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Roots of Unity

In Praise of Proofs by Contradiction that Aren’t

Opposing arrows, a common conclusion to a proof by contradiction.

If you don’t know what to do, do something. That’s one of my mottos when I teach math (and it’s probably good life advice too). Last year, I taught introductory analysis (basically calculus with the juicy bits left in), one of the first proof-oriented classes students take. Writing proofs is hard, and sometimes the hardest [...]

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Roots of Unity

What Is the Goal of a Math History Class?

An illustration from Oliver Byrne's 1847 edition of Euclid's Elements. Image: Public domain, via Wikimedia Commons.

I’ll be teaching a math history class for the first time this semester. I’m excited to be teaching it, but I’ve noticed that preparing for this class has been very different from preparing for other classes I’ve taught, which have all been math content courses. I know how to teach a math content course. I [...]

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Roots of Unity

What T.S. Eliot Told Me about the Chain Rule

T.S. Eliot, who probably never thought about the chain rule while he was writing poetry. Photograph by Lady Ottoline Morrell. Public domain, via Wikimedia Commons.

“We shall not cease from exploration And the end of all our exploring Will be to arrive where we started And know the place for the first time.” —from Little Gidding by T.S. Eliot If you took calculus in high school or college, you might remember the chain rule. One of the main topics in calculus [...]

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Roots of Unity

Can a Closed Set Be Open? Can an Open Set Be Closed? When Math and Language Collide

A set that is neither open nor closed. The solid arc on the top of the half circle indicates that the boundary is included in the set, while the dotted line at the bottom indicates that the boundary is not included in the set. This set could also be described as the set of all points (x,y) that are less than or equal to 1 unit away from the point (0,0) and have a strictly positive y-coordinate. Image: Evelyn Lamb.

I gave my first midterm last week. I’m teaching a roughly junior level class for math majors, one of their first classes that is mostly focused on proofs rather than computations or algorithms. It is more abstract than most math classes they’ve taken up to this point. I love teaching this class because a class [...]

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