End of Semester Final Post

    As of this coming Monday, we will have reached the end of this semester's CSC165 lectures, all that is left to do now is to complete Assignment #3 and study for the final exam. Looking back on this course as a whole, I can honestly say that I enjoyed it quite a lot. The course has not only aided my ability to think logically, but it has also built up my overall confidence in writing proofs immensely. Such confidence has allowed me to find excitement in writing proofs and inspired me to pursue a double major in Mathematics and CS. All I can say is thank you to my TA Madina and Prof. Heap, you have helped greatly to make my first semester at U of T as enjoyable as possible.

Assignment 3 and Reactions to Lectures

    Because of the fall break, I have much less to say about lectures this week than normal. This being said, the introduction of halting is a somewhat difficult concept for me to wrap my head around and I think a fair amount of review and practice is required. I am currently searching for any other student's SLOG who has covered halting in a clear manor, though it seems that finding such a SLOG seems more challenging than the concept of halting.

    With regards to Assignment number 3, I have been exceptionally excited about proving some of the statements. So far I have completed 2 of the 6 proofs (or disproofs) and have been greatly stimulated by each, I can only look forward to my completion of the other 4. More specifically, I found the first statement somewhat challenging to think about and to prove or disprove simply because of my eagerness to complete epsilon delta type limit proofs. This is normally an advantage for me as it was in Assignment 2, however thinking about the statement in this way helped me none during the discovery phase but helped me to improve my problem solving tactics which I found quite enjoyable. Due to my previously mentioned feelings on halting, I do somewhat fear the final proof on Assignment 3 but at the same time believe that it will be an excellent way for me to improve my comfort with this concept.

More Interesting Proofs

    This week's material has been quite interesting, our work on more complex proofs involving big-oh and big-omega definitions have been good fun for me and I look forward to practicing more proofs as well as reading over past lecture slides. I believe this may be because I take MAT137 and, as a result, am exposed to many proofs (though I think this course has made me feel much more confident in writing proofs). As a result of this, and now that the step counting has passed, I believe that my overall enjoyment of this course will be restored back to normal. This being said, I do think that step counting will be important on the exam and future courses so I will continue to familiarize myself with this by completing exercises at home and actively participating in CSC108 lectures on the same topic. So far, I can already see a great increase in my abilities to count steps in Python programs and derive upper and lower bounding functions for their worst case scenarios.

    This problem solving episode looks interesting. I am not sure that I understand it completely but I will read it over again, attempting to make some sense at a later date.
http://andrewgoupilcsc165.blogspot.ca/2014/11/week-9-problem-solving.html

     In addition, I received my marks back for our second term test and scored 29.5/30. I am quite pleased with this mark as the proof I felt was the most weak (referenced in last week's post) got a 10/10, but one I felt most confident about (the last proof) lost half a mark. In typing this I have realized that I completely forgot to pick up my graded test from Prof. Heap's office today... but I am quite eager to see what I did incorrectly on the last proof.

    Finally, I thought to share a song I like that relates to math. This song is based off pi , the bass drum pattern corresponds to each digit in pi up to 71 decimal places and there are many other subtitles that I do not care to type. The description of the YouTube video has a quite good description of said subtleties.

Term Test and Tutorial

    This week in class, we continued the topic of bounding sorts and explored big Oh proofs a bit more detail. As stated last week, the actual proofs for big Oh aren't especially challenging for me, however I am still having issues with looking given code and writing equations that bound it, particularly from below. This week's tutorial was certainly helpful for me, however I believe that I scored poorly on the last part of the quiz. Even worse (or perhaps better), I figured out the solution in my head on my way out of the Bahen Centre. This may be a good sign of my grasping of this concept, however I feel that further practice in tutorial  and for homework is most definitely needed.

    We also had our term test this week on Wednesday. I think it went OK for me, out of the three questions I feel quite confident about two. I am, however, bothered about the second question (the almost epsilon-delta style statement), I had a solution in my head and I knew how the proof was supposed to go but there was one issue with the floor function which I could not seem to overcome. Later, in Prof. Heap's office hours, we went through it together and I was missing one easy step that I knew fully well how to do (maybe my sleep deprivation is catching up with me). I do hope that my proof structure and the steps that I wrote are worth some of the 10 possible marks for that question and that I earned a more than mediocre mark. I suppose only time will tell, I will post about the results in my next entry.

In addition, I found this person's slog entry rather interesting.
http://juliaslog.wordpress.com/2014/10/27/a-series-of-unfortunately-inconclusive-events/

Although the problem solving episode was inconclusive, their thought to use python to gain a greater understanding of the problem was quite fascinating for me as I quite often find myself working out some problems using python. Perhaps this is as a strategy I will use in future problem solving episodes.