Week 11

Of course the professor saves the best for last. Or not.

This week the stuff on halting function and countability I felt like were a little confusing. I don't know if it's summer but I am rather confused. The idea of not having a proof or solution to solve a halting function really baffled me not just conceptually but also mathematical (proof-wise). It really baffled me that no one has yet to create such a function though it seems rather like an easy question. As for the proof of it, I really have no clue on how to use reduction to show that a certain function is non-computable knowing halt is impossible to compute. Maybe I just need to see more examples for this to be clear but definitely just hearing it once in lecture isn't good enough.

And for the problem-solving episode, I will use the product of sums problem. The problem states to find the maximum product for the sum of a certain number. My approach to this solution was through trial and error. At first I knew that number of its square always produce the largest sum and thought this was correct. However, a sum of [2, 3, 3] or (8) is 18 and not 16. From this example, I used the idea of having the longest possible length for your sum of the number and having each number in the list different from one another by exactly one or the same. So then I used example, [3, 3, 3, 3] or (12) and found this to also work for my solution as well as [3, 3, 3, 3, 3] or (15). Here this I knew the general idea to finding the solution to the problem though to be honest I wasn't able to come up with some sort of general expression.

And it was a fun time blogging. And I hope you enjoyed this as much as I did. :)