trying to be a mile wide AND a mile deep
In a number of tests for series convergence and divergence, you locate or calculate a quantity and draw conclusions based on its value. Here’s a table of which values give what conclusions, for five such tests. Note that the table assumes the series is of the correct form for the test to apply at all […]
1. There is no one multiplication for vectors. You can define multiplication-like operations; some give scalars (dot product and other inner products) and some give vectors (cross product). Nicely, these behave like regular products when it comes to vector-valued functions: the product rule applies when you differentiate (though you must maintain ordering with cross product!). […]
This is a page I made for my statistics students in Spring of 2010. I can’t guarantee it’s perfectly accurate with a current version of Excel because I don’t have Excel on my current computer, but I assume it should still be very close. In all of the below, “data” (“x-data”, “y-data”) stands in for […]
1. Drawing causation conclusions Ski and snowboard sales tend to rise and fall together, but sales of one don’t lead to sales of the other – they are both tied to an outside factor. Throughout grade school, mathematical skills correlate positively to height. Height doesn’t make you good at math, but older children are on […]
The three properties of relations learned first are reflexivity, symmetry, and transitivity. Reflexivity is an existence property; a possession property. If you contain this entire particular set of pairs, you’re reflexive. If not, then not. Symmetry and transitivity are implications; closure properties. Now some pairs don’t come for free – they require other pairs be […]
If you disagree, feel free to append “IMNSHO” to each. Respect your students: Learn their names. Start and end on time to the best of your ability. Admit your mistakes and when you don’t know an answer. Answer questions without implying they are stupid ones. Set out all expectations in the syllabus and stick to […]