While the topic of the course has switched to theory of
computation, and more specifically algorithm analysis, I have been more focused
on the regular math proofs we have been doing. This is largely due to the
assignment that is due on Monday and the midterm that is on Tuesday. While it
is surprising that my ability to solve proofs is getting better very quickly, I
am noticing some common trends in where I am stuck with solving proofs. I seem
to be able to find a conclusion and then show how I came to that conclusion but
I struggle with identifying the entry point of where to start in that proof. This
is especially true when trying to prove a statement with a format such as p Ù q. You cannot assume p
and so where do you begin in your proof to prove p? There must be some base
assumption of p that is legitimate to start with. My problem seems to be
identifying what is the correct base assumption. I have had to rewrite numerous
proofs as I realized I was starting with the consequent and deriving the
antecedent.
One of the most useful (but perhaps obvious) lessons I have
learned this week related to base assumptions is that proofs cannot start with
a tautology. When trying to show that two different things are equal, I tried
to show how you can start with p = p, which could be derived to show that p =
q. However, as the proof started with a
tautology it is invalid. I had to go back and find an attribute of p that would
later link it to q. In the end it was successful but it was not the most
intuitive step to take.
Overall, while I am getting better at writing proofs, the
ordering of steps and the entry point of a proof is still something I need to
work on. Hopefully with some more practice, it will become more
natural.
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