Gah... someday my body will tell me to stop doing my assignments on the last day it is due, today I've already handed two assignments in, now for the next one due tomorrow...
Assignment 1 is brutal, not in the sense of being extremely hard, nor the question being too ambiguous. It is challenging in the way that requires me to brainstorm, then to think about a possible way of writing a valid proof for that question.
Interesting enough, exploring the assignment questions can lead to valuable results. By looking into question 2, I found a binary way of proving the question (the real trouble is actually doing the proof - to tie this information together).
Today's class we started on proving recursively, the same stuff we did in CSC165. If only my brain is not that tired yet...
Monday, September 29, 2008
Saturday, September 27, 2008
End of third week
Date: Late by one day, grr...
I've handed in my second problem set to the instructor, the first part is extremely easy as it is just the exact problem we did in class with different numbers. The second part is, however, not quite as easy.
The main reason to this is that we can't use induction efficiently to proof the statement (it is still possible). I ended up doing it using proof of contradiction, and I doubt I'll get full mark for it because of that. Next time, I'll start the problem set way earlier so that I don't have to panic the day before the problem set is due.
In class we spent the whole class critiquing three different proofs, it was mildly funny to see that a proof can be constructed even though the base case can be wrong. I got lost on the more wordy proofs, but they were interesting in their own ways.
Back to the first assignment, I have to say that the assignment is quite challenging, and will take people awhile to figure out a reasonable proof to a question. I've figured out the pattern for question 2 already but I'm stuck at how to convert the pattern into a proof. Other than that, I just have to keep on trying :).
I've handed in my second problem set to the instructor, the first part is extremely easy as it is just the exact problem we did in class with different numbers. The second part is, however, not quite as easy.
The main reason to this is that we can't use induction efficiently to proof the statement (it is still possible). I ended up doing it using proof of contradiction, and I doubt I'll get full mark for it because of that. Next time, I'll start the problem set way earlier so that I don't have to panic the day before the problem set is due.
In class we spent the whole class critiquing three different proofs, it was mildly funny to see that a proof can be constructed even though the base case can be wrong. I got lost on the more wordy proofs, but they were interesting in their own ways.
Back to the first assignment, I have to say that the assignment is quite challenging, and will take people awhile to figure out a reasonable proof to a question. I've figured out the pattern for question 2 already but I'm stuck at how to convert the pattern into a proof. Other than that, I just have to keep on trying :).
Wednesday, September 24, 2008
Messing with bases.
After understanding the lecture taught in last class, I find today's lecture to be slightly easier. It is basically a modified version of induction where the base cases are unusual and has to be found and proved.
Writing out the proofs for today's problem is not that hard as well, the only thing I need to improve my proving (or problem solving) technique is to understand the question quickly and get a rough idea going as soon as possible, that way I can save valuable time for actually determine the solution. But this doesn't come easily as I need to get more exercises to practice, other than that, this will be the end of this post.
P.S. I hope my blog is not too messy (filled with entries).
Writing out the proofs for today's problem is not that hard as well, the only thing I need to improve my proving (or problem solving) technique is to understand the question quickly and get a rough idea going as soon as possible, that way I can save valuable time for actually determine the solution. But this doesn't come easily as I need to get more exercises to practice, other than that, this will be the end of this post.
P.S. I hope my blog is not too messy (filled with entries).
Monday, September 22, 2008
Overwhelmed
Date: Same day, finally I caught up!
We started off with a proof about the Principle of Well Ordering (PWO), then I kind of get lost on what Danny is teaching (I'm extremely tired today).
Basically, it's about the relations between PWO, Simple Induction (PSI), and Complete Induction (PCI). Which means a cycle or chain of implications joining them: PWO => PCI => PSI => PWO, and a few proofs on that.
Need sleep terribly, guess I'll review this lecture at some other time.
We started off with a proof about the Principle of Well Ordering (PWO), then I kind of get lost on what Danny is teaching (I'm extremely tired today).
Basically, it's about the relations between PWO, Simple Induction (PSI), and Complete Induction (PCI). Which means a cycle or chain of implications joining them: PWO => PCI => PSI => PWO, and a few proofs on that.
Need sleep terribly, guess I'll review this lecture at some other time.
Stamp like crazy!
Date: September 19, 2008
We handed our problem set 1 to the prof today, I wouldn't say it is too hard as the questions are just a variation of the proofs we did in lecture, still... I'm pessimistic that I might not get a high mark (from last year's experience with CSC165 assignments) since I'm afraid that I didn't explain every step clear enough.
Continued on with this course, we did a question that was given to us as an exercise back in CSC165, the question simply asks what postage can be formed with 2 different valued stamps.
I remembered solving this question rather easily in CSC165, but looking at the proof Danny wrote kind of threw me off at first, but I understood it right afterward.
We also managed to write down the definition of the Principle of Well Ordering, which is states as: every non-empty subset of natural number has a smallest integer. It's a rather obvious fact, but proving it will be kind of hard...
Back to the second problem set, oh dear... what number > k can I form a postage with 5 and 11 cent stamps...
I always have this kind of problem... staring blankly at a proof, guess it takes awhile for me to get the question and the rough idea to sink deeply in my head.
We handed our problem set 1 to the prof today, I wouldn't say it is too hard as the questions are just a variation of the proofs we did in lecture, still... I'm pessimistic that I might not get a high mark (from last year's experience with CSC165 assignments) since I'm afraid that I didn't explain every step clear enough.
Continued on with this course, we did a question that was given to us as an exercise back in CSC165, the question simply asks what postage can be formed with 2 different valued stamps.
I remembered solving this question rather easily in CSC165, but looking at the proof Danny wrote kind of threw me off at first, but I understood it right afterward.
We also managed to write down the definition of the Principle of Well Ordering, which is states as: every non-empty subset of natural number has a smallest integer. It's a rather obvious fact, but proving it will be kind of hard...
Back to the second problem set, oh dear... what number > k can I form a postage with 5 and 11 cent stamps...
I always have this kind of problem... staring blankly at a proof, guess it takes awhile for me to get the question and the rough idea to sink deeply in my head.
Trees and chocolates
Date: September 17, 2008
Today's lecture covers FBT (Full Binary Tree) and Complete induction. I find that I needed to catch up again with the basic properties of a Full Binary Tree, as I'm not good with this type of question back in CSC165.
Besides the trees, we also did a quite interesting problem with the chocolate bar (that makes me hungry by the way). The problem states: Every chocolate grid of n squares can be broken into seperate squares with n - 1 breaks.
As usual, we have our time to write out our own ideas about this question, which I think I did pretty good on that.
Now, the real challenge for me is to keep this up for every question I've encountered...
Today's lecture covers FBT (Full Binary Tree) and Complete induction. I find that I needed to catch up again with the basic properties of a Full Binary Tree, as I'm not good with this type of question back in CSC165.
Besides the trees, we also did a quite interesting problem with the chocolate bar (that makes me hungry by the way). The problem states: Every chocolate grid of n squares can be broken into seperate squares with n - 1 breaks.
As usual, we have our time to write out our own ideas about this question, which I think I did pretty good on that.
Now, the real challenge for me is to keep this up for every question I've encountered...
Second week
Date: September 15, 2008
After wasting off my weekend (besides being busy of course), I'm back at school again in the second week of my second year.
We learned Prime factorization, which is defines as: Prime factorization of n is a sequence of prime numbers with product of n. Something useful for proofs and was talked about it in CSC165.
As well, we moved on from the Principles of Simple Induction to a new flavour of induction called - Complete induction. Complete induction basically means if every elements up to n-1 implies P(n), then that suggests every n is true for a given claim (P(n)).
The special thing about Complete induction is that you don't need base cases at all (yipee?), well... it still wouldn't hurt to follow the structure in CSC165 by putting a few in. Complete induction is extremely useful in the case when the base case is either ambiguous or cannot be formed completely, so that we can just move along with the induction step.
Basically this is today's lecture, using Complete induction on claims relating to Prime factorization, oh well... that's it for this post!
After wasting off my weekend (besides being busy of course), I'm back at school again in the second week of my second year.
We learned Prime factorization, which is defines as: Prime factorization of n is a sequence of prime numbers with product of n. Something useful for proofs and was talked about it in CSC165.
As well, we moved on from the Principles of Simple Induction to a new flavour of induction called - Complete induction. Complete induction basically means if every elements up to n-1 implies P(n), then that suggests every n is true for a given claim (P(n)).
The special thing about Complete induction is that you don't need base cases at all (yipee?), well... it still wouldn't hurt to follow the structure in CSC165 by putting a few in. Complete induction is extremely useful in the case when the base case is either ambiguous or cannot be formed completely, so that we can just move along with the induction step.
Basically this is today's lecture, using Complete induction on claims relating to Prime factorization, oh well... that's it for this post!
Saturday, September 20, 2008
Experience after the first week
Date: September 12, 2008
A week has gone by for my second year, and it just seems so different from the start of my first year. I still remember the confusion of first year, running around trying to find the right lecture room, the massive workload, the amount of new material there is to learn...
It's all different now, with the workload and schedule lowered drastically, it's much better for me to spend time equally for all my courses, so that I won't repeat the mistake of CSC165.
Again, we cover induction from CSC165, it really isn't that hard. Strangely, the proof that we did in the first week is actually applicable in a course like STA247... how handy!
To be honest, compared to my other courses, this course has the most workload out of all 5. My reasoning is that we needed that much more practice and experience to get the most out of it for this course, as we can be better prepared for higher level CSC theory courses.
...I'm not (really!) complaining about the workload here, as I have to say CSC165 followed this pattern and that everything I learned is through though assignments and exercises, and the information is very valuable and useful in courses besides Computer Science.
A week has gone by for my second year, and it just seems so different from the start of my first year. I still remember the confusion of first year, running around trying to find the right lecture room, the massive workload, the amount of new material there is to learn...
It's all different now, with the workload and schedule lowered drastically, it's much better for me to spend time equally for all my courses, so that I won't repeat the mistake of CSC165.
Again, we cover induction from CSC165, it really isn't that hard. Strangely, the proof that we did in the first week is actually applicable in a course like STA247... how handy!
To be honest, compared to my other courses, this course has the most workload out of all 5. My reasoning is that we needed that much more practice and experience to get the most out of it for this course, as we can be better prepared for higher level CSC theory courses.
...I'm not (really!) complaining about the workload here, as I have to say CSC165 followed this pattern and that everything I learned is through though assignments and exercises, and the information is very valuable and useful in courses besides Computer Science.
The beginning of a new semester
Date: September 10, 2008
Yes, the date above is wrong, but I'm a bit late at writing this, so... I'll try to not confuse too many people from now on. I'll try to keep my CSC165 way by writing a post after every lecture.
Distractions aside:
After all the administration and stuff, I finally get the first taste for this class. We start with basic "principles of simple induction" that was taught in CSC165 as well, but I'm not so sure whether this was a review or not.
Again, the uncomfortableness started again, at times I still can't believe how much time and energy is saved from relaxing the structure of a quick induction proof. For lazy people like me this is a good thing, but without the support of a properly placed structure, I get confused rather easily.
The proof in the course is also not that hard to begin with, as I did the question (and it's many variations) back in high school. I could still recall with horror the brutality of my high school "Algebra and geometry" test/exam. The experience from that course, even if it is horrible, did get me prepared for most of university courses.
Yes, the date above is wrong, but I'm a bit late at writing this, so... I'll try to not confuse too many people from now on. I'll try to keep my CSC165 way by writing a post after every lecture.
Distractions aside:
After all the administration and stuff, I finally get the first taste for this class. We start with basic "principles of simple induction" that was taught in CSC165 as well, but I'm not so sure whether this was a review or not.
Again, the uncomfortableness started again, at times I still can't believe how much time and energy is saved from relaxing the structure of a quick induction proof. For lazy people like me this is a good thing, but without the support of a properly placed structure, I get confused rather easily.
The proof in the course is also not that hard to begin with, as I did the question (and it's many variations) back in high school. I could still recall with horror the brutality of my high school "Algebra and geometry" test/exam. The experience from that course, even if it is horrible, did get me prepared for most of university courses.
Welcome to CSC 236 Course Log!
Heh... guess I'm a bit late at this.
Hello all, this is my journal entry for CSC 236, where I will put my own personal reactions (to the course), problem solving solutions and what I've learned here on this blog.
First off, I will discourage anyone from viewing this blog unless they are a part of CSC236, either a fellow classmate or the instructor/TAs. Just in case they don't understand what I'm talking about and wasting their own time :P.
Onwards:
First Class (September 8, 2008):
After a relaxing summer, it's time to go back to school for my second year at U of T!
The knowledge of first year told me to never-ever take two courses right next to each other and as well not to take early morning courses. Well, there's nothing I can do about this course (unfortunately, I think that 10 a.m. classes are still way too early), so I guess I'll have to handle it for this semester.
CSC236 is, in my opinion, the continuation of CSC165 with more depth and material, having gone through CSC165 I thought I'm prepared with most of the course material...
...And I was so wrong, well... not what we are learning of course. Induction was taught over and over again in high school and rather forcefully in MAT137, so I have a clear grasp on that. But after reading through chapter 0 in the course note, I discovered that I still have a bit more gap to fill in order to succeed in this course.
Not only that, I *almost* forgot a lot of 165 material (thankfully it didn't take that long to get everything back in my head) due to the 4 month break. I'm also a bit not used to relaxing the proof structure that was done for the whole semester in 165, guess I'll have to get more comfortable with that.
The last thing that I'm uncomfortable with is to write the course journal out in public like this, I really wished to have the old CSC165 wiki/SLoG back.
Hello all, this is my journal entry for CSC 236, where I will put my own personal reactions (to the course), problem solving solutions and what I've learned here on this blog.
First off, I will discourage anyone from viewing this blog unless they are a part of CSC236, either a fellow classmate or the instructor/TAs. Just in case they don't understand what I'm talking about and wasting their own time :P.
Onwards:
First Class (September 8, 2008):
After a relaxing summer, it's time to go back to school for my second year at U of T!
The knowledge of first year told me to never-ever take two courses right next to each other and as well not to take early morning courses. Well, there's nothing I can do about this course (unfortunately, I think that 10 a.m. classes are still way too early), so I guess I'll have to handle it for this semester.
CSC236 is, in my opinion, the continuation of CSC165 with more depth and material, having gone through CSC165 I thought I'm prepared with most of the course material...
...And I was so wrong, well... not what we are learning of course. Induction was taught over and over again in high school and rather forcefully in MAT137, so I have a clear grasp on that. But after reading through chapter 0 in the course note, I discovered that I still have a bit more gap to fill in order to succeed in this course.
Not only that, I *almost* forgot a lot of 165 material (thankfully it didn't take that long to get everything back in my head) due to the 4 month break. I'm also a bit not used to relaxing the proof structure that was done for the whole semester in 165, guess I'll have to get more comfortable with that.
The last thing that I'm uncomfortable with is to write the course journal out in public like this, I really wished to have the old CSC165 wiki/SLoG back.
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