Here we define the cross ratio of four extended-complex numbers (typical a+ib and infinity). We use it to answer the question "how many extended-complex numbers determine a Möbius Transformation?"
Sure, I did the masters program at Mizzou and passed the qualifying exams for the PhD program along the way. There were some standard courses in measure theory, complex analysis, differential geometry and topology, and algebra that all the masters students had to take, but you could also take the more specialized “topics” classes with the PhD folks as electives. What’s yours like?
@@DrMcCrady not there yet just asking around from your current vantge point you feel like standard courses benffited your research or the specialized “topics” did more for you?
Oh the topics ones for sure. I haven’t thought about measure theory since that class lol. The topics classes aligned more with my interests (algebra and algebraic geometry). But the other classes outside of my area were still really useful getting reps practicing making coherent proofs, getting a little bit of perspective on the history of subjects and how they overlap, etc.
Do complex integrals and the residue theorem please
do you remember your masters program?
Sure, I did the masters program at Mizzou and passed the qualifying exams for the PhD program along the way. There were some standard courses in measure theory, complex analysis, differential geometry and topology, and algebra that all the masters students had to take, but you could also take the more specialized “topics” classes with the PhD folks as electives. What’s yours like?
@@DrMcCrady not there yet
just asking around
from your current vantge point
you feel like standard courses benffited your research or the specialized “topics” did more for you?
Oh the topics ones for sure. I haven’t thought about measure theory since that class lol. The topics classes aligned more with my interests (algebra and algebraic geometry). But the other classes outside of my area were still really useful getting reps practicing making coherent proofs, getting a little bit of perspective on the history of subjects and how they overlap, etc.