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Category Archives: Math
AMS Notices Spotlight October 2017
Hello and welcome to the October AMS Notices Spotlight. As we are now into the swing of the busyness of the semester it is sometimes nice to take a break and think about math not related to our classes. With … Continue reading
Posted in Algebra, AMS, Mathematics in Society, Topology
Tagged Algebraic Topology, AMS, Notices
Comments Off on AMS Notices Spotlight October 2017
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
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
A Pretty Lemma About Prime Ideals and Products of Ideals
I was trying to prove a theorem in algebraic geometry which basically held if and only if this lemma held. Here’s the lemma: Lemma: Given any ring $A$, a prime ideal $ \mathfrak{p} \subset A$, and a finite collection of ideals … Continue reading
An Infinite Understanding
“Have you ever thought about how strange it is that we think about infinity every day, but most people think about it only on the rarest of occasions, if ever?” This is the text message I recently sent two of … Continue reading
Posted in Math, Math in Pop Culture, Mathematics in Society
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