trying to be a mile wide AND a mile deep
For a statistics exam, I wrote a question about the regression effect in application that I quite like. Here it is, with the answer this time. Q. A lab assistant in charge of measuring how long it takes for rats to run a maze predicts that usually a rat will take less time on its […]
1. “Sufficiently large” is an important concept in sequences and series. In essence it means any crazy thing can happen for as long as it wants to happen, so long as there is a finite point after which the sequence or series starts behaving in a controlled/predictable way. A finite number of terms can’t affect […]
I like examples. diagonalizable not diagonalizable invertible I_n, rotation about non-axis line by, say, 60 degrees in R^3, rotation 90 degrees in R^2: not invertible zero matrix, rotation 90 degrees plus projection onto yz-plane in R^3:
I like to present totally cooked-up examples demonstrating the reason for certain hypotheses or limitations in calculus, in the hope that they will help students remember and correctly apply the theorems more easily. Here are a few. Note that the sequence has limit 0 but the function oscillates. This is why you can use convergence […]
1. Willie Nelson’s song “I’d Have to be Crazy” contains the line I’d have to be crazy to fall out of love with you. Based on that hypothesis, he asserts The place where I hold you is true, so I know I’m all right. Is this a logically valid argument? That is, is still being […]
Honestly, I never made use of Turing machine simulators when I taught computability theory, but they can be quite fun to play with and allow you to run programs that are far more complicated than you could ever step through with pencil and paper. The list below could be considered an update of the list […]