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Category Archives: Math
What is a Manifold? (6/6)
In posts 13 we were able to reduce all of the geometry of a curve in 3space to an interval along with two or three realvalued functions. We also discussed when two sets of such data give equivalent (overlapping) curves. This … Continue reading
What is a Manifold? (5/6)
In our last post, we invented a new geometry by rescaling the inner product of the usual Euclidean plane. This modification did not change any of the angles in our geometry, in the sense that if two curves intersected in a particular Euclidean … Continue reading
See, Accept, Affirm
The mathematical community is one, which—while not as diverse as it could/should be—counts as members individuals from all backgrounds and of all identities. These individualities are something we as a community should cherish and support. One outlet for such support … Continue reading
Posted in Diversity, Grad School, Math, Social Justice, Teaching
Tagged Commitment, Inclusion, Inculisivity, Safe Space, Social Justice
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What is a Manifold? (4/6)
After our luxurious treatment of 1d manifolds, we turn to 2d manifolds. My story of surfaces starts in a beautifully weird morning when I got up to realize that life in the usual Euclidean plane had changed dramatically. Vectors had shortened, areas … Continue reading
Mathematical Democracy: Mission Impossible? Maybe not…
In 1950, a 29yearold PhD candidate at Columbia published a stunning theorem that later won him a Nobel Prize: “There is no such thing as a fair voting system.” Or so the legend goes. Let’s dive into this claim and … Continue reading