time on Piazza and in office hours in order to get the assignment done. I understood what each question was asking but I was not entirely sure on how to answer them. For the first question, it asked us to negate an English statement and write the negated statement symbolically. At first, I negated the statement then wrote it symbolically. But after visiting office hours, it was recommended to symbolically write the statement, negate the symbols, and convert it to English. This greatly helped and made me understand what I was writing.

 Finally, the term test is coming up this week. Kind of nervous. Took me a while to understand the material up to now, so I hope I will get a better understanding while studying. I'll update you guys on my first test! Wish me luck this week!

WEEK 2 + 3

Update from Week 1: I think I have an understanding of the material! The tutorial really seemed to have helped. For Week 2, we continued with some quantifiers and started to examine statements. I understood what the symbols meant in each basic statement, but I came into trouble when we started to discuss negation and contrapositive. When negating statements, I was not certain on where to apply the negation. This then stumped me with the contrapositive of statements since the contrapositive is the negation of the converse. Again, with the help of the tutorial, I was able to get some understanding about my issue.

For Week 3, we touched upon conjunction, disjunction, negation transformation and De Morgan's Law. The topics of conjunction and disjunction were fairly straightforward. Negation transformation helped me realized where to push the negation and how it changes some of the symbols. Assignment #1 was also given during Week 3. At first, I had a lot of confusion with the topics discussed in Week 2 and 3, so the assignment looked daunting and almost impossible for me to do. However, with the help of tutorials, I think I will be able to do well on it!

First Impressions + WEEK 1

Well, this week showed that CSC165 will be my most challenging, or one of my most challenging courses this year. The first lecture essentially went over the topics and ideas that will be discussed in this course. The majority - if not all - of the course is based upon having an abstract way of solving problems and communicating on how the problem is solved. Now throughout high school, my weaknesses have been in thinking/inquiry and in communication, so hearing this about the course made me very nervous and somewhat scared. However, I hope I can adjust to this course within the first couple of weeks.

For the second lecture, we talked about sets and had a little exercise about the relationships between two sets. The "any/not any" and "all/not all" terms sort of confused me, but after breaking down each return statement, the relationships made a lot more sense. The third lecture, on the other hand, stumped me quite a bit. I did not really understand the Venn diagrams and the placements for the 'X' and check mark. I expect get a better understanding of this before the next lecture and tutorial. Besides all of that, the quantifiers section was pretty basic.

I heard many interesting and delightful things about this course - mainly about the way it improves your critical thinking capabilities, but also that this course is pretty challenging. I hope that I find this course straightforward, but still intriguing and thought-provoking. Wish me luck!

We also did a weird, but interesting, problem in class:

A: haven’t seen you in a long time! How old are your three kids now?

B: The product of their ages is 36.

A: That doesn’t really answer my question…

B: Well, the sum of their ages (in years) is —[at this point a fire engine goes by and obscures the rest of the answer.]

A: That still doesn’t really tell me how old they are.

B: Well, the eldest plays piano.

A: Okay, I see, so their ages are—[at this point you have to get off, and you miss the answer]

     

(Using Polya's approach, as suggest in class)

Understand the Problem: 

- B has 3 kids whose ages, when multiplied, is 36

- B has an eldest child, so one of the ages is greater than the others

- since A was not sure about the ages of each child by the sum, there must be set of numbers whose product equals 36 and have the same sum

Devise a Plan:

- list all possible combinations of numbers whose product is 36

- with that list, find the sum of each set

Carry Out:

Child 1 | Child 2 | Child 3| Sum

    1       |      1      |    36     |   38

    1       |      2      |    18     |   21

    1       |      3      |    12     |   16

    1       |      4      |     9      |   14

    1       |      6      |     6      |   13

    2       |      2      |     9      |   13

    2       |      3      |     3      |    8

    3       |      3      |     4      |   10

Looking Back:

- by realizing that A could figure out the ages by the sum, sets of numbers must have the same sum, in this case, (1, 6, 6) and (2, 2, 9)

- although that these sets have the same sum, the only possible answer is 2, 2, 9 since one of the ages must be the largest in order to satisfy the "eldest" characeristic

Therefore the ages of the children must be 2, 2, and 9.

Commented on:

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