Assignment two appears to be progressing nicely.
Question#1
The OMCOFS recursive definition ended up being easy to find....once I realised that for string length 5 there is 8, not 7 possibilities (11011 alluded me for a stressful 10min ). Completing the question after that was not exceedingly difficult.
Question#2
Showing the intuitive non-decreasing property was easy. Showing that T(n) is of order log(n) is slightly more difficult for me because I forget how to show Big Theta. Currently I am waiting for the prof to post his most recent lecture notes and I'm sure it will shed a bit more light on the situation or if worse comes to worse I'll have to revisit the the dark, dark abyss; my notes from 165.
On an unrelated note I have noticed that where ever I walk there seem to be stray dogs, so I hypothesised that stray dogs must have at least 3 noses so they can better tell my position and walk near me. And believe it or not I was able to prove it:
Proof. No dog has 2 noses. Since one dog has one more nose than no dog, it must have three noses.
Carl
Sunday, 28 October 2012
Sunday, 21 October 2012
We meet again Big O
Ah time complexity,
Seems reasonable that in a course called Introduction to the Theory of Computation we'd examine run-times. I must say although it took a while to grasp in 165 and will probably take an equally long time to RE-grasp in 236 this is a topic I am genuinely interested in. It's nice to know the fewest cuts to break apart chocolate but not actually practical. nor does it have any important implications. Understanding how long a program will take to run on the other hand seems VERY important. I am reminded of a story Diane told us in CSC108 in which her and her colleagues were going to solve a complex problem relating to U of T student data but upon examining the run time it just wasn't feasible.
To help me understand time complexity I decided I would apply it to my everyday life and decided to measure the time complexity of my dinner last night, unfortunately my calculations were off because I kept 'goin back four seconds'.
Carl
Seems reasonable that in a course called Introduction to the Theory of Computation we'd examine run-times. I must say although it took a while to grasp in 165 and will probably take an equally long time to RE-grasp in 236 this is a topic I am genuinely interested in. It's nice to know the fewest cuts to break apart chocolate but not actually practical. nor does it have any important implications. Understanding how long a program will take to run on the other hand seems VERY important. I am reminded of a story Diane told us in CSC108 in which her and her colleagues were going to solve a complex problem relating to U of T student data but upon examining the run time it just wasn't feasible.
To help me understand time complexity I decided I would apply it to my everyday life and decided to measure the time complexity of my dinner last night, unfortunately my calculations were off because I kept 'goin back four seconds'.
Carl
Sunday, 14 October 2012
Reflections on A1 + Test
Well, CSC236 is quickly becoming twice the beast CSC165 was, I'm spending nearly everyday studying for it and it is consuming most of my time. Thus I propose a new proof strategy used by many leaders throughout history that might help all of us out and save loads of time.
-> Proof by Imagination: "Well, We'll pretend its true."
A1:
Assignment 1:
I was able to solve questions 1,2,4 in reasonable amounts of time. The problem then became making sure that I could formalise them rigorously. Question 3 on the other hand took a bit more time, I quickly recognised the combination formula buried in the question and notice the relationship between the successive steps. I was just unsure how to explain via set logic the connection; then I thought back to Danny's lecture where he described the 2^n subsets problem. In it he took to parts to the problem; all the sets with the last element and all without, he then appended the last element to the first group of sets to obtain the second group. Once I established this connection and applied similar logic the problem was doable.
Test 1:
I am hesitant to see my Test 1 result. Although I believe it was a fair test, during tests/quizzes I tend become flustered and problems which would easily have been solved on my own become much more difficult now that there is a time limit. I have started implementing a new strategy in studying where I time myself doing old tests yet it doesn't seem to replicate the anxiety of actually writing the test.
Carl
-> Proof by Imagination: "Well, We'll pretend its true."
A1:
Assignment 1:
I was able to solve questions 1,2,4 in reasonable amounts of time. The problem then became making sure that I could formalise them rigorously. Question 3 on the other hand took a bit more time, I quickly recognised the combination formula buried in the question and notice the relationship between the successive steps. I was just unsure how to explain via set logic the connection; then I thought back to Danny's lecture where he described the 2^n subsets problem. In it he took to parts to the problem; all the sets with the last element and all without, he then appended the last element to the first group of sets to obtain the second group. Once I established this connection and applied similar logic the problem was doable.
Test 1:
I am hesitant to see my Test 1 result. Although I believe it was a fair test, during tests/quizzes I tend become flustered and problems which would easily have been solved on my own become much more difficult now that there is a time limit. I have started implementing a new strategy in studying where I time myself doing old tests yet it doesn't seem to replicate the anxiety of actually writing the test.
Carl
Friday, 5 October 2012
In The Beginning
This is certainly the most unique assignment I have received as of yet in University. Who would have expected a connection between Blogging and Induction....I guess this is the proof.
Although I did average in 165 I found that I spent 95% of my studying time on it with the demanding Exercises, Assignments, and Tests it was the single most difficult course I have ever completed. Luckily I had good background knowledge in all the other courses so they turned out fine. I found 165 hard because on top of the weekly demands; it was brand new material and. there wasn't exactly a wealth of written easily interpreted resources to learn from.
So, naturally entering 236 I had many reservations and was not exactly eager. In the 165 lectures I couldn't see the board, and tended to fall asleep while the material was being presented.
These 236 lectures conversely have been a pleasant surprise. The Prof is clear and engaged as he teaches in a manner which both make you think, but more importantly understand the material covered. The fact he uses a Projector rather then the Blackboard in itself is a HUGE help as I can finally see what's going on!
One thing I did prefer in 165 was the exercises per week vs the quizzes per week we have in 236. The time constraints are too much pressure even with the simpler problems.
This course will prove to be a tough one, and I may have to cut back on the hours of political videos I watch and public policy articles I read per day. At least this course will definitely give me a deeper understanding in the field of mathematics and make every other course seem WAY easier.
Carl
Although I did average in 165 I found that I spent 95% of my studying time on it with the demanding Exercises, Assignments, and Tests it was the single most difficult course I have ever completed. Luckily I had good background knowledge in all the other courses so they turned out fine. I found 165 hard because on top of the weekly demands; it was brand new material and. there wasn't exactly a wealth of written easily interpreted resources to learn from.
So, naturally entering 236 I had many reservations and was not exactly eager. In the 165 lectures I couldn't see the board, and tended to fall asleep while the material was being presented.
These 236 lectures conversely have been a pleasant surprise. The Prof is clear and engaged as he teaches in a manner which both make you think, but more importantly understand the material covered. The fact he uses a Projector rather then the Blackboard in itself is a HUGE help as I can finally see what's going on!
One thing I did prefer in 165 was the exercises per week vs the quizzes per week we have in 236. The time constraints are too much pressure even with the simpler problems.
This course will prove to be a tough one, and I may have to cut back on the hours of political videos I watch and public policy articles I read per day. At least this course will definitely give me a deeper understanding in the field of mathematics and make every other course seem WAY easier.
Carl
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