Compact and Semi-simple Lie algebras

I just read about (why I care about) compact and semi-simple lie algebras (again) and want to concentrate all my knowledge here. (Source: M Hamilton - Mathematical Gauge Theory (Springer))

Read More

Triple Jeopardy

So I talked about why linear functions, not exponential functions, are equal to their own derivative. Now I want to try and convince you that it is in fact true for every function.

Read More

a meditation on the Carathéodory criterion

My gap between learning this definition and actually making (at least some) sense of it was longer than I usually have with situations in analysis. Here’s one thing I’ve come up with to explain what it’s trying to do.

Read More