Understanding probability
Math with Bad Drawings is in the midst of a series about probability to try to explain the concepts without the computations. It is wonderful so far, and promises to cover a lot of territory.
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Distinguishing related rates and optimization
One of the main things students struggle with on exams is identifying the method to use on each problem. When they are learned in class, they are segregated by type, and their distinguishing features are not always highlighted. Here’s a brief cheat sheet on related rates and optimization. optimization related rates sample keywords maximize, minimize, […]
Optimization
As with related rates, optimization is sometimes approached with some dread. Fortunately, although the calculus has more steps than in related rates, the process is somewhat more cut and dried. A. Make two-word phrase of goal, where first word is minimize or maximize and second word is the name of a quantity. B. Name quantities […]
Related Rates
These are perhaps the epitome of the dreaded “word problem.” Fortunately there is a step by step method for solving them. A. Assign variables to your quantities and find relationship equations for them. B. If relevant, simplify the equations to remove extraneous variables. C. Express given and asked-for rates of change in terms of d/dt. […]
Linear Algebra Presentations
Here are slide presentations for a linear algebra class that claims to include applications, but really barely has enough time to cover the nonapplied material. I made two presentations that could be done in 20 minutes of class time. These are both incorporated to some degree into the math club linear algebra talk I gave, […]
Invertibility and the Determinant
I didn’t really like the cofactor construction of the inverse of a matrix with nonzero determinant, to prove said inverse exists. I’m willing to accept the equation det(MN) = det(M)det(N) on faith, since I am confident I could work that out if I really had to. With that in my pocket, here’s an explanation of […]