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..

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!

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.