Week 11
Of course the professor saves the best for last. Or not.
This week the stuff on halting function and countability I felt like were a little confusing. I don't know if it's summer but I am rather confused. The idea of not having a proof or solution to solve a halting function really baffled me not just conceptually but also mathematical (proof-wise). It really baffled me that no one has yet to create such a function though it seems rather like an easy question. As for the proof of it, I really have no clue on how to use reduction to show that a certain function is non-computable knowing halt is impossible to compute. Maybe I just need to see more examples for this to be clear but definitely just hearing it once in lecture isn't good enough.
And for the problem-solving episode, I will use the product of sums problem. The problem states to find the maximum product for the sum of a certain number. My approach to this solution was through trial and error. At first I knew that number of its square always produce the largest sum and thought this was correct. However, a sum of [2, 3, 3] or (8) is 18 and not 16. From this example, I used the idea of having the longest possible length for your sum of the number and having each number in the list different from one another by exactly one or the same. So then I used example, [3, 3, 3, 3] or (12) and found this to also work for my solution as well as [3, 3, 3, 3, 3] or (15). Here this I knew the general idea to finding the solution to the problem though to be honest I wasn't able to come up with some sort of general expression.
And it was a fun time blogging. And I hope you enjoyed this as much as I did. :)
Friday, 5 April 2013
Week 10
So this week really wasn't a challenge. The stuff on Big-Omega, solving a problem for two functions, bounded functions and the limit property was pretty straight forward. Specifically the contents as Big-Omega as it was literally the same as Big-Oh except one sign was just switched around. Bounded proofs was like using Big-Oh but just solving for an upper and lower bound instead of just one one bound. Limits is just basic calculus.
Hence this week was rather relaxing for me. :)
So this week really wasn't a challenge. The stuff on Big-Omega, solving a problem for two functions, bounded functions and the limit property was pretty straight forward. Specifically the contents as Big-Omega as it was literally the same as Big-Oh except one sign was just switched around. Bounded proofs was like using Big-Oh but just solving for an upper and lower bound instead of just one one bound. Limits is just basic calculus.
Hence this week was rather relaxing for me. :)
Thursday, 28 March 2013
Week 9
For some reason the contents this week seemed to make more sense to me than last.
At first I was a little bit confused on what and how to do these proofs and I was little confused with the idea of over and under-estimating certain terms when doing this. But all in all it's just really showing for what values of f(n) that is greater than (for big-O) or less than (for delta), therefore we can just overestimate/underestimate and omit certain values to make the equality still true. Proofs with complexity I find is not as bad as I've heard it to be. It seemed to have made more sense when not dealing with the amount of steps in a piece of code (for me at least).
For some reason the contents this week seemed to make more sense to me than last.
At first I was a little bit confused on what and how to do these proofs and I was little confused with the idea of over and under-estimating certain terms when doing this. But all in all it's just really showing for what values of f(n) that is greater than (for big-O) or less than (for delta), therefore we can just overestimate/underestimate and omit certain values to make the equality still true. Proofs with complexity I find is not as bad as I've heard it to be. It seemed to have made more sense when not dealing with the amount of steps in a piece of code (for me at least).
Week 8
So this week we continue doing more of the complexity stuff but this time we introduce proofs into them.
The stuff on proofs using complexity I find is rather confusing. I find it the main problem for me is how to come up with a general expression from a piece of code.
Next, we did stuff on slicing and how it would affect run time. I am actually still rather confused about how the idea of how certain run times work and how many steps are involved in this. And as stated above I find it confusing to form a general expression for number of steps for a piece of code.
So this week we continue doing more of the complexity stuff but this time we introduce proofs into them.
The stuff on proofs using complexity I find is rather confusing. I find it the main problem for me is how to come up with a general expression from a piece of code.
Next, we did stuff on slicing and how it would affect run time. I am actually still rather confused about how the idea of how certain run times work and how many steps are involved in this. And as stated above I find it confusing to form a general expression for number of steps for a piece of code.
Week 7
Reading week was nice and only another half a semester to go. However, remaining of the semester I heard is rather difficult when we begin to do proofs with complexity.
So this week, we finished off the using proofs structures and were introduced a new way called proof by cases. My first thoughts on this was it really wasn't that difficult. It was really simply proofing a certain claim for more than one cases but in one statement. So overall, the proofs I feel relatively fine with.
For rest of the week, we began determining the run time of certain code (otherwise called complexity). I'm still rather slow on how many steps and what is meant by the upper bound and lower bound when doing these; so I am rather a little bit scared for this in the future.
Reading week was nice and only another half a semester to go. However, remaining of the semester I heard is rather difficult when we begin to do proofs with complexity.
So this week, we finished off the using proofs structures and were introduced a new way called proof by cases. My first thoughts on this was it really wasn't that difficult. It was really simply proofing a certain claim for more than one cases but in one statement. So overall, the proofs I feel relatively fine with.
For rest of the week, we began determining the run time of certain code (otherwise called complexity). I'm still rather slow on how many steps and what is meant by the upper bound and lower bound when doing these; so I am rather a little bit scared for this in the future.
Saturday, 2 March 2013
Week 6
And now for the fun part. From doing proof structures, now we begin the actually proofs themselves.
So far this week, the professor has showed us the basic ideas of how to prove a certain proof. The proofs themselves really are just a bunch of algebraic manipulations to make the antecedent and consequent the same; which seems relatively easy for now. Some of the other things we started was using the contrapositive to prove a claim because it simplifies proving the claim as opposed to using direct proof (solving the proof as it is on the question). We also started slightly on the proof structures for the existential. Like the universal proofs, the structure is rather very simple to follow and as for the proofs for the existential, we get to set variable(s) -- which shows that it is in domain -- then substitute that variable into the claim and show that claim is true.
Some of the proof stuff is rather strange, because we need to define certain words when proving a claim. For example, in certain proof it is necessary to show that the definition of an odd number is n = 2k + 1. But as for the proofs so far, they seem a little bit understandable but I'm not so confident in my abilities to solve them.
And now for the fun part. From doing proof structures, now we begin the actually proofs themselves.
So far this week, the professor has showed us the basic ideas of how to prove a certain proof. The proofs themselves really are just a bunch of algebraic manipulations to make the antecedent and consequent the same; which seems relatively easy for now. Some of the other things we started was using the contrapositive to prove a claim because it simplifies proving the claim as opposed to using direct proof (solving the proof as it is on the question). We also started slightly on the proof structures for the existential. Like the universal proofs, the structure is rather very simple to follow and as for the proofs for the existential, we get to set variable(s) -- which shows that it is in domain -- then substitute that variable into the claim and show that claim is true.
Some of the proof stuff is rather strange, because we need to define certain words when proving a claim. For example, in certain proof it is necessary to show that the definition of an odd number is n = 2k + 1. But as for the proofs so far, they seem a little bit understandable but I'm not so confident in my abilities to solve them.
Week 5
Here is where I hear things begin to get interesting. The beginning of proofs. Several of friends have told me that the content on proof is where things seem to get rather strange.
My thoughts so far on the introduction of proof is rather simple; we started the small details of proofs such as writing them with structure first to get the hang of them before actually proving certain claims. The basic idea of the proof structures are to assume certain parts of the claim such as the what set x (just a random variable) belongs to and the antecedent. This is to apparently introduce the set as well as the implication (which is written at the bottom from basic structuring) which is then eventually proves the consequent is true.
So far, so good but I am rather scared.
Here is where I hear things begin to get interesting. The beginning of proofs. Several of friends have told me that the content on proof is where things seem to get rather strange.
My thoughts so far on the introduction of proof is rather simple; we started the small details of proofs such as writing them with structure first to get the hang of them before actually proving certain claims. The basic idea of the proof structures are to assume certain parts of the claim such as the what set x (just a random variable) belongs to and the antecedent. This is to apparently introduce the set as well as the implication (which is written at the bottom from basic structuring) which is then eventually proves the consequent is true.
So far, so good but I am rather scared.
Monday, 25 February 2013
Week 4
Though I believe I have gotten a lot better at manipulating certain claims, I am rather unsure of how I did on assignment 1. A part of me believe that I did rather while a part of me feels as if I did the assignment completely wrong. As was, my partner and I did not have many arguments on the assignment; as we had no idea what we were even doing in all fairness.
Now for this week's content, the claims on limits didn't really make sense to me. I didn't understand what the professor meant when he outline two lines near a point horizontally and vertically. I had a rough idea that it was on limits but I didn't understand how this applied to claims. As was, the stuff on the my enemy and me choosing a certain variable to make a claim true didn't make any sense to me at all. I didn't get how the position of E (exists), A (all) changes the claim... Anyways, it looks like it is back to hours and hours and reviewing for me.
Though I believe I have gotten a lot better at manipulating certain claims, I am rather unsure of how I did on assignment 1. A part of me believe that I did rather while a part of me feels as if I did the assignment completely wrong. As was, my partner and I did not have many arguments on the assignment; as we had no idea what we were even doing in all fairness.
Now for this week's content, the claims on limits didn't really make sense to me. I didn't understand what the professor meant when he outline two lines near a point horizontally and vertically. I had a rough idea that it was on limits but I didn't understand how this applied to claims. As was, the stuff on the my enemy and me choosing a certain variable to make a claim true didn't make any sense to me at all. I didn't get how the position of E (exists), A (all) changes the claim... Anyways, it looks like it is back to hours and hours and reviewing for me.
Sunday, 27 January 2013
Week 3
Thinking back this semester has seem to gone by pretty quick. And yet this course has been nothing but frustration since the beginning.
The contents that were covered this week made somewhat sense to me. Things such as the truth tables, negation, De Morgna's Law and disjunction and conjunction made sense to me; since these ideas were often used in python. But the other things such as the tautology, satisfiability, and unsatisfiablity had me a little confused.
And to end off, I would like to say that posting sample questions with solutions definitely helped a lot. Prior to the quiz, I was baffled as to how I was suppose to get good at doing claims (and getting a good grade) when I simply can't practice and apply what I am and was learning.
Thinking back this semester has seem to gone by pretty quick. And yet this course has been nothing but frustration since the beginning.
The contents that were covered this week made somewhat sense to me. Things such as the truth tables, negation, De Morgna's Law and disjunction and conjunction made sense to me; since these ideas were often used in python. But the other things such as the tautology, satisfiability, and unsatisfiablity had me a little confused.
And to end off, I would like to say that posting sample questions with solutions definitely helped a lot. Prior to the quiz, I was baffled as to how I was suppose to get good at doing claims (and getting a good grade) when I simply can't practice and apply what I am and was learning.
Sunday, 20 January 2013
As the days get colder, the CSC165 course gets harder. Meanwhile people are talking how they are struggling to shovel snow and deal with winter's nightmares, I will be talking about my struggles of the difficulties yet achievements this past week.
As soon as I thought I was beginning to understand the content the week before, things started picking up and began to become rather difficult. The thing that has me baffled this time around is using "natural" language and expressing them into an implication of P -> Q. What has me confused is how to interpret certain phrases and distinguishing which word/phrase represents P or Q. Although I have somewhat of an idea of how certain P or Qs are the way they are, I find distinguishing which one is which on my own rather troublesome.
Another concern I have is understanding the vacuous truth. But even so nothing but a little bit of reviewing would this make a little bit more sense as I am actually more scared of the assignment more than anything else. Sometimes I feel like this course makes me feel Dumb.
Friday, 11 January 2013
Winter is coming; or at least the Winter 2013 Session at the University of Toronto. With a new semester ahead, there awaits many challenges and opportunities that are presented to us. One of those challenges include the course CSC165 (Mathematical Expression and Reasoning for Computer Science).
Coming into this course, I was actually very scared. I have heard the many stories of how difficult this course was and how my friend almost failed. So far my first impression of this course is that it seems fairly different but for me I find that this course is more frustrating than enjoying for me. That is because a little different than the MAT135 (Calculus I) course, the CSC165 uses certain claims about statements and decide whether they are universal or whether there exists such a claim. This style of thinking is a lot similar to the MAT135 stuff, in terms of the certain mathematics claims like whether a function is continuous function is a differentiable. However, I was never very good at these kinds of mathematical concepts and theories instead I was stronger at the computing aspect of calculus than its theorems. And this is probably the reason why this course has been nothing but pain and frustration for me so far.
In specific what has been challenging for me in this course is adapting to understand what the correlation the Venn diagrams had with a claim and how the quantifiers functioned. The Venn diagrams in specific was most troubling to me. The reason being was and are things that were placed within the Venn diagram. I didn't understand what the question mark, circle, X symbols mean and how these symbols proved a certain claim false or true. However, having spent 1-2 hours a day reviewing over my notes again and having gotten help in tutorial, the content began to become clear and made more sense. Another one of my frustrations included how a list comprehension functioned and how it is used in a certain claim. The idea of whether one list of elements is a subset of another list of element had me confused for several days as well as the symbols that are associated with them. Having said that, my first intention was to try and test out these quantifiers function and see what the outcome would produce. At first, I didn't understand why the outcome were what they were but sooner or later, some of the code started to make sense. I started to understand what code did and this helped me greatly towards understanding how it is used in the claim. And having learned how the code functioned did this course really start to make a little bit more sense.
Though I have expressed many negative reactions to the course material, I feel a little confident about the course material so far. For example, some of the things that I've learn this week includes how to verify or falsify a claim using both universal and existential quantifiers, how claims can be represented in Venn diagrams, what certain symbols meant in a claim, and what a list comprehension is. As to my achievements this week, I would consider writing the quiz with rather great confidence an achievement in itself. The reason being is that before I had written the quiz, I was completely lost as to what we were doing in class. I even almost cried as I began leaving the classroom. Strangely enough, the night before the quiz, the content started to make sense to make after hours of reviewing the course notes. Not only did that help me but the exercise we did in tutorial was a great confidence booster as it left many doubts I had about the content behind.
As you can tell by now this course has been rather troublesome but in a way still somewhat doable. Although, I feel a little bit more confident with the course material so far, I have already prepare for the worst and intend on seeking office hours sometime in the near future until all this sense makes sense. But until then all I can do is Dream On.
Coming into this course, I was actually very scared. I have heard the many stories of how difficult this course was and how my friend almost failed. So far my first impression of this course is that it seems fairly different but for me I find that this course is more frustrating than enjoying for me. That is because a little different than the MAT135 (Calculus I) course, the CSC165 uses certain claims about statements and decide whether they are universal or whether there exists such a claim. This style of thinking is a lot similar to the MAT135 stuff, in terms of the certain mathematics claims like whether a function is continuous function is a differentiable. However, I was never very good at these kinds of mathematical concepts and theories instead I was stronger at the computing aspect of calculus than its theorems. And this is probably the reason why this course has been nothing but pain and frustration for me so far.
In specific what has been challenging for me in this course is adapting to understand what the correlation the Venn diagrams had with a claim and how the quantifiers functioned. The Venn diagrams in specific was most troubling to me. The reason being was and are things that were placed within the Venn diagram. I didn't understand what the question mark, circle, X symbols mean and how these symbols proved a certain claim false or true. However, having spent 1-2 hours a day reviewing over my notes again and having gotten help in tutorial, the content began to become clear and made more sense. Another one of my frustrations included how a list comprehension functioned and how it is used in a certain claim. The idea of whether one list of elements is a subset of another list of element had me confused for several days as well as the symbols that are associated with them. Having said that, my first intention was to try and test out these quantifiers function and see what the outcome would produce. At first, I didn't understand why the outcome were what they were but sooner or later, some of the code started to make sense. I started to understand what code did and this helped me greatly towards understanding how it is used in the claim. And having learned how the code functioned did this course really start to make a little bit more sense.
Though I have expressed many negative reactions to the course material, I feel a little confident about the course material so far. For example, some of the things that I've learn this week includes how to verify or falsify a claim using both universal and existential quantifiers, how claims can be represented in Venn diagrams, what certain symbols meant in a claim, and what a list comprehension is. As to my achievements this week, I would consider writing the quiz with rather great confidence an achievement in itself. The reason being is that before I had written the quiz, I was completely lost as to what we were doing in class. I even almost cried as I began leaving the classroom. Strangely enough, the night before the quiz, the content started to make sense to make after hours of reviewing the course notes. Not only did that help me but the exercise we did in tutorial was a great confidence booster as it left many doubts I had about the content behind.
As you can tell by now this course has been rather troublesome but in a way still somewhat doable. Although, I feel a little bit more confident with the course material so far, I have already prepare for the worst and intend on seeking office hours sometime in the near future until all this sense makes sense. But until then all I can do is Dream On.
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