November 28, 2014 - Week 12
The end of the semester has finally arrived. Only one more assessment left for this class. The truth is that this is course is probably one of the most difficult courses that I have taken this semester. Reflecting back to the first weeks, I was hopelessly lost with concepts such as "if...then", "unless", and "if and only if". Now we are finishing up with the course. This week we were discussing counting and induction. I was extremely confused with the concept that that was shown in class. Although there were many similarities such as the the base case, I was confused with the multitude of for-all and there exists that existed in the statement. To me, it look like the course was repeating itself and had many differences with what I had already learned in MAT137.
We also discussed the idea of diagonalization. The professor showed us that it is impossible to count all the outputs; therefore it is imperative that we apply induction to generate a hypothesis so that if it work for n = k + 1 then it will work for n = k. Sounds counter intuitive right? We are basically assuming the thing we want to prove and using it to prove for k + 1 greater.
Although this resembled the proof statements found in MAT137, after looking at examples, I still had no clue what was occurring. Guess that is what studying is for before the final exam is...
Thank you for sticking through and reading my posts. Until next year.
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