week7

This week I learned something about inference and sorting. If we know A and B, we can conclude A separately or B separately. if we want to disprove a statement, we need to prove its negation. By taking csc108 and csc148, I have learned lots of ways to sort like Bubble sort or selection sort. every way of sorting has its efficiency. Some ways are fast, some are slow. Also every way of sorting has worst case. After few weeks, I will get a better idea about big-ou and deeply know how sorting works. Sorting is very important in computer science. It can help people solving things with very complex function.  

week6

This week we still learned something about proofs.  Sometimes if the origin statement is hard to prove, we can disprove it. Sometimes we need to break down the statement. For example, ‘the floor of x is the largest integer <or= x’, we need to show the floor of x is integer, it is the largest and it is <= x. sometimes we need to prove by cases. For instance, ‘for any positive integer n, n^2 + n is even’, so we need to consider the cases where n is odd and where n is even. Proving is abstract and needs every step is reasonable. 

week5

This week went so fast. We did the term test and learned many ways of proving. The term test is not difficult. Some questions are very similar to the previous. Given some python Boolean functions, and work out the output. We were also given the question about negation. By doing lots of exercises during the tutorial, all of these are easy. The lectures of this week were mainly about proof. When we don’t know how to prove the origin statement, we could prove its contrapositive.

week4

This week I learned something about transitivity, the order of ‘for all, one’ and ‘one for all’, and proof. I thought that the order of the symbols ‘for all’ and ‘exist one’ does not matter before I took the class. After this week, I know this order is important, especially when we write some programs. Computers will give us different answers with different orders. Proof is always the hardest part. Just like the math class I am taking, the structure is important, and we need to know what we want to show. Proving takes long time to think and understand every step, and we need to make our proofs convincing. The tutorial of this week is showing the equivalence. Implication rules and DeMorgan’s laws are important. Every small symbol is important.