Category Archives: Expository

The Spectrum of Rigour: PDE Theory, Shocks, and the Devil’s Invention

An overly simplistic (and hence incorrect) view of science is one in which we think all scientists have the same level of certainty in their descriptions of natural phenomena. One might suggest that different scientific fields could be arranged by … Continue reading

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Percolating Ideas

Today I want to write briefly about some of what I have been learning about Percolation Theory. I will try and make this interesting to the layperson, but some of the details require a bit of¬†mathematical maturity. As always, questions … Continue reading

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A Stroll Through Dynamics (and some Random Walks too)

Dynamical Systems is a vast area of mathematics, and one in which I have some small experience with a small bit of the research community. I won’t go into the overall field and all of its various subfields. Rather, I … Continue reading

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Measurable Counterexamples

There are many important perspectives to take when trying to understand something. A very common theme in really understanding mathematical ideas is to conceptualize them as Theorems, and understand intuitively why the assumptions and criteria become useful conditions for the … Continue reading

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