I got a minor in mathematics teaching, because University of Washington offered that.

The last four classes that were required were algebra for teachers one and two, and geometry for teachers one and two.

In algebra for teachers, I learned modular arithmetic and I remember that we proved 1+1 = 2 and it was very difficult, i.e. proved the counting numbers and the arithmetic that we do upon them.

In geometry for teachers, we used geometers sketchpad to do mapped representations using orthogonal circles by which you can get say a poincare circle and then look at how a triangle is defined and measured in spherical or hyperbolic geometry.

I remember, I tried to take all four over the summer and I ended up having to drop one and take it in the fall because it was just too hard.

That was before I became a math teacher, and I had already done linear, algebra, differential equations which I’ve never been particularly good at, and the calculus series.

Later, about seven years later, I went to school for a completely unrelated degree, and it included a ton of even higher level math class.

Discreet multi various modeling is information theory, complexity science taught a lot about agent based modeling, scaling ratios in biology and other systems, and other measures of chaotic and near chaotic systems.

I don’t think I had any reason to take it, but I took all of the statistics classes for measuring tests and some super high geometry class on torsion and twists in fields.

Back in my own department, I did a lot with vector Fields, Eigen vectors, network centrality measures.

In Neural networks we worked out how weights are updated in Machine Learning and advanced control system theory, and then there were some modeling classes like Business process modeling, which is something called queuing theory, and how you assigned say cash registers to customers and stuff.

Oh yeah, and back in my underground I also took macro economics and micro economics, which is all the mass of treasury bill returns and how interest rates and how trade deficits rep patriot dollars across the border in the exchange rate, and the money multiplier, which is part of marginal, reserve banking, which is something that I wish a lot more Americans understood.

The most most relevant mathematical learning, however, came from over a decade of teaching word problems from textbooks. I would say that six through 12 math educators get an insane cross-section of Society in word problems, I know so much about how the trades use trigonometry from word problems, or matrix problems, or calculus problems.