Week 6

There were no lectures on Monday which meant no tutorial this week as well. I hope everyone had a great thanksgiving. This week we learned more about proofs. One thing I find frustrating about proofs is that they can seem so obvious when looking at the solution, but when I am trying to figure it out for the first time, I can sometimes get lost. One example is this proof below:

By selecting B = 100, it makes the inequality much easier to work with and is actually very simple when looking back at it. I think the key is to do enough practice problems so that if you do get a difficult one, it will be one that you have seen before.

We also received our midterm marks back this week and I managed to get perfect on the first test (humblebrag). My other midterms this week also went well so everything has been good so far. I hope to keep it up for the rest of the year. Thanks for reading once again.

Week 5

I had fun studying for my 2 midterms this week. My cheat sheet is completely filled up and actually looks like a work of art. I did put a lot of proofs on the sheet but I don't think they will show up on the midterm. I am feeling pretty good about both of these midterms so hopefully I will be able to do well. This week's tutorial was on proofs and it definitely helped understand how to structure proofs properly and how to introduce quantifiers and operators.

Here as an example of the structure of a proof.

Whenever we make an assumption, we indent the next line, and once we have proven our conclusion, we can unindent and start introducing the operators and qualifiers that were assumed. Something new I learned this week is that the closure of sets can be very useful for use in proofs. For example, real numbers are closed under addition, subtraction, and multiplication and natural numbers are closed under addition and multiplication.

Post midterms:

So both midterms that I had went well. The one for this course was very similar to the previous year's test and did not end up using my cheat sheet but it did help me learn. Proofs were not on it so I will be looking forward to those on the second midterm. For the very last question, creating a truth table was useful for coming up with sets that would make one statement false and the other true. Another 2 midterms coming up next week but things look to be calming down after that. I also started my work-study this week. Hoping to get some relevant work experience and see if it is related to what I want to do in the future. So far it has been very fun and enjoyable. Thanks for reading once again.

Week 4

This week's tutorial was helpful as usual. I think our TA definitely does an amazing job at explaining the material. The quiz was once again very similar to the tutorial questions, but I think having weekly quizzes forces me to keep up with the material and this will help me when preparing for the midterms and exam. The first assignment was a pain to type out in LaTeX, especially the Venn diagrams, but I am glad I did because it turned out very well.

This week, we started looking at proofs. I think this will be one of the most important topics we learn from this course that will carry on to other courses. I haven't done proofs like this before so it is definitely something new. The professor also mentioned that we will get a cheat sheet for the midterm so that will make things much easier.

Another course I am currently taking is PHL245 - Modern Symbolic Logic. There is a lot of material overlap with CSC165. I initially took the course to fulfill a breadth requirement, but it was a good elective to take because I have taken things that I learned from one course and applied it to the other. Even though the notation used is different, we also happen to be starting proofs in this course and use a lot of the rules that we use in this course. Next week is the first midterm so I definitely have some studying to do this weekend. It just so happens that the midterm for PHL245 is right before this midterm so hopefully I can manage that as well.

Week 3

An interesting topic we learned about this week was vacuous truths. This says that in an implication, if the antecedent is false, the implication is always true, regardless if the consequent is true or not. This was not intuitive to me and took me some time to understand. One example I thought explained it well is from Wikipedia: "For example, the statement "all cell phones in the room are turned off" may be true simply because there are no cell phones in the room. In this case, the statement "all cell phones in the room are turned on" would also be true, and vacuously so, as would the conjunction of the two: "all cell phones in the room are turned on and turned off"."

This week's tutorial exercise was much more difficult than last week's. The last questions in question 1 were especially tricky and took me a little thinking to fully understand, but the tutorial sessions definitely helped me clarify the problems I had. I had an easier time understanding question 2 after I came up with examples and checked to see if the examples worked in each direction. Thankfully, the quiz was much easier than expected, but I will have to do more practice problems like this in preparation for the midterm.

We had an interesting class on Friday. Instead of having a normal lecture, we were given an activity to do. The problem was to try and predict the sequence of ups and downs for a given number of times you fold a strip of paper in half. The problem can be solved by looking at the pattern using the first few folds. Using D for down and U for up.

Folds	Sequence
1	D
2	UDD
3	UUDDUDD
4	UUDUUDDDUUDDUDD

The formula for this sequence would be to first take the previous sequence and mirror and flip it (the sequence backwards and D's become U's and vice-versa) and then append a 'D', and then append the previous sequence to the end. This could be done using recursion and I plan to implement it in Python when I have time.

We also received the first assignment this week. I managed to finish a majority of it without much trouble. I look forward to brushing up my Latex skills in order to format this thing correctly. Thanks for reading.

Week 1 & 2

This is the start of my SLOG to record my experiences in CSC165. This is also my first time writing a blog post.

It has only been two weeks since school started but I have gotten into school-mode faster than expected. Hopefully I will be able to keep up my study habits throughout the year and handle all of my courses.

In terms of CSC165, we've learned about things such as universal and existential claims. We also learned how to solve mathematical problems by following George Polya's four steps and were also given some puzzles to solve. The material has not been very difficult so far but interesting nonetheless. I am looking forward to learning about proofs and program run times. Something new I learned this week was set and list comprehension in Python. It is a very useful and concise way to generate sets in a single line while also being readable at the same time. For example, the following code returns the set of numbers in set S that are even:

 S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}  
 {x for x in S if x % 2 == 0}

We also had our first tutorial and quiz this week which went well. The TA took up the problems on the problem set and helped clarify some of the problems I had. The quiz was very similar to the problems from the homework and I look forward to these tutorials in the future. Also, tutorials end 30 minutes early so that was a pleasant surprise.

I was looking through some of the SLOGs from my classmates and one that I found interesting was here: http://fmello.com/Blog/csc-165-slog-wk1. He provides a table with the definitions and examples for a few of the mathematical symbols we will be using in this course like the quantifiers and operators. This blog is also very nice to look at and designed very well and responsive, so hats off to whoever it is that wrote that blog!

I hope to benefit from writing these logs and maybe it will even inspire me to create a personal blog of my own.