I am currently a student about to come towards the end of my 2nd year at University. I had a great professor at the start of the year, and I was interested in trying something outside of traditional studies. I approached him and asked whether I could start trying out some research and whether he would supervise and guide me. He agreed and even provided some nice topics.
We've decided on a topic and I'm ready to get started.
Question. Does anyone have any general advice for me, so that I can make the most of this opportunity? What types of skills should I aim to pick up? With what attitude should I approach this research to make it as fruitful as possible?
I am only just starting research, so I don't have a lot of background behind how it works, and what are some ways of getting familiar with a given field? Any useful websites or ideas are appreciated!
What would be a reasonable goal? Publishing a paper?
Would publishing a paper require actual new mathematical discovery, or for a start would compiling together various core theorems and ideas and re-proving them from different existing papers count as well?