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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
Posted in Advice, Grad School, Grad student life, Starting Grad Schol
Tagged Advice, Grad School, graduate students
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Real Numbers Base…Factorials! And A Byproduct
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
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 twoquestion quiz every single day had a myriad of good aspects. You can check out why I loved this method in Part … Continue reading
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
Posted in Mathematics in Society, Statistics, Technology & Math
Tagged AI, Artificial Intelligence, mathematics, statistics, Technology
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Gauge Theory and LowDimensional Topology (Part II: Smooth FourManifolds)
In the last post, I attempted to give an overview of the state of affairs in fourmanifold topology leading up to the introduction of gauge theory. In particular, we discussed the correspondence between (topological) fourmanifolds and their intersection forms afforded by … Continue reading