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Joshua Bowman
1,530 followers -
Mathematician and aesthete
Mathematician and aesthete

1,530 followers
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existence and uniqueness for some simple ODEs
Last week in my analysis class we discussed ordinary differential equations (ODEs) and their solutions. The proof of the existence and uniqueness of solutions to ODEs is one of my favorite examples of an extremely abstract theorem (in the case, the contract...

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OK, so I've done it. Here are specifications regarding the work I expect my analysis students to do this fall, and how that work will be translated into grades. Feedback welcome. Don't be gentle.

http://thalestriangles.blogspot.com/2016/08/specifications-in-analysis.html

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specifications in analysis
Earlier this week, I wrote about expectations for my analysis class this fall (which also apply broadly to upper-level math classes) and some things I learned about specs grading this summer . In this post, I’ll share the specifications I have created for a...

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taking specs seriously
I’ve been an advocate of standards-based grading since I started using it over three years ago. It has addressed many of the concerns I had about the dominant point-based grading system and encouraged students to move forward in their understanding rather t...

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expectations in analysis
I’m working on the syllabus for my (junior and senior level) analysis class this fall, and I’d like to share some parts of it, hopefully thereby eliciting feedback. The main thing I’m concerned about is the type of specifications grading I’m adopting for th...

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why I do math
I spent the past week on retreat with fellow faculty members. During part of this time, we each shared our “vocational journeys,” or the stories of how we have been led to this job and these fields of scholarship. I thought that part of my essay might have ...

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Homology modulo 2
Last week, I was chirping on Twitter about “homology modulo 2”: how closely it matches my geometric intuition of what homology should measure, despite my never having thought seriously about it before, and how its computational simplicity makes it seem like...

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Snell and Escher
A few weeks ago, Grant Sanderson posted a video on the brachistochrone , with guest Steven Strogatz . The video explains Johann Bernoulli’s solution to the problem of finding the brachistochrone, which is a clever application of Snell’s Law . ( image source...

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I've moved from absolutely hating related rates problems to believing they provide some of the best opportunities in a calculus class for demonstrating how math helps us understand how the world works. In this post I explain why. (Bonus: a "real-world" application to pouring drinks!)
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