I deem the information taught in the past
few lectures to be forever useful. The approach to problem solving that was
taught in class has fundamentally changed my basic concept of problem solving.
Admittedly, since I am quite familiar with solving problems, I knew most of the
points that Professor Heap taught us. However, the point about thinking of
alternate solutions and re-wiring my brain will surely help me overcome my
functional fixedness, enabling me to think outside the box and make me a more efficient problem solver.
Furthermore, my knowledge about mathematical sets has
increased vastly. Prior to starting the course, I had a slight idea of what a
set was, but now I am familiar with the notation and important concepts derived
from sets. This proved to be useful when Professor Heap encouraged us to think
of the existential quantifier in terms of sets and not just a single element.
What he said makes complete sense; if there exists an element with some
property, then a set that contains these kinds of elements is non-empty. Using
logical quantifiers together with sets makes expressing ideas clearer since the
notation is more concise.
Additionally, I found the process of looking through a set to be tedious but it proved to be useful because it helped us describe what must be done in order to prove and
disprove certain claims. I hope that my knowledge about logic and proofs
continues to develop at this rate as the course progresses since it will surely
improve all aspects of my computer science career.
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