This has probably been the busiest week of my entire life...
Let's see, Monday I had a 236 Assignment, 236 Problem Set, 207 Excersise ... Wednesday I had a 207 Midterm, Thursday a MAT137 Problem Set, and today Phase II for 207. Jeeeeeeeeeeeze, oh well, at least I managed to survive through it...(so far anyway)...
Assignment 2 went pretty well I guess. The ternary tree question was by far the toughest and took the longest to finish. I think my recursive formula works though, which is a good sign. I think after doing that question I can now solve similar type questions for all types of trees (binary, ternary, quanary(sp?)... because they're all sort of the same type of question.
I'm just really tired. I can't wait to just be finished with today and catch up with all the sleep I missed out on during the week. I'm going to write up a longer entry over the weekend just to summarize everything we've been learning in lecture throughout the week. Basically we're focusing more on analyzing code, proving it works, and other sorta stuff like that... But yeah, I'll write more later, cya!
Friday, October 31, 2008
Sunday, October 19, 2008
6th Entry
So I managed to finally figure out the solution for Problem Set 3! It took some work, but with the help of my friends and some time to think it over, I realized I was a lot closer then I thought!
I unwound G(n) to the point where I found the geometric sequence -- I just wasn't sure if this was a "closed form" of G(n). A friend of mine spoke to Danny and realized that we had it down, it was just a matter of manipulating the closed form to get the equation: (1 - r^n+1 / 1 - r) -- which I then used simple induction on to prove for the n and the n+1th term. So yeah, at least I think I did it right!
Next week is going to be really busy. We have started our first "sprint" in CSC207, so balancing that out with a Problem Set and Assignment in 236 is going to be tough. Once everything gets rolling it should be ok, it's just a matter of getting things to "roll" in the first place...
I'm happy with my mark on the first midterm. I expected to do a little better, but I totally messed up the Fibbonacci question. I used complete-induction like we were supposed to, but I don't think I "used" it efficently enough to prove the question. Oh... and I only used 1 base case instead of 2. I should've known Danny was going to put a question in with 2 base cases!
So yep, week 7 starts tomorrow and I'm ready for it. I want this recursive stuff to be over with soon... I'm curious to see what we're going to learn about next!
... And now I'm all up to date on my Slog posts too. Yesssssss.
Thursday, October 16, 2008
5th Entry
Yikes, two late entries in a row..
So, the midterm? Honestly.. it went pretty well. I find all of Danny's midterms and finals to be extremely fair. I hate walking into a midterm after studying very hard weeks prior, and then not knowing how to answer even one question. With CSC165 and CSC236 so far.. that's never been the case. I might not always do extremely well on them, but I always walk out confident and happy with the way it went.
I'm working on Problem Set 3 as we speak and I'm trying to figure out some sort of conjecture after unwinding of G(n) to its limit. I think I'm really close.. we'll see, I saw a topic on the bulletin board that Danny posted about a hint, so I'm going to check that out as soon as I'm done with this entry to see if it helps me out in any way. I did extremely well on the first assignment, and thats really kept me motivated to keep on top of my work and try to understand everything that's going on in lectures and on the assignments. I just noticed that A2 was posted, and I'm going to get to work on that this weekend..
Anyway I better go finish this Problem Set.. Other then that, everything is going awesome.. I feel like some of this recursive stuff is a little over my head, but like I said.. I'm sure after working on A2 things will start to make a bit more sense!
So, the midterm? Honestly.. it went pretty well. I find all of Danny's midterms and finals to be extremely fair. I hate walking into a midterm after studying very hard weeks prior, and then not knowing how to answer even one question. With CSC165 and CSC236 so far.. that's never been the case. I might not always do extremely well on them, but I always walk out confident and happy with the way it went.
I'm working on Problem Set 3 as we speak and I'm trying to figure out some sort of conjecture after unwinding of G(n) to its limit. I think I'm really close.. we'll see, I saw a topic on the bulletin board that Danny posted about a hint, so I'm going to check that out as soon as I'm done with this entry to see if it helps me out in any way. I did extremely well on the first assignment, and thats really kept me motivated to keep on top of my work and try to understand everything that's going on in lectures and on the assignments. I just noticed that A2 was posted, and I'm going to get to work on that this weekend..
Anyway I better go finish this Problem Set.. Other then that, everything is going awesome.. I feel like some of this recursive stuff is a little over my head, but like I said.. I'm sure after working on A2 things will start to make a bit more sense!
Tuesday, October 7, 2008
4th Entry
It's been a very very busy last couple of days. That explains why I haven't been able to update this thing 'til now.. Let's just say my workload has picked up. And I'm not just talking about 236, I'm talking about all of my classes. I hate it how for a week or two you could have absoultely nothing to do, and then all of a sudden you're bombarded with a million things at once! Oh well, I guess that's school..
We have our first midterm for 236 this Friday ... Matter of fact, it's my first midterm of the new school year. I'm kind of nervous.. though I can't say I've spent too much time studying yet, and I'm sure once I dive into my notes and the text-book I'll feel more confident. Now that induction is almost behind us, I'm having more trouble understanding the material in lectures now-a-days.. It's all *kind-of* new stuff to me, so it'll definitly take some getting used to. My goal for today is to make sure I know how to do that "unwinding" technique that Danny used in lecture last week, and of course get more comfortable with the different types of induction.
I hate midterms! - I wish everything was based on problem-sets and assignments. Then again, I guess midterms and exams really show if you understand the material or not. I used to be terrible at taking tests, but I can say in the past two years I've been at UofT I've improved a lot.. I'm just hoping that this one on Friday goes well...
I'm really looking forward to getting A1 back... Other then that, I can't wait for the long weekend! I think I need a little break, juggling math problem-sets, comp sci projects and 236 problem-sets along with my other course-work has started to take it's toll on me.. Haha, oh well, only another 7 months of school left! I plan on updating this on Friday after the midterm just to give my thoughts about it..
So until then, cya!
We have our first midterm for 236 this Friday ... Matter of fact, it's my first midterm of the new school year. I'm kind of nervous.. though I can't say I've spent too much time studying yet, and I'm sure once I dive into my notes and the text-book I'll feel more confident. Now that induction is almost behind us, I'm having more trouble understanding the material in lectures now-a-days.. It's all *kind-of* new stuff to me, so it'll definitly take some getting used to. My goal for today is to make sure I know how to do that "unwinding" technique that Danny used in lecture last week, and of course get more comfortable with the different types of induction.
I hate midterms! - I wish everything was based on problem-sets and assignments. Then again, I guess midterms and exams really show if you understand the material or not. I used to be terrible at taking tests, but I can say in the past two years I've been at UofT I've improved a lot.. I'm just hoping that this one on Friday goes well...
I'm really looking forward to getting A1 back... Other then that, I can't wait for the long weekend! I think I need a little break, juggling math problem-sets, comp sci projects and 236 problem-sets along with my other course-work has started to take it's toll on me.. Haha, oh well, only another 7 months of school left! I plan on updating this on Friday after the midterm just to give my thoughts about it..
So until then, cya!
Sunday, September 28, 2008
3rd Entry
Whew.
I've finally finished my first 236 assignment! As of around 2'0clock this afternoon I've been stress free, as I was able to submit the assignment quite earlier then I would've expected. Usually at this time I'd be either struggling to finish one of the tougher questions, or proof-reading some of my answers - but nope! I'm done.
The question that gave me the most difficulty was #3. Now I don't want to say too much about the answer, since the deadline hasn't officially passed yet, but if it wasn't for those TA hours I'd probably still have no clue what to do. The whole thing just really confused me. Even after I re-read it a couple of times, it just never really clicked as to what I was supposed to do. After brainstorming with some friends and countless visits to the aid center, I was able to piece everything I leared together and come to some final solution.
The thing that confused me the most was implementing the POW into it all -- I really really don't like using the POW technique, mainly because I still don't really see what's so significant about it. I'm sure Danny has a lot to say about that, and don't get me wrong I'm not saying POW is useless -- its just I find that Simple/Complete induction is a lot more straight forward. Maybe I just don't like it because I can't really figure out when to use it .. or how to use it .. or why I'm using it .. I just don't like it!
This week is going to be really brutal in terms of work. I have a lot to do and I'm expecting another Problem Set will be due this Friday, so yeah, it just keeps piling on. I'm glad I got A1 out of the way and I feel confident with all of my answers, so we'll see how it goes. I usually never do as well as I expect on assignments (or at least that was the case in 165) so I'm crossing my fingers! Oh well, like I said, we'll see!
Anyway that's it for this week, expect more next Saturday.. I looked at my calendar and realized that the first test is approaching -- kinda scared, not gonna lie. So yeah, 'til next time, cya..
I've finally finished my first 236 assignment! As of around 2'0clock this afternoon I've been stress free, as I was able to submit the assignment quite earlier then I would've expected. Usually at this time I'd be either struggling to finish one of the tougher questions, or proof-reading some of my answers - but nope! I'm done.
The question that gave me the most difficulty was #3. Now I don't want to say too much about the answer, since the deadline hasn't officially passed yet, but if it wasn't for those TA hours I'd probably still have no clue what to do. The whole thing just really confused me. Even after I re-read it a couple of times, it just never really clicked as to what I was supposed to do. After brainstorming with some friends and countless visits to the aid center, I was able to piece everything I leared together and come to some final solution.
The thing that confused me the most was implementing the POW into it all -- I really really don't like using the POW technique, mainly because I still don't really see what's so significant about it. I'm sure Danny has a lot to say about that, and don't get me wrong I'm not saying POW is useless -- its just I find that Simple/Complete induction is a lot more straight forward. Maybe I just don't like it because I can't really figure out when to use it .. or how to use it .. or why I'm using it .. I just don't like it!
This week is going to be really brutal in terms of work. I have a lot to do and I'm expecting another Problem Set will be due this Friday, so yeah, it just keeps piling on. I'm glad I got A1 out of the way and I feel confident with all of my answers, so we'll see how it goes. I usually never do as well as I expect on assignments (or at least that was the case in 165) so I'm crossing my fingers! Oh well, like I said, we'll see!
Anyway that's it for this week, expect more next Saturday.. I looked at my calendar and realized that the first test is approaching -- kinda scared, not gonna lie. So yeah, 'til next time, cya..
Saturday, September 20, 2008
2nd Entry
Wow, I can't beleive it's already been two weeks! I've made it through my first 236 Problem Set, and I've gotta say, I'm really happy the way it turned out. I was initially scared after reading the questions, but then after I took a breath and calmed myself down, I realized that they were extremely similar to examples we did in class. In the first question I had to prove (using simple induction) that the right-most unit digits of 4^n (n being from the set of all natural numbers) were either a 1, 4 or 6. I used the example from class with 3^n to help me set up and structure the proof, but more importantly, I understood everything I was doing and why I was doing it. The second question on the other hand, took a little bit more thinking..
I'm not going to retype the entire question because I'm sure whoever is reading this knows what it was about haha, but I stumbled on this proof for a few unexpected reasons. I figured out the induction step pretty easily after doing some scratch work, but trying to explain the reasoning behind the induction step is where I had trouble. I went to Danny's office hours this week and overheard him talking to another student about how some proofs can consist of just writing, and that mathematical mumbo-jumbo isn't always neccessary. I think the way a person expresses themselves and conveys their thoughts into writing is super important, and it's actually one of the hardest parts of the proof. The math part is either right or wrong and is entirely based on whether you understand what you're doing -- but proving something using nothing but words? That's tough. I mean, what really makes a well-written, clear and concise proof?
What I realized is that it takes a lot of time and rough-drafts to get a proof exactly the way you want it. I swear I wrote up the answer to question two a million times before it met all of the TA's and Danny's requirements. What I thought were such little, trivial things actually constituted as major parts of the proof. I had everything written down, but in a somewhat unorganized and unclear manner. I didn't properly convey the connection between the claim and the Induction Step, and not because of what I had written down, but the way it was written down. However with some help and a little rephrasing I was able to write up a proof I couldn't have been happier with -- and now that I know the importance of "techincal writing", I think I'll be more prepared for future problem-sets, tests, quizzes and assignments.
Anyway, this is already turning out to be too long of a post so I'll try to wrap it up as quick as I can. The use of the tablet in lecture is awesome - I love it. Makes everything a lot easier to read and we have access to all the notes online, which is really cool. The 1st Assignment is coming along slowly but surely haha, I'm going to try to spend a lot of tommorow working on it. Other then that I'm just trying to grasp the concept of Complete Induction and figure out a strategy to know which one to use (Complete vs. Simple). Anyway I'm going to stop writing now because this is turning into a novel, but yeah, I'll be writing more next week.. so.. cya!
I'm not going to retype the entire question because I'm sure whoever is reading this knows what it was about haha, but I stumbled on this proof for a few unexpected reasons. I figured out the induction step pretty easily after doing some scratch work, but trying to explain the reasoning behind the induction step is where I had trouble. I went to Danny's office hours this week and overheard him talking to another student about how some proofs can consist of just writing, and that mathematical mumbo-jumbo isn't always neccessary. I think the way a person expresses themselves and conveys their thoughts into writing is super important, and it's actually one of the hardest parts of the proof. The math part is either right or wrong and is entirely based on whether you understand what you're doing -- but proving something using nothing but words? That's tough. I mean, what really makes a well-written, clear and concise proof?
What I realized is that it takes a lot of time and rough-drafts to get a proof exactly the way you want it. I swear I wrote up the answer to question two a million times before it met all of the TA's and Danny's requirements. What I thought were such little, trivial things actually constituted as major parts of the proof. I had everything written down, but in a somewhat unorganized and unclear manner. I didn't properly convey the connection between the claim and the Induction Step, and not because of what I had written down, but the way it was written down. However with some help and a little rephrasing I was able to write up a proof I couldn't have been happier with -- and now that I know the importance of "techincal writing", I think I'll be more prepared for future problem-sets, tests, quizzes and assignments.
Anyway, this is already turning out to be too long of a post so I'll try to wrap it up as quick as I can. The use of the tablet in lecture is awesome - I love it. Makes everything a lot easier to read and we have access to all the notes online, which is really cool. The 1st Assignment is coming along slowly but surely haha, I'm going to try to spend a lot of tommorow working on it. Other then that I'm just trying to grasp the concept of Complete Induction and figure out a strategy to know which one to use (Complete vs. Simple). Anyway I'm going to stop writing now because this is turning into a novel, but yeah, I'll be writing more next week.. so.. cya!
Saturday, September 13, 2008
1st Entry
I've been searching through my old notes and trying my best to get back on track, seeing how four monthes of a very relaxing summer has finally caught up with me. Regardless, I was really happy with how I did in CSC165 last semester and I've actually been looking forward to being in CSC236. Using proofs and logic is something I never thought I'd enjoy, but now that I've finally got it, I love it. I'm now able to understand and solve problems that I never think I would've before. Last year's class also helped me relearn the fundamental rules of math that I chose to ignore throughout highschool, which is why instead of being scared and unsure like I was at the beginning of CSC165 -- I'm confident and excited to see how I do in 236.
Now I'm not going to lie, simple induction isn't really my thing. I understand all of the examples in class, but finding the forumla for the induction step is what seems to give me trouble. I worry that I won't be able to get to the answer without Danny up at the board going step by step through the solution. Eventually I'm sure I'll be able to find some sort of pattern or strategy, but for now it's just somewhat of a struggle. The same thing happened to me last year with proofs, so I guess in the end all it takes is time and a lot of practise.
I'm going to begin working on Problem Set 1 tommorow and then take a look at the 1st Assignment at the beginning of the week. The questions in the first problem set seem familiar to what we've been doing in class. Finding the base case is usually straight-forward for me (...until Danny mentioned the possibiliy of more then one, or in some cases none ... haha) it's just using all the cases to form the formula ... or equation ... the Induction step, basically.. that's we're the trouble comes in.
I'm sure the course-work will pick up a lot this week with more examples and topics to learn. I'll probably be posting in this blog once a week, like I did last semester. Maybe a couple of in-between posts too. I think that worked out pretty well. Anyway, better get to work! Cya.
Now I'm not going to lie, simple induction isn't really my thing. I understand all of the examples in class, but finding the forumla for the induction step is what seems to give me trouble. I worry that I won't be able to get to the answer without Danny up at the board going step by step through the solution. Eventually I'm sure I'll be able to find some sort of pattern or strategy, but for now it's just somewhat of a struggle. The same thing happened to me last year with proofs, so I guess in the end all it takes is time and a lot of practise.
I'm going to begin working on Problem Set 1 tommorow and then take a look at the 1st Assignment at the beginning of the week. The questions in the first problem set seem familiar to what we've been doing in class. Finding the base case is usually straight-forward for me (...until Danny mentioned the possibiliy of more then one, or in some cases none ... haha) it's just using all the cases to form the formula ... or equation ... the Induction step, basically.. that's we're the trouble comes in.
I'm sure the course-work will pick up a lot this week with more examples and topics to learn. I'll probably be posting in this blog once a week, like I did last semester. Maybe a couple of in-between posts too. I think that worked out pretty well. Anyway, better get to work! Cya.
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