Dear Blog,
For my last blog of the course, I thought I would just conclude everything about this course, and by everything, I mean my feelings, struggles, achievements, etc. This was definitely a challenging course, probably the most challenging course I had all semester. But it was also probably my favourite. I thoroughly enjoyed the challenges this course brought me.
My favourite topic was probably proofs as a whole. I enjoyed proving functions to be bound below or above each other. My least favourite topic has probably been counting steps and halting. These two concepts are still make me struggle and I most definitely must review them before the final exam.
For the most part, my marks in this course have fluctuated, but the most important thing is the final exam. I did pretty well on Assignment 1, not so well on Assignment 2 and mediocre on the mid terms and tutorial quizzes. I hope to get a fairly good mark on my slogs to give me a bit of an extra mark boost. I really want a good mark in this course to ensure I get into the CS subject post in my second year. I'll need at least a 60% in this course, and a 60% in CSC148 with an average of 67% between the two.. so wish me luck.
If you get the chance, take a look at this student's blog. http://csc165judy2014.blogspot.ca/. I thought it was really well done. The layout was spectacular and the posts were sufficient and informative. It's difficult to find well done blogs like that one. I really enjoyed her post on November 19, her problem solving episode. It was quite the brain teaser.
Well, thanks for reading all of my posts throughout the term. Wish me luck on the final!
Over and out,
-J.M.
Tuesday, December 2, 2014
Problem-Solving Episode
Dear Blog,
I am going to walk you through a problem-solving episode, using Polya's problem-solving technique. This problem is one we tried during a lecture. It is called Penny Piles. The problem states that you are sitting in front of two drawers. The left drawer contains 64 pennies and the right drawer contains 0 pennies. The problem is to figure out if you can arrange the drawers so that one has 48 pennies using the following operations of l and r.
l: if the left drawer has an even number of pennies, you may transfer half to the right drawer
r: if the right drawer has an even number of pennies, you may transfer half to the left drawer.
After doing this, you must choose a number other than 48 in the range [0,64] and try to arrive with that many pennies in one drawer with the same initial position. It then asks if there are any numbers in that range that are impossible to achieve.
1. Understand the problem:
At first glance, this problem was super confusing, but after re-reading the problem a few times, I fully understood it. Basically you start with 64 pennies in one drawer and 0 in the other. You are allowed to take half of the pennies from the drawer with 64 and put them in the other, leaving you with 32 and 32. You can continue doing this with both drawers as long as they contain an even number of pennies.
2. Devise a plan:
I started out by trying to make one drawer have 48 and one have 16, satisfying the first condition.
I will then try to get other numbers in the range [0,64], by continuously dividing numbers by two and trying to arrive at new numbers.
3. Carrying out the Plan:
Simply through trial and error, I realize that every number in the range [0,64] is possible to achieve. (This took a while).
4. Looking Back
Since this step involves looking back, I did just that, and I realized, there has to be a much easier way to solve this problem without going through every possible number combination. So, I devised a new plan. I tried many times to think of an equation for this problem, but have so far failed. But this problem has stuck with me and every now and then I still try. I have drawn out many branches of combinations and it seems to me that it if this is a function, it is an exponential function, and it may be important to start at an even square, like 64 or 144. For the time being, I am stumped, but this is a very interesting problem.
Thank you,
-J.M
I am going to walk you through a problem-solving episode, using Polya's problem-solving technique. This problem is one we tried during a lecture. It is called Penny Piles. The problem states that you are sitting in front of two drawers. The left drawer contains 64 pennies and the right drawer contains 0 pennies. The problem is to figure out if you can arrange the drawers so that one has 48 pennies using the following operations of l and r.
l: if the left drawer has an even number of pennies, you may transfer half to the right drawer
r: if the right drawer has an even number of pennies, you may transfer half to the left drawer.
After doing this, you must choose a number other than 48 in the range [0,64] and try to arrive with that many pennies in one drawer with the same initial position. It then asks if there are any numbers in that range that are impossible to achieve.
1. Understand the problem:
At first glance, this problem was super confusing, but after re-reading the problem a few times, I fully understood it. Basically you start with 64 pennies in one drawer and 0 in the other. You are allowed to take half of the pennies from the drawer with 64 and put them in the other, leaving you with 32 and 32. You can continue doing this with both drawers as long as they contain an even number of pennies.
2. Devise a plan:
I started out by trying to make one drawer have 48 and one have 16, satisfying the first condition.
|
Steps
|
Left
|
Right
|
|
0
|
64
|
0
|
|
1
|
32
|
32
|
|
2
|
48
|
16
|
I will then try to get other numbers in the range [0,64], by continuously dividing numbers by two and trying to arrive at new numbers.
3. Carrying out the Plan:
Simply through trial and error, I realize that every number in the range [0,64] is possible to achieve. (This took a while).
4. Looking Back
Since this step involves looking back, I did just that, and I realized, there has to be a much easier way to solve this problem without going through every possible number combination. So, I devised a new plan. I tried many times to think of an equation for this problem, but have so far failed. But this problem has stuck with me and every now and then I still try. I have drawn out many branches of combinations and it seems to me that it if this is a function, it is an exponential function, and it may be important to start at an even square, like 64 or 144. For the time being, I am stumped, but this is a very interesting problem.
Thank you,
-J.M
Monday, December 1, 2014
Other Slogs
Hello,
This will be a short blog because I just wanted to express some disappointment in my blog. Throughout the term, I would check other slogs to maybe gain some new insight or see how other people are finding the course material but almost all of the slog URLs that I clicked on contained 1 or 2 entries. It was tough to find some interesting information.
In other news, my group and I just handed in assignment 3. The last couple of questions were definitely difficult. I found it extremely difficult proving that there exists a function that is not in big O(g) and not in big Omega(g). I had to create a piecewise function for g and I hope my answer sufficed. Proofs involving limits on that assignment also confused me quite a bit. It is just the structure of the proof that I struggle with. Other than that, I will just be focused on the finals for all of my courses, especially this one as it is the most important. I need a good mark in this course to get into the CS subject post.
Wish me luck!
-J.M
This will be a short blog because I just wanted to express some disappointment in my blog. Throughout the term, I would check other slogs to maybe gain some new insight or see how other people are finding the course material but almost all of the slog URLs that I clicked on contained 1 or 2 entries. It was tough to find some interesting information.
In other news, my group and I just handed in assignment 3. The last couple of questions were definitely difficult. I found it extremely difficult proving that there exists a function that is not in big O(g) and not in big Omega(g). I had to create a piecewise function for g and I hope my answer sufficed. Proofs involving limits on that assignment also confused me quite a bit. It is just the structure of the proof that I struggle with. Other than that, I will just be focused on the finals for all of my courses, especially this one as it is the most important. I need a good mark in this course to get into the CS subject post.
Wish me luck!
-J.M
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