Proof Example

Greetings I am back!  Finally a week without a midterm!  I only have the assignment for this course and a linear algebra problem set to do this week, this is practically a week off at U of T.  Do you want to know something scary?  One of my friends has yet to write any blog posts, and I am not even sure if he has set up blogger!  Yikes!  In this post I will be writing a nice proof of our quiz 5 question.  Last week I did not attend my usual tutorial time because of a time conflict so I got the chance to see another TA do proofs.  I can say that for the most part both TA's did proofs the same, but there were a few subtle differences.  Anyway, without further ado:

I answered this a bit differently on the quiz by leaving the j variable blank at first and then setting it after I had solved, but I think this way is cleaner and more logical.  I have noticed that I am pretty good at algebraic proofs like this one, but still have some trouble with epsilon delta style proofs.  Another proof is incoming this week! Until then!

Busy Week

This is going to have to be a very short post because I am in the middle of studying for calculus and linear algebra midterms that are back to back over the next two days, and I also have a Jewish culture essay due Wednesday.  I just want to say that I really like the way U of T marks in computer science courses because it appears that they truly want to give you credit if you have shown you know something.  I feel like in calculus they are actively trying to find ways to take marks away, for example generally the last question on the calculus midterm is out of 8 and it has a disclaimer that it is marked very strictly and unless you have the correct solution you will receive little to no marks.  Also I like the concept that if you really don't know a question you can skip it and write that you cannot answer it to prevent you from spending too much time on questions you don't know.  

Midterm Experience

I am extremely frustrated this week!  I did not get question 3 correct after spending half of the exam working on it!  Within the first two minutes of starting the question I thought I solved it with two sets that were the same for P and Q, but I didn't explicitly tie it together with D and then I ended up changing my answer.  From this point I tried everything I could think of from two empty sets, one empty set, two different sets etc.  However again I came under the syndrome I talked about in my previous blog post, the more I thought about the question the more confused I made myself and the further from the answer I got.  It ended up becoming a mad scramble with the last 10 minutes being a blur and then me scribbling down an answer.  I may have been better off just writing "I cannot solve this question", but there is no going back now, live and learn.  Unfortunately spending all that time on question 3 also prevented me from checking questions 1 and 2 over, which should have been a priority because I answered them quick.  Next test I am going to do a much better cost benefit analysis of marks vs time.

After reading several of the blogs for this week it is clear that everyone is discussing proof format and generally they are terrified to actually begin proving things.  I have to admit I am somewhat in that category as well, but that is not what I was going to mention in this blog.  Several people are discussing the format, but not including any comments in their work.  Comments are very important and should not be forgotten!  Remember beside your assumptions and introductions you should have those #'s!  (ie. domain assumption, antecedent etc)  That is all I have to say for now,  good luck this week to everyone in CSC148!

So Begins the Midterms

It's time for another weekly blog post, sandwiched nicely between a linearly algebra assignment and calculus review.  I had a great tutorial last week that cleared up a lot of the issues that I was having.  For example one of the biggest issues being how to tackle statements that involved many sets.  I was previously trying to think about what was going on intuitively, to picture it in a Venn diagram or use a truth table.  However the issue with this is that Venn diagrams become too complex to draw, truth tables become rather large and thinking about things intuitively just won't work when you are dealing with many sets.  It all just clicked for me when my TA said that you should understand the arithmetic rules with two sets but once you add more it is impossible to think about things intuitively so you should just apply the rules.  Although I somewhat figured as much through problem solving, hearing this cleared my head and made me feel like I understood how to tackle large statements with many sets.

I have to agree with Andy L (http://andylslog165.blogspot.ca/) when he says that he almost certainly would not be able to do an Epsilon Delta proof without previously seeing one in calculus.  I think that Professor Heap did a good job explaining what the statement was saying when he said if e is chosen first by your worst enemy you can find a d to make the statement true, however if d were chosen first your opponent could easily disprove it with an e.  The only problem is I wouldn't naturally draw a connection between the statement and limits, so I wouldn't prove it that way.  Although seeing as the term test is this week after heavy review I may feel differently.

Me and my partner both found that while doing assignment 1 the more we continuously talked about a question without taking a break the further from the answer we got.  For example we had thought we figured out 5d by thinking about which statement was the subset, and at the time thought statement d included 0 so S2 must be the subset.  In the end with fresh eyes we realized that 0 wouldn't be a part of statement d because it is divisible by odd prime numbers so both statements implied the same sets when all possible values of T were considered.  So it was S2 if and only if statement d.  We are using this as a lesson to take breaks while thinking about questions in the future.