SLOG 8 November 9th 2014

During this week's CSC165, i was primarily focused on studying for the second term test on proofs.  Prior to the test, i had just finished assignment 2, and felt pretty confident about proving universal and existential claims, as well as how to write the format of proofs in general.  I studied last year's test, and found it to be very easy, especially since there were only 3 questions.  After writing the test, i found question 1 and 3 to be very standard, however question 2 was not as easy.  For question two, i was asked to disprove a statement, so i took its negation and began attempting to prove it.  However, due to my being conditioned to relate variables e and d to limits, it took me a long time to understand the actual statement and its negation, and even then i made the mistake of defining one of my variables d as e times 2 instead of e plus 1.  This lead to many problems as i continued my proof, and only did i realize my error when time was up.  Alas, i had written the proof structure so hopefully i wont lose too many marks on that question.  Before this week, i was also quite confused about the 'steps' and big O notation that we had been covering in class, but after the tutorial exercise that focused on counting the steps of an algorithm, and finding its worst case scenario (which is when every loop is evaluated for the maximum number of times).  On Friday, the professor showed some more proofs of how some functions are of big O notation, and from these proofs, i learned that there is much more freedom in manipulating variables and inqualities when proving big O.  For example, when showing that 3n^2 + n is of On^2, the professor showed that we can simply turn n into 2n^2, because 2n^2 is always bigger than n, and then express 3n^2 + n with an less than inequality as 5n^2.