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Joshua Bowman
1,464 followers -
Mathematician and aesthete
Mathematician and aesthete

1,464 followers
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Here is a new blog post about my calculus syllabus for the fall. I've made several changes from the last time I taught the course, with the twin goals of clarifying expectations and streamlining assessment. That means more of this is untested than usual, so I plan to share updates later in the semester about how things are going.

http://thalestriangles.blogspot.com/2018/09/2018-calculus-syllabus.html

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2018 calculus syllabus
In my last post , I explained a bit about how I feel like my syllabus is a work-in-progress, even though the semester has started and I’m already using it. In this post I’ll give some more details and even more history. I’ll quote extensively from my syllab...
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New post: “prologue to a syllabus”
http://thalestriangles.blogspot.com/2018/09/prologue-to-syllabus.html
In which I explain why I haven’t shared my syllabus for the fall yet.

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prologue to a syllabus
(This was originally supposed to be the post in which I describe my syllabus for the fall. I started writing some preliminary comments, and they got out of control. I’ll get back to the syllabus itself in my next post.) First, I must express some gratitude....
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“Create Your Own” part 1
Today was the first day of calculus for the fall semester of 2018. As a first-day activity, I wanted to do something that didn’t require any calculus knowledge and could break students out of the mindset that doing math is always about solving particular pr...
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dialectics in mathematics
This post is part of the Virtual Conference on Mathematical Flavors , and is part of a group thinking about different cultures within mathematics, and how those relate to teaching. Our group draws its initial inspiration from writing by mathematicians that ...
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summer activities
This summer I had a fair amount of travel and conference/workshop activities. I’ve also been working on several projects that need finishing, and of course I have an eight-month old daughter. So I haven’t been blogging, even though several ideas for posts h...
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angels’ staircases
Here’s a pair of facts I hadn’t much considered before the last time I taught real analysis : The only kind of discontinuity a monotone function can have are jump discontinuities . A monotone function can have at most countably many discontinuities. One thi...
angels’ staircases
angels’ staircases
thalestriangles.blogspot.com
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boxes and fractions
Last week at MathFest , Dusa McDuff gave an excellent series of lectures on symplectic geometry . I enjoyed the second one the most, because in it she described the solution to a concrete problem that had a beautiful and expected answer, and used several to...
boxes and fractions
boxes and fractions
thalestriangles.blogspot.com
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addition of fractions is bilinear
The prototypical example of a bilinear operation is multiplication, \(b(x,y)=xy\). For a function of two variables, bilinear means “linear in each variable.” That means multiplication has the following properties:
\[
b(x_1+x_2,y) = b(x_1,y) + b(x_2,y)
\]
\[...
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