Monthly Archives: September 2017

Applying to grad school? Here’s what you need to know: Part I

I put together my grad school applications when I was studying abroad in St. Petersburg, Russia, which meant that they were cobbled together in a string of internet cafes, fueled by little more than espresso and impatience. I dashed off … Continue reading

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Real Numbers Base…Factorials! And A By-product

PROPOSITION 1:  For a real number  x  there exists a sequence $ x_1, x_2, x_3,…$ of integers such that $ \hspace{4cm} x=x_1 +\frac{x_2}{2!}+\frac{x_3}{3!} + \cdots + \frac{x_n}{n!} + \cdots,  \hspace{2cm} (*) $ where $x_1$ can be any integer, but for … Continue reading

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Daily Quizzes: the Good, the Bad, and the Ugly—Part 2

You may recall that quite some time ago, I tried to convince you that giving your students a one- or two-question quiz every single day had a myriad of good aspects. You can check out why I loved this method in Part … Continue reading

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Shedding light on AI’s black boxes

A recent special issue in Science highlights the increasingly important role that artificial intelligence (AI) plays in science and society. Providing a small but compelling sample of the types of challenges AI is equipped to tackle—from aiding chemical synthesis efforts … Continue reading

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Gauge Theory and Low-Dimensional Topology (Part II: Smooth Four-Manifolds)

In the last post, I attempted to give an overview of the state of affairs in four-manifold topology leading up to the introduction of gauge theory. In particular, we discussed the correspondence between (topological) four-manifolds and their intersection forms afforded by … Continue reading

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