Math I Ought to Learn

27 Jun 2016 13:18

Some of you may have had occasion to run into mathematicians and to wonder therefore how they got that way...
---Tom Lehrer, "The Great Lobachevsky"

I know so little math for someone in my position that frankly I sometimes feel like a fraud. And much of what I do know is the half-wrong physicist's version.

Abstract algebra (beyond group theory): universal algebra, category theory, lattice theory, Galois lattices. Functional analysis (for real, not just the rudiments needed for probability and Markov processes). Algebraic geometry (for algebraic statistics). Matroids.

See also: Basis Selection in Function Decomposition; Cellular Automata; Computation, Automata, Languages; Dynamics; Economics; Ergodic Theory; Gödel's Theorem; Graph Limits and Infinite Exchangeable Arrays; Information Theory; "Math Methods"; Mathematical Logic; Optimization; Physics; Probability Theory; Statistics; Operator Semigroups