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I often tell people that I love math, but math is big and I don't love all of it, certainly not in the same way.

This past calendar year I taught two very different introductory courses in Abstract Algebra and Analysis. Both are foundational---they were categories on my oral comprehensive exams in graduate school---but as different as night and day in terms of the style in which the topics act. The first one focused on articulating structures that would be useful in different contexts; the latter identifying what the notion of closeness means in different contexts.

Many topics in math have very different styles. I've taught a special topics course twice on Combinatorics which has such a very different way of approaching problems (articulate collections relevant to the context and count the size of the collections in different ways).  Multivariable Calculus for all of its techniques have some basic principles (run a curve through it, use the Chain Rule) that makes it easy to keep in my head as a teacher.

For the past couple of months I have been struggling with rereading yet again about tensors in the context of General Relativity. The basic concepts are appealing but the notation for expressing them is in my humble opinion God-awful, as in leading me to pray to my deity for swift release.  

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