The title of this blog seems to imply that this is the second in a series of blogging my mathematical blunders and in a way it is. The first blunder went untitled as such and I am almost afraid to bring attention to it again but was placed in the entry, “I should be fired!”. As I have pondered the content of this blog, I have decided that Monday is Blunder Day. (Yeah, I know it’s Tuesday, but I was sick yesterday, boohoo). It just seems appropriate that the hardest day to get through with out making dumb mistakes at the board should be a day honored by blogging about the careless errors I have made over the last week. The hope is that by doing so, I identify where my tend to make most of my mistakes and rectify that problem. I had in mind the blogging of some great ones, but realized that most of the mistakes I make are rather uninteresting. So, lucky for you, I decided to blog them anyway.
“So, ” you ask, “what was the most significant blunder of the week?” In preparing a Calculus Exam over Infinite Series and Sequences, I had given a review sheet to the class explaining that the test would be made up of very similar questions to the review. So on the review, one of the questions was simple enough:
a. Find the Taylor series expansion for [tex]f(x)=\ln (x)[/tex] centered at 2.
Thus, in quickly revising for the test I made simple change by switching to another innocent looking function, not thinking I’d changed the problem significantly.
a. Find the Taylor series expansion for [tex]f(x)= \sin(x^2)[/tex] centered at 2.
It’s the centered at two that is ugly. Now for the math majors or mathematicians out there that read this. Let me ask you to do this. Find the answer and write it in a general summation form. Then tell me how long it took you to discover the pattern needed to write the general formula for the nth term of the series. Then answer me this: Was I unreasonable to make this one of 10 problems for an hour and 15 minute exam?
For you non-mathematicians, you may remember me as the cruel beast of a teacher how discovers the difficulty of his tests only after he “inflicts” them upon his students. Wah ha ha ha ha! (evil laugh)