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Hypothesis Testing and its Discontents, Part 3: What Can We Do?
Hypothesis testing is central to the way we do science, but it has major flaws that have encouraged widespread shoddy research. In part 1 of this series, we looked at the historical origins of...
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Why I’m Not Scared of the New Chatbots
If you haven’t already heard about AI chatbots, you probably haven’t been on the internet in the past couple of months. In November, OpenAI released ChatGPT, which can engage in text conversations with...
View ArticleWriting Calculus Tests with ChatGPT
Last week I talked about the new chatbots, like ChatGPT and Bing’s chat interface. I argued that they while they produce language they can’t really analyze it or check it for errors; and that this is a...
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Motivating the Integral with Euler’s Method
I have a fun idea for how to teach and think about the integral in the context of freshman calculus. I’ve never actually used this in a class, and I suspect it’s not actually a great idea. But it’s a...
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A Fictional History of Numbers, Part 1
In graduate school I studied number theory. The joke goes that number theory is the kind of math where you never use anything recognizable as an actual number. And it’s true that advanced mathematics...
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A Fictional History of Numbers, Part 2: Measurement, Estimation,...
This week we continue our exploration of what numbers are, and where mathematicians keep finding weird ones.In part 1, we started with the natural numbers, the most basic numbers we use to count...
View ArticleEvaluating Students is Important, Too
There’s a classic dry academic joke that I retell frequently. My entire salary is just to pay me to grade; I do the rest of my job for free.And this is first an apology for not writing much lately; we...
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A Fictional History of Numbers, Part 3: Computability, Reality, and Leaving...
Today we’re going to finish our discussion of the real numbers. We’ll see that they really are quite strange, in ways that are uncomfortable to think about, and then see why we keep using them anyway....
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A Fictional History of Numbers, Part 4: Imagination, Complexity, and the...
Welcome back to our survey of the different types of “numbers” that mathematicians work with, and what kind of questions lead us to study those numbers. This week we’re going to put a bow on the first...
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Old Books and the Passage of Time
I recently got a couple books that I’ve had on my “to read” list for several years: Frank Abagnale’s The Art of the Steal and Joseph Heath’s Enlightenment 2.0. And I’ve been enjoying both books, but...
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