Magnussen Institute for Applied Fun · notes
The Blog
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Möbius
Inclusion-exclusion as counting the elements that are "new" to each set, drawn as a lattice, and its structural cousin: coproducts and pushouts.
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Dirichlet's Theorem
Infinitely many primes of the form $an+b$. Factoring the harmonic series into an Euler product, and a first try at $3n+1$ versus $3n+2$.
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An Unintuitive Guide to Linear Algebra
From relational structures up: dimension as the longest flag, exact sequences, tensor products as homsets, and primary and Jordan decomposition. With exercises and some solutions.