Welcome back (or welcome, if this is your first time) to another episode of my take on mathematical expressions and reasoning! After the past week, I feel fairly confident that I can complete a big-Oh proof and its negation without serious trouble. What unnerves me is the increasing scope of the proof (e.g., proving general statements about more than one function via the big-Oh). I cannot help but picture a lengthy series of questions that requires me and other students to take two different pieces of code, calculate the bounds of their worst cases, and then prove a general statement between some combination of the four functions. A massive undertaking that could not be successful unless no mistakes are made. I am certain there are well-paying jobs for this; the ability to calculate code and determine its strengths and weaknesses for a software company on paper must be valuable.
Another remark: I recoil from the fact that some example proofs we do in class have "omitted book-ends" within them. I recognize that the class is not long enough for these book-ends to be included while staying on track with what must be taught, but unless these book-ends are included in the Course Notes posted online for the course, or these book-ends are nothing more than elementary arithmetic (I have not had time to complete these book-ends as of late), it seems somewhat counter-productive to the primary goal of education. If we were to solve these book-ends incorrectly, and convince ourselves when we study that what we did was correct/complete, we harm our own academic growth. Understanding how to structure a proof is vital--but the same can be said for the proof itself. One helps build and solidify an answer, and the other is the answer. Hopefully, if I can make time during this excessively busy month, I will be able to ask my professor or my TA about these "omitted book-ends."
Thank you for reading.
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