Maybe-Mathematical Musings
Math, Teaching, Literature, and Life
April 03, 2023
Mathematicians deal with lots of different kinds of "numbers". But where do they come from? In this series we'll see where different types of exotic numbers came from, and what reasonable questions we need them to answer.
In Part 1, we're starting off with the simplest types of numbers: the algebraic numbers. We'll see how we could have invented square roots and weirder things on our own, just by asking one reasonable question after another.
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March 15, 2023
I realized you can "prove" the Fundamental Theorem of Calculus by using Euler's method for solving differential equations. It's a fun way to motivate the integral, but not one that I'm actually going to use in class.
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March 08, 2023
ChatGPT is cool, but doesn't seem useful yet for doing serious intellectual work. But is it useful for more routine stuff? I wanted to see if I could use ChatGPT to write test questions for my calculus courses. I'm experimenting with using ChatGPT to write test questions. My verdict: not completely useless!
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February 27, 2023
Modern AI chatbots like ChatGPT are impressive, but they work in very specific and limited ways. They produce surprisingly human-like text—as long as the human isn't paying attention. And that tells us a lot about what we can expect this technology to do for us.
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July 25, 2022
This is the third part of a three-part series on hypothesis testing.
Hypothesis testing is central to the way we do science, but it has major flaws that have encouraged widespread shoddy research. In this essay we consider methods that can help us draw better conclusions, and avoid the pitfalls of hypothesis testing. We start with some smaller and more conservative ideas, which basically involve doing hypothesis testing _better_. Then we'll look at more radical changes, taking the focus away from hypothesis tests and seeing the other ways we can organize and contribute to scientific knowledge.
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