Assignment 3, limits AGAIN...

The last week of classes has been crazy for me with 3 different assignments due (this slog being one) and knowing that in less than a week, I will be writing my first exam has made it even worse.
One of the remaining 2 assignments was assignment 3 for csc165. And now that it is done, I can look back and reflect upon what I did. I don’t intend to write a detailed exclusive post of assignment 3 as I did for assignment 2 (don’t know why, just don’t feel like it, I guess). However, there is something that came up on assignment 3 that I would like to discuss:

Limits !!!!!

Limits have come up quite a lot in all calculus courses I have taken so far (which are not that many); they came up in high school calculus, 1st year university differential calculus and 1st year University integral calculus. And although in each of these courses we have extensively studied techniques to manipulate these limits and get all sorts of answers, we have not talked about what they actually mean as much. Sure, there would be a section of the book talking about deltas and epsilons, and the professor would discuss what they mean in 3-5 minutes, but at the end we always hear that we “don’t need to know them for the test” or that we “don’t really need to worry about them unless [we] want to major in math.” And therefore the meaning of limits is taught extensively in only these math courses that prepare students to be math majors.

In short, I was taught to solve the limit but not to interpret it.

In csc165, the definition of limits came up at the very beginning of the course when we were just talking about ∀ and ∃. Lately, it has come up again and been linked to determining the algorithms’ complexity.

In csc165, we have spent lots of time trying to understand what a limit means and to visualize it using graphs.And now that I understand what a lim of x going to infinity means, I think it is quite great that stuff we are taking in cs can link back to stuff we took in calculus courses.

ALL you need to know about assignment 2

Hey again

I know it is sort of late to talk about assignment 2. However, I just noticed that while other blogs have intensively discussed assignment 2, I have only briefly mentioned it in the previous post and thus figured out that I should give the assignment more credit so here you go,

EVERYTHING YOU MAY (or may not) WANT TO KNOW ABOUT ASSIGNMENT 2:

• BEFORE:

In general, I think most students in this course (including me) prefers proofs to the first part of the course; they are challenging, fun, and you feel pretty smart once you have finished one.

However, most of us (again, including me) were worried that we won't be able to solve proofs we have never seen before.

• DURING:

Luckily, I think the assignment was quite fair in terms of easiness especially that tons of office hours were available.

However, it is important to note that this assignment was our first major course work regarding proofs. And as you might expect, different people had different opinions about the assignment. 

Here are some I quote from other blogs/slogs:

http://165uoft.blogspot.ca/ :I found this assignment wasn't as bad as the first. I'm finding this one more concise in terms of its statements. The hardest question I would have to say is number 6 as it utilizes a small trick

http://annakovale.blogspot.ca/: I think Assignment 2 was great practice for proofs and I liked it more than the first assignment (I like proofs)...... I feel like it deserves a separate post.

http://slogjourney.blogspot.ca/:Oppose to watching the professor write the proofs and unanimously agreeing, this assignment was great practice in independently building up my proofs.

So, overall, the assignment was a great chance to practice for the test.

and as you might expect lots of questions were asked:

Here are couple of questions posted by http://1d10terror.blogspot.ca/:

is if there is a statement that I know a counter example for, can I state the counterexample and reach the conclusion thatP(x) -> notQ(x) for all values? Will that be enough to invalidate the entire statement? Also if I have a statement that has a for all assertion in the consequent, what on earth do I do? For example x in D, P(x) -> ( y in D, Q(y) ^ P(y)), is there anything I can do to solve this or am I completely boned and should view the statement from a different angle?

again, I know I am answering these after the assignment but I guess, it is better than never (we still have an exam to write anyway).
So here is my attempt at answering these questions:

1.     If you are trying to negate P(x) -> q(x), you shouldn't prove that p(x)-> not q(x) since this (as discussed in class) is proving "too much" than what you actually need to prove all you need is one example in which P(x) is true and q(x) is not 

2.     proving a for all in the consequent should be treated as any for all: by assuming that y is a generic element of D and then trying to prove that the predicates p and q apply to every single element in D (by proving that they evaluate as True to the generic element y). It might have been confusing due to the many /for alls/ . Personally, what I do to minimize confusion is to go over the statement from left to right in order, writing assume...... for every for all or implication, pick... for each there exists. This way by just building the "skeleton" of the proof, you have given yourself a head start to how your proof will look like and what exactly do you need to find out (to fill in the blanks).    

• AFTER:

I think the assignment was a really good exercise and an awesome preparation for midterm 2. Proof: most people did well on term test 2. 

News so far......

I know it has been a long time since the first post but that’s because I was preparing some cool program Danny had challenged us to do but since I am still not done yet (have not started actually J, it has been a busy week) and haven’t posted anything new, I figured it is time for me to post something before I actually tell you about the cool mental experiment we did in class (probably, I will have enough time by the reading weak). So wait for that, but for now, here is what has been happening in csc165 so far:

we have had our 3^rd tutorial this week and OUR FIRST ASSIGNMENT. I can’t describe the assignment as hard but I can’t describe it as easy either. Well, that’s the weird thing about this course. You might think your answer is right just because it makes sense to you and turns out it is completely wrong. That is why you must read what you have written from many different angles and try to prove yourself wrong (which is a common thing between all sciences). I hope I did well on the assignment.

As for the lectures, I really loved the part when we try to prove that one statement is equivalent to another statement (since now, you can actually know if your answer is right or wrong). We are starting proofs so I guess that should be fun and I am looking forward to it.