This week, we learnt more techniques for proofs. Proofs by cases are sometimes handy when I am stuck at certain proofs. The cases are required to cover everything in the sets, and start proving it using the given definitions. We also learnt the introduction rules and the elimination rules. And it comes to an end to the proofs and we get to touch on some more complicated materials--algorithms. Running time is the most important factor when computer scientists decide which algorithm to use.
For proofs, I need to do lots of practices and start from
finding certain pattern. I can use the rules to keep trying. This will make me
get closer to the target. After two weeks of proofs, I found proofs are not as
hard as I thought before, maybe because I practice a lot and I learnt more
techniques for the proofs. For algorithms, this is important in computer
science. We can sort a list using different algorithms. Like bubble sort and
merge sort. Different sorting algorithms take different amount of time. Some
have more steps than the others. Once we have a super long list, we would want
to use the algorithms with less steps, because that will save lots of time. I
need to get familiar with how each algorithms work before analyzing it.
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