Better Late Than Never... Problem Solving on Diagonals

It seemed simple when I first received this problem in February, but I found out from a couple of other students that it's not as simple as it seemed. Might as well get this out before the end of the course.

Problem: Draw a diagonal line in a rectangle that consists of m rows and n columns and determine how many grid squares are passed through by the diagonal line.

Process: Using graph paper in class, I drew some examples down on paper and found some patterns.
This is what I found comparing m and n (before I ran out of space).

    n 
m       1  2  3  4  5  6  7  8

    1    1  2  3  4  5  6  7  8              RED: Whenever n = m
    2    2  2  4  4  6  6  8  8              GREEN: Whenever n = m are odd
    3    3  4  3  6  7  6  9 10             YELLOW: Whenever n and m are odd
    4    4  4  6  4  8  8 10 8
    5    5  6  7  8  5 101112
    6    6  6  6  8 10 6 1212
    7    7  8  9 101112 7 14
    8    8  8 10 8 121214 8

I wasn't so sure about the pattern that I found, because it seemed to look like it was all over the place.
I initially thought that there was a pattern whenever n or m are odd or whenever n or m are even, but then I had to look at whenever n = m, where the pattern would break. There also seems to be a pattern when looking diagonally across this chart.

Overall, I'm not entirely sure of what to make of this, even though "answer" were already given. I felt that if possible, I'd want to discuss this with Danny about this, but it's already the end of the course, so oh well.

The final stretch...

So here we are, at the last week of the school year.
I'm feeling a rush from a sense of urgency trying to get my assignments finished before Friday and I'm not going to let up until they are done. Meanwhile, the 3rd assignment is going surprisingly well with the concepts of Big-O, Big-Omega and limit notations becoming more familiar to me. However, the concept I can't seem to grasp seems to be the halting principle which is the basis of the last question of the assignment and a major part of chapter 5 in the course notes.
I hope that the last tutorial can help me with grasping the halting principle so I can finish the assignment and get focused on the final exam later in April.
Things are going fine for me these days, the ideas of diagonalization seem to be simple, yet very abstract in its description. Hopefully, I can grasp this concept before next class then.

Overall, this class wasn't really as bad as I had heard last term. It's probably because the teacher was very clear in his descriptions, posted everything on his website and was all around, very helpful when we had a question ask about something we didn't understand.

About the the problem-solving progress, I had a vague description for a problem based on what we looked at in class, but I'll need another post to describe what I got.

Been a while...

So I'm currently at the second-to-last week of the school year at U of T. I've been trying to get through all of my work, including keeping up with my CSC165 work.

The test for CSC165 went very well, just as much as last time and I'm determined to ensure that the final exam goes just as well. I'm getting very good at proofs now and I've learned a lot from the proofs assignment. Now I have to learn about how to get the big-O and big-Omega proofs down and it's not as easy as I thought. Hopefully, me and Justin can get through this new assignment together through sharing ideas and concepts. What's concerning me though is the fact that I have to do another assignment in CSC148 and I'm not sure that I can get both done efficiently in time.

Here's hoping that by next week, everything will be done in time and I can prepare for my exams.

Meanwhile, I'm hoping that I can keep my sanity intact during these last two weeks.

It's gonna be a long month

Hoo boy, with all the work I've have this month for all my courses, I'm not really sure if I can keep up with all of this before April.

First off, the concept of worst-case scenarios and steps seem to feel a bit obtuse. Although I do understand how "steps" work and the sorting algorithms (somewhat) due to my experience in other CSC courses, I'm not really sure about time complexity under worst-case scenarios. Complexity was something that I didn't get before this course and I'm very sure that I'll be able to understand these concepts better.

On the other hand, I'm trying my best to get proofs so I can finish the assignment. Proof structures are not really a problem anymore, and I'm trying to get how to fill in the missing proofs to complete them.

Finally, there's the inevitable term test. I don't know what's going to be covered on the test, but I'm very sure that it's going to cover proofs and some other concepts that we had learned after Reading Week. After the assignment, I'm going to try to prepare for the test a bit earlier than before by writing down notes. I hope that things will go well, and I can say the same for my other courses which are also filled with work.

Reading week now

Whew! I'm satisfied by my term test mark which was completely unexpected.

The test wasn't too bad, and I found it to be pretty decent, but I never expected to get a mark this high. Especially when I didn't give any explaination for the answers in question 2.

Anyways, proofs (or proof structures) are getting easier to describe and I have tried to practice them in the tutorials. Hopefully, I'll be able to solve the actual proofs themselves after I have become more confident in making the proof structures. Assignment 2 is going to be a tricky one, so I'll need to understand this (with a little help from others) so I can fill in all the questions.

What a week...

Last week must have been one of the busiest times of the school year. I had two tests (including the CSC165 test), a reading response to write up on, a project in CSC148 that I'm still working on and a MAT137 assignment to deal with.

On the other hand, I've been trying my best to understand the functions and methods used in 165 and seen in Chapter 2 in the course notes. Negation, contrapositives, conjunctions/disjunctions and quantifiers are several examples that I have begun to recognize more. The test went surprisingly fine, despite my fears from the horror stories told by other CSC65 students, although I need to work on explaining symbolic forms better.

The next concepts will be proofs, as seen in Chapter 3 of the course notes and although I know how to do the beginning and end of proof structures, I don't really understand how to do the middle proof. I hope that I'll be able to understand better like I did with the Chapter 2 concepts and that I can fully grasp this course.

First assignment done!

Well, I finally got the first assignment done, but I feel that this is only the beginning of my struggles in this class. The test is looming near and I'll need to get as much aid for the test so I can understand the material. Combined that with my other subjects, and another test in CSC next week and this is going to be a very tough week.

I believe that if I keep this up, I could get through this week and eventually, the month of February just fine.

Thankfully, I understood the concept of implication a lot better than I did just a week ago and negation has become a habit for me in logic. The topics I enjoyed looking at were DeMorgan's Law, the law of equivalence and the truth tables, now that I have understood them better. It seems that the next topic is about proof and I am not very efficient in providing proof to my answers, so I am very cautious about this topic.

Thankfully, I've been focusing a lot more in class, and I've started taking notes on certain functions that are brought up, so maybe I can finally start learning properly because I believe that February is going to be a brutal and challenging month.