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Calculus, statistics, linear algebra, modeling and more
Once or twice a month, I’ll post material that I think might be useful for educators. What level of education and what classes will vary, and I’ll note that in the headers so you can skim easily or read them all because they are here due to being potentially useful in the classroom but, more importantly, interesting. In some cases, it may be worth just showing students some of this so they see where math is being used. Please share this with anyone who teaches.
Hierarchical clustering plus a sin(x) and cos(x) model
There is plenty of modeling and statistics going on in the article Increasing ocean wave energy observed in Earth’s seismic wavefield since the late 20th century, but I’ll point out two. The first is hierarchical clustering. The article has links to the data that could be used in a data science course.
If you just want to show students that people use sin(x) and cos(x) to model the world, then here you go:
Calculus, statistics, sustainability, and QL
Nate brings up the logistic curve and says that it’s derivative is a normal curve, “without getting too mathy.” He also talks about the area under a curve representing total fossil fuel consumption and the different possible curves that might model the future. You can jump to the 8-minute mark to save a little time as you preview the video.
Average rate of change and QL
The EIA posts almost always have lots of percentages and graphs that are great for QL or wherever percentages are taught (I don’t know where this happens in K–12). Here is an example from EIA expects U.S. annual solar electricity generation to surpass hydropower in 2024.
Solar power outpaced hydropower again this summer due to exponential growth in installed solar capacity. From 2009 to 2022, installed solar capacity increased at an average rate of 44% per year, and installed hydroelectric capacity increased by less than 1% each year.
I talked about the whale pump as a carbon sink in Thursday's Quick Take. The paper Whales in the carbon cycle: can recovery remove carbon dioxide? (3/2023) includes discrete time modeling. Below are two screen shots. One of the things I’m finding is that there is a lot of neat mathematics happening in an applied setting that we should get into mathematics classes. The problem is, how does this happen, and who has the time? Contact me if you have thoughts.
Population models and Poisson random variables
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