Entry #5 -Term Test 2 and counting costs and steps

This week we did proofs and Danny also introduced more proof structures. I felt that I was so lucky to take 165 this  semester. 165 helps me a lot since most of questions in mat237 are proofs. By writing down the proof structure that Danny taught us, I could focus on the few part which I get stuck on. I could have a clear picture about proofs. 

We did a formal proof about limit this week. Instead of graphing it, we wrote down the whole proof structure. I found it was more easier to understand in this way rather than the way we did in mat137. The things we used or we assumed were written in the comments. I finally understood why we had to choose the minimum number of the two. Since d is the number that we could control, I could choose any number that we want. 

The review on the proof was helpful as well. I was kind of looking forward to taking the term test 2. 

In lectures, we learned how to calculate the steps of an algorithm. I heard that from somewhere else that efficient algorithm sometimes saves billions of dollars in industry, also sometimes saves life. So, it is so important to calculate algorithm's step. 


There is rule of counting step of each of these actions:

method call: 1 step + steps to evaluate each argument, + steps to execute the method.
return statement: 1 step + steps to evaluate return value.
if statement: 1 step + steps to evaluate condition.
assignment statement: 1 step + steps to evaluate each side.
arithmetic, comparison, boolean operators: 1 step + steps to evaluate each operand.
array access: 1 step + steps to evaluate index.
member access: 2 steps.
constant, variable evaluation: 1 step.