I must apologize in advance, as I suspect these posts are becomes increasingly tedious and poorly written.
The new car smell on CSC236 is wearing off, and it is revealing itself as what it really as: a course about algorithms! Who saw that coming. And I'd be lying if I claimed to be on top of things at the moment. So far, a combination of the knowledge I acquired in the lectures, a review of the annotated slides, and a review of the Course Notes got me through any topic. But times are changing. I cannot follow the lectures completely, because at some point, they all become dialogues between Prof. Heap and a couple of students who grasp the material. It is totally and absolutely my fault for not voicing this in lectures, but hey, I have an image to maintain! As a result, I think I am going to make use of Prof. Heap's office hours a lot more in the coming weeks. The annotated slides are only useful if you have a good pre-existing understanding of the material from the corresponding lecture, which is not always the case anymore. And the lecture material seems to be beginning to diverge from the Course Notes. Understanding everything in the lecture is become more and more key, and at the same time, harder and harder. At least for me.
In other less depressing news, I spoke to Prof. Heap about the structure of my proofs on the term tests (see Week 2), and he told me that they seemed valid to him!! That was such a sigh of relief for me. At least two extra marks, here I come!
Sunday, 28 October 2012
Monday, 22 October 2012
Recurrences and the mid-term
I got my mid-term back and I can't really say I am happy with my mark. I lost 3 marks, all for starting my proofs with an existential assumption (ex. "Assume there exists n in natural numbers, such that P(n)"). I absolutely believe that such an assumption is valid at the start of a proof, especially given that the proof is preceded by a base case. I think that differentiating between "Assume there exists n such that P(n)" and "Let there be n such that P(n)" is not very intuitive. What does "be" mean anyways? Doesn't it signify the existence of the subject? In any case, I plan to go and speak to Prof. Heap during his office hours, so that I can either be proven wrong, or make sure that a re-marking appeal is a reasonable option for me (really hoping for the latter).
Other than that, I'm hanging on the course material with the skin of my teeth. These recursive functions are tricky, and doing proofs about them requires a level of trial and error, and certain tricks, that I'm not completely comfortable with. I've been referring to the Course Notes a lot more lately to help me grasp the material. Some steps and assumptions in the Course Notes seem very arbitrary at this point to me. For example, splitting the coefficient 'k' in knlog(n) (MergeSort) to two separate constants 'c' and 'd', was something that I could not have come up with on my own, even if I stared at the problem (proving the upper bound for the runtime of MergeSort) for a year. Hopefully by spending more time going over the Course Notes, things will get better soon.
Other than that, I'm hanging on the course material with the skin of my teeth. These recursive functions are tricky, and doing proofs about them requires a level of trial and error, and certain tricks, that I'm not completely comfortable with. I've been referring to the Course Notes a lot more lately to help me grasp the material. Some steps and assumptions in the Course Notes seem very arbitrary at this point to me. For example, splitting the coefficient 'k' in knlog(n) (MergeSort) to two separate constants 'c' and 'd', was something that I could not have come up with on my own, even if I stared at the problem (proving the upper bound for the runtime of MergeSort) for a year. Hopefully by spending more time going over the Course Notes, things will get better soon.
Thursday, 11 October 2012
Bounds, Well-ordering, and A1
We're already a month into the semester! They say time flies by when... actually time flies by all the time. Before I know it, I will be a broken down old man. But for now, I will continue to distract myself from my mortality by doing things like going to school, and learning about computers.Which swiftly bring me to the topic at hand: my favorite course of all time, CSC236!!
I was perhaps ten minutes into the first CSC236 lecture of the year, when I high-fived myself out of pure joy. I was really glad that I had taken MAT137 over MAT135 ("Calculus!" not "Calculus") last year. When I told my friend about my experience of extensively using induction last year in relation to limits, behaviours of functions, bounds on series, and a lot of other stuff, the response that I got was a blank stare. So while a few of my friends struggled for the first few classes to wrap their minds around the concept of induction itself, and why it is valid at all, I certainly felt like I had a head-start in the course.
By the time "Well Ordering" had arrived, the course was beginning to get a tiny bit more challenging. Even though I had used the same principle in the aforementioned math course in relation to bounds and sequences, the "round-robin tournament" proof done in class by Prof. Heap threw me off. While I understood the logic of the proof, it still felt invalid to me. So I went home, read over the annotated slides (by the way, THE GREATEST IDEA OF ALL TIME), and I still felt that the proof was invalid. So I did what any scholar in this day and age does: I loaded up Wikipedia. More specifically, the "round-robin tournament" page. It turned out that I had a false understanding of what a round-robin tournament was to begin with. My understanding was that the tournament is a elimination-style one-match-at-a-time tournament, while that is not the case at all. Either I had a lapse of concentration in the lecture and the concept was explained, or that everyone knows what a round-robin tournament is and I just had a gaping hole in my knowledge. In any case, everything was back to normal.
I felt like I was ready for the final exam right then and there... but then Assignment 1 happened. Three straightforward questions which collectively took 45 minutes, and then a monster in the form of question 4. Binary strings. Occurrences of 10s and 01s. I must have written 3 or 4 separate proofs for that question, but none of them felt completely valid to me. It was Friday, the assignment was due that night, and I was stuck. I didn't know what to do. It was actually Prof. Heap's hint in class about starting out with a stronger claim that gave me the idea. So like any geniuses I've seen in the movies who get a great idea in the middle of a class, I got up and left and knocked over everyone's papers and almost tripped on someone's bag, walked to the closest window and took out a marker and started writing on the glass. OK, none of that happened, but I finished my proof after class, and just to make sure that my approach was valid, I went to the extra office-hours on Friday, and indirectly, and without getting into too much detail, explained my approach, and Prof. Heap indirectly, and without getting into too much detail, replied that it sounded valid.
I must apologize for having such a long post, and I feel for Prof. Heap and the TAs who have to read several hundred of poorly written, very similar posts about students doing proofs. But hey, that is what you get when you shut down the alternative "Student Tweets" assignment, which would've made life easier for all parties involved.
Stay tuned for a preview from next week's episode of SIAMAK'S CSC236 SLOG:
.
.
.
Mid-term exam!!! Was it a success or failure? Find out if this student aced the test, or if he was dealt a tough hand! Next week on SIAMAK'S CSC236 SLOG.
I was perhaps ten minutes into the first CSC236 lecture of the year, when I high-fived myself out of pure joy. I was really glad that I had taken MAT137 over MAT135 ("Calculus!" not "Calculus") last year. When I told my friend about my experience of extensively using induction last year in relation to limits, behaviours of functions, bounds on series, and a lot of other stuff, the response that I got was a blank stare. So while a few of my friends struggled for the first few classes to wrap their minds around the concept of induction itself, and why it is valid at all, I certainly felt like I had a head-start in the course.
By the time "Well Ordering" had arrived, the course was beginning to get a tiny bit more challenging. Even though I had used the same principle in the aforementioned math course in relation to bounds and sequences, the "round-robin tournament" proof done in class by Prof. Heap threw me off. While I understood the logic of the proof, it still felt invalid to me. So I went home, read over the annotated slides (by the way, THE GREATEST IDEA OF ALL TIME), and I still felt that the proof was invalid. So I did what any scholar in this day and age does: I loaded up Wikipedia. More specifically, the "round-robin tournament" page. It turned out that I had a false understanding of what a round-robin tournament was to begin with. My understanding was that the tournament is a elimination-style one-match-at-a-time tournament, while that is not the case at all. Either I had a lapse of concentration in the lecture and the concept was explained, or that everyone knows what a round-robin tournament is and I just had a gaping hole in my knowledge. In any case, everything was back to normal.
I felt like I was ready for the final exam right then and there... but then Assignment 1 happened. Three straightforward questions which collectively took 45 minutes, and then a monster in the form of question 4. Binary strings. Occurrences of 10s and 01s. I must have written 3 or 4 separate proofs for that question, but none of them felt completely valid to me. It was Friday, the assignment was due that night, and I was stuck. I didn't know what to do. It was actually Prof. Heap's hint in class about starting out with a stronger claim that gave me the idea. So like any geniuses I've seen in the movies who get a great idea in the middle of a class, I got up and left and knocked over everyone's papers and almost tripped on someone's bag, walked to the closest window and took out a marker and started writing on the glass. OK, none of that happened, but I finished my proof after class, and just to make sure that my approach was valid, I went to the extra office-hours on Friday, and indirectly, and without getting into too much detail, explained my approach, and Prof. Heap indirectly, and without getting into too much detail, replied that it sounded valid.
I must apologize for having such a long post, and I feel for Prof. Heap and the TAs who have to read several hundred of poorly written, very similar posts about students doing proofs. But hey, that is what you get when you shut down the alternative "Student Tweets" assignment, which would've made life easier for all parties involved.
Stay tuned for a preview from next week's episode of SIAMAK'S CSC236 SLOG:
.
.
.
Mid-term exam!!! Was it a success or failure? Find out if this student aced the test, or if he was dealt a tough hand! Next week on SIAMAK'S CSC236 SLOG.
Tuesday, 9 October 2012
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