Penny Piles

On the March 13th lecture, we spent the day working with partners trying to figure out whether we can arrange two piles of pennies in order to get every number in the range of [0, 64]. The way me and my partners did this was by reducing the range to [0, 32]. We knew that if we could create piles of pennies that had every number in this range, than it would be true of the range [0, 64] as well. So we proceeded by using a brute force method and calculated that every number in the range [0, 32] could be created by using a combination of dividing the left and right piles. The simplest way this could be done would be to work backwards. For example, the combination (13, 19) could be created from this progression:

(13, 19), (26, 6), (20, 12), (8, 24), (16, 16), (0, 32). 

First we would divide the pile a few times, then work backwards, and attempt to fill in the gap between the two parts. This does seem like a good approach, but perhaps not the best one. At first I did not think this would be possible for all numbers in the range, [0, 32], but it turns out I was wrong. I also do not really see a different way of doing this, but I do remember different methods being discussed at the end of lecture, I just don't really remember what they were. A tree diagram was also mentioned on the handout, but I just figured that would be a different way to organize the results while still using the brute method approach. Overall, I think this was an interesting problem, and one that I did not expect to be true as well.

SLOG 10

During this week's lecture we began chapter 5, which is about computability theory. This seems to be an interesting part of the course, but I feel it will also be the hardest part. I was confused about the halt problem but I thought it was very cool. Just thinking about how someone would be able to write an algorithm that could determine if another algorithm would have an infinite loop was pretty neat. I mean the only way to truly determine if a program has an infinite loop is to allow it to run infinitely, but what good would that do? Anyway, the halting problem is pretty challenging to understand but I feel this is probably the most interesting part of the course.

It was also Good Friday on Friday this week so we had a day off, which was good because I've fallen behind in basically all my courses, so I need to start catching up. Hopefully this upcoming week goes well and won't be too busy since it is the last, and that the tutorial/quiz goes smoothly as well.

SLOG 9

For the 10th week of class, we continued discussing proofs using big-oh notation, and we also began discussing big-omega notation proofs. All I know is that these are supposed to be the upper and lower bounds of a function, but I'm still confused about what the purpose of a breakpoint and constant is. I guess I'll have to look through the course notes and review the lectures to make sure I understand all of this.

I also did not understand the tutorial handout for this week, but I managed to get a grasp of the material during the tutorial with help from my TA and another student, so I do think I did decently on the quiz this week.

This week we also got back our tests and I did pretty well, it was actually the best mark I have gotten on any piece of work (other than the quizzes). Hopefully the trend continues and I do well on the final as well!

SLOG 8

During this week we continued talking about proofs involving big-oh notation. I was fairly lost at this point, but it's more because I spent my time studying for the upcoming test than because the material is very difficult, but maybe it'll turn out that the material is in fact really hard (but I hope that is not the case). I don't really understand what the whole pick a constant and pick a breakpoint is supposed to signify, or how to manipulate an equation in order to turn it into something that we want so that we can assign values to the constant and breakpoint, but since this stuff is not on the upcoming test, it isn't a priority for me right now.

Me and my partner also submitted the second assignment this week. Hopefully all goes well; the only problem we really had any difficulty with was the last one, but I'm optimistic that we did well.

We also spent an entire lecture trying to solve a penny pile problem. I did this problem with 2 other students, and will make a separate post about this later on.

The test was also this week and I think I did pretty well, despite having to catch up on a lot of the material for proofs.

SLOG 7

First of all, sorry for the late entry, I haven't really been keeping up with the slog part of this course. Anyway, during this week of lecture we continued our discussion of step tracking, and also began looking at proofs using big-oh notation. I found this to be pretty hard to understand at first, and was lost for most of the lectures were we discussed this, but I found that doing the tutorial handouts did help me understand the material a bit better. When we were also looking at the max_sum function, I was completely lost, and I still do not really understand it that well because I have not asked for help yet, even though I should. The i and j accumulators in the loop also made it really confusing. I guess however, that once I start doing assignment 3 this will all start to make sense, as the trend so far in this course has been me being confused about several topics, and then cramming to learn all of it before an assignment is due. Since it's too late to change any of these habits, I might as well just continue doing things the same way and hope for the best.

The second assignment was also due this week. I think it went fairly well, but the last question, the one about proving the gcd(m, n) = gcd(n , m-n) was pretty hard and, unfortunately, I do not think I got the correct solution. I feel I should have gotten more help from the TA's, but oh well.

SLOG 6

The first week back from reading week (which we didn't have any CSC165 homework to do over, which is nice) we continued talking about proofs, and we also learned about different techniques on how to solve proofs, and then began discussing counting the steps of a program. I found this part pretty hard, even on the first day of the new topic, so I can't even imagine how hard the next topic in CSC165 will be. To my understanding, the way to count the steps of an algorithm and calculate the run time is to first determine how many times a line will execute for a set of size n, and then add each line together. The hard part is actually determining how many times each line will execute, as that part can be tricky, especially with nested loops.

Also this week we had our regular tutorial and quiz. I felt pretty confident with the material on proofs, but my structure is quite horrible, which lead me to doing poorly on the quiz this week. I really wish that proofs only required you to do the math to actually prove something, and that all the "assume", "then" statements could be left out. I think this would make it much simpler, but I guess that's not the way it is. 

I also began working on assignment 2 with my partner. Some of the proofs seemed straightforward, but the last two were quite hard. I found structuring my proofs to be a bit challenging. From my perspective the proofs I wrote were fairly good, but they actually were pretty weak. I guess you have to treat proofs as if the person reading it has no knowledge of the math you are using to complete the proof, which requires you to be very detailed and write comments where they are needed. Overall, the second assignment was harder than the first one, but it did give me a lot of practice with proofs, which is a good thing.

SLOG 5

It's been a while since my last post, so I'll try to make a new post for each week of class, that way there will be no massive wall of text to read.

So after the first test, we continued discussing proofs and how to solve them. I found the part about proof about limits to be pretty confusing, and I still don't really understand it quite well. We also learned how to disprove a statement, which requires you to negate the statement. For example, if an existential statement needs to be disproved, you would negate the statement and prove that for all elements of a set, the negation is true.

The tutorial handout that we also did during this week required us to write the proof structure for various proofs and then complete the proofs themselves. I'm not really sure if I did this handout correctly, and I also didn't write the quiz because I missed the class, but I feel the practice I had writing proofs for assignment 2 was a good way to learn the material that I missed and didn't learn.

SLOG 4

This week in CSC165 we continued learning about proofs. So far the examples in lecture haven't been too hard. We would focus on getting the outline of the proof, and then actually write the proof afterwards. Although it hasn't been too bad so far, I feel writing proofs is going to become a lot more complicated. Some of the proofs we did in lecture could also have been difficult to figure out by myself, and could have taken some time to figure out.

We also didn't have a tutorial this week, which was good because it gave us some extra free time, but it also meant that we would not get a chance to ask our TA's any questions that we might have.

This past week we also had our first term test, and I think I did well. I found the structure and some of the questions to be similar to a previous test that was on the CSC165 website. The test also didn't cover as much as I thought it would have, which is a good thing because there are some concepts that I don't fully understand yet, such as proving equivalency. Overall, I'm starting to feel better about this course, and hopefully this next week before reading week is easy and goes well.

SLOG 3

So this past week I worked on my assignment for CSC165. I feel it went okay, but some questions were definitely hard. I especially found questions 3 and 4 difficult, and converting a statement from English to symbolic notation, because of the ambiguity of the English language. Sometimes I would do a question, then do the same question a day later and get a different answer, which was very frustrating. It was very good practice though, and the practice questions that the prof posted were also very helpful in completing the assignment.

The tutorial went fairly well, too. My TA and another classmate helped clear some of the confusion I had about proving equivalency, and I feel I did well on the third quiz.

The material covered this past week in lecture includes more about bi-implication, limits (which I found to be very confusing), and proofs, which seem pretty complicated. I found the material this past week to be generally confusing, but I'll be looking at some of the practice questions to get a better understanding.

The midterm for CSC165 is also coming up on Friday, and I am not ready for it at all. I also have another midterm on Wednesday (I'm pretty sure most people in CSC165 have this test as well), as well multiple projects and assignments due the week of the 11th. It's going to be a bit hard trying to find time to study, but when I do get around to it, I'll check out the previous tutorial handouts, the assignment, problem questions, and previous exams. I am really getting swamped with homework now, so hopefully this next week of class and the midterm go well.

Week 2

This week, CSC165 was harder than the first week. In the past few lectures we discussed negation, implications, vacuous truths, converting English claims into symbolic ones, and using venn diagrams to illustrate implications. Understanding these concepts is becoming a challenge, and I know it's only going to become harder. The tutorial handouts and assignment are also much more difficult than what we learn in lecture. The second tutorial handout took me about 2 hours to do, and about 85% of my answers were wrong anyway, despite feeling good about the material during lectures. I'm also not sure how I did on the second quiz, and I hope I do well on the next one. I also haven't even started the assignment that's due in 4 days. Overall, my confidence in this course is dropping fast. I should probably do more readings and extra homework to make sure I understand what is going on in this course. If I am unable to keep up with CSC165, I may drop it and retake it in summer school, which isn't that bad since I'm doing summer school anyway. Right now, my goal is just to get this first assignment done. Oh well, there's only 9 weeks left of class.

CSC165 - Week 1

     I feel my first week of CSC165 went very well. I was fairly familiar with the set notation we covered in class, since I learned it in high school as well. I did forget some of it however, but I spent some time reading and relearning all the symbols that are used in sets. I also wish that the instructor included a table somewhere in the slides that just listed all the symbols used in set theory, since that way I wouldn't have spent some time during lecture trying to figure out what the symbols meant, when I should have been paying attention to the lesson instead. This wasn't a big issue however, because it only took about 20 minutes to relearn most of what I had forgotten. This was basically the only difficult part about CSC165 so far, and it wasn't all that bad. My plan for whenever I get stuck in this course is to just reread lecture notes, do practice problems, and get help whenever I need to. I prefer these methods because it allows me practice the course material in CSC165 in a comfortable environment. I was also familiar with the use of venn diagrams in set theory, so it was just a matter of relearning the concepts that are part of the diagrams. Some new things I learned this past week were quantifiers, and existential and universal claims, as well as their anti-symmetric pattern. I learned how to verify and disprove both types of claims and give proof as to why they are true or false. I also learned about the proper ways of problem solving (understanding the problem, making a plan, solving it, and then reviewing the problem). Nothing so far that we have covered in CSC165 has caused any problems or given me any real challenges, and because of this my confidence in the course material is high. My tutorial also went well and I feel I did well on the quiz. The handout for the tutorial was fairly straight forward, except the very last question, but my TA helped clear my confusion. I find the course material interesting as well because I like mathematics and may consider pursuing it as a double major. I also find statistics and probability interesting, so hopefully this course will cover some topics that are in those fields of mathematics. So far my first week of CSC165 has gone well, and hopefully I can stay on top of the material and do well in the course, but I know that I will have to work hard in order to make sure I can grasp all the concepts that will be taught.