CSC165 WEEK6

We finished the study of proofs and started to learn algorithm analysis this week.  
 
By taking this week's lecture , I  learned that sometimes we need to discuss different situations in a problem and prove the problem by cases.For example, we need to assume a number n as both odd and even numbers, which splits the proof into two cases. Just as many math problems, we need to consider all possible cases to find the result. And the professor gave us an extreme example of proof by cases: the four colour theorem, which states that four colours are enough to colour any map, so that no two adjacent regions will have same colour. Although it seems not difficult to prove since the four colour map shows the feature visibly, it actually takes a computer 1000 hours to solve it and all counter-example of proof  can be at least 1936 cases! And this makes me understand that we need to be really careful to find all cases in a proof. And I feel fortunate that most  problems in csc165 only  require up to 3 cases.

The professor also showed us a ' funny' video titled as "the right emotion about finding a proof'. The man who found a difficult proof felt so agitated and can't help crying. It looks funny, but I understood we should enjoy the sense of achievement of finding out a proof so that we can take those proof problems seriously.