How to evolve from a student to a researcher?

The question in the title is actually what puzzles me a lot, and since I’m living on campus, I have heard how PhD students and young researchers are suffering. Some of these complaints, especially those about programmers, are of course jokes, but I also know…

Random algebraic thoughts

Extension fields and automorphisms are the most amazing thing I have ever learned. Essentially, when you think of them together, they are like a flower whose petals communicate with each other, but the center remains fixed.   I’m still reading the part on extension fields and…