WEEK 7

6 weeks have been past, which means we have spent half of semester already. How time flies! And we have already learned so many things; I think it is time for me to have a mid-term review!

What I Learnt

        This week we focused on more complicated proofs: proof by cases. It was not hard to me. I needed to take several situations into account. Just like cutting one problem into pieces and solving them one by one as what I did before. Thus, this was just the further application of the old knowledge, nothing new actually.

Here, I learnt these two parts together with comparison and contrast:

Part A:

To prove, we let k = 7i^2 + 2i in order to connect antecedent and consequence together.

Part B:

To disprove, we use the theorem that the quotient and remainder are unique.

Just find an n^2 equals to 7k+1, and n not equals to 7i+1

          1^2 equals to 7 * 0 +1, and 1 equals to 7 * 0 +1

          6^2 equals to 7 * 5 +1, and 6 not equals to 7i+1

Then we use n = 6

What I Need To Do

    Like what Abhinav Chawla mentioned: ” It made me realize that it's only practice that would help me out to harden my concepts of writing a thorough proof.”(http://abhinavchawlacsc165.blogspot.ca/2014/11/week-7.html) Till now, we have a number of manipulation laws and many different-typed problem needed to solve. I need more practice to familiar them and improve my speed of solving a problem.