Weeks 8 and 9

Over the past two weeks a number of important things happened.  My group and I worked on Assignment 2, which was due last week.  Of the eight proofs we had to write, three were challenging.  We completed the five easier proofs quickly and spent most of the remainder of our time focusing on the other three proofs.  Although we knew why one of these proofs was true, we weren't sure how to explicitly prove it.  However, by using proof by contradiction, we were able to convert our reasoning into a properly structured proof.  For the second proof, we came close to finding values that would work, except for one special case.  A slight modification of our values produced the correct answer.  The last difficult proof, however, had us stumped.  We knew that it was false, but we struggled to find values that would prove the negation.  Finally, less than an hour before the deadline, we found a set of values that worked. 

Also this past week we had our second and final term test.  Like Assignment 2, the test was difficult.  The first question was fairly straightforward, but the second and third questions were challenging.  I was able to solve the third question fairly quickly as I had a similar proof written down on my aid sheet.  This left me most of the test time to focus on the second question.  After negating the statement, I realized it would be easier to solve by taking the contrapositive.  I then looked for a value that would staisfy the statement, and found one fairly quickly.  I verified my answer by testing both cases of the statement and this gave me an idea as to how to structure the middle of the proof.  I finished the test with about fifteen minutes remaining, which allowed me to check over my proof structures and  add comments where necessary.

In lecture these past two weeks, we have been learning algorithm analysis.  This topic is completely new to me so I was excited to find out what it was about.  In the beginning I found it very confusing, especially the part about finding the number of steps that a function executes.  However, over these two weeks, I have become more comfortable with proving the upper and lower bound expressions. Luckily, in CSC 108, we are starting searching and sorting which has some overlap with algorithm analysis. Hopefully, this will help me better understand counting the steps of a function.