There are multiple online guides to the email etiquette and efficient email communication in the student-professor situation. Here are a couple of useful links:
I don't have any positions open, be it researh, teaching, or grading. I don't have any lab or research group you can apply for. I don't have any research projects below the Ph.D. student level. If you are a student wishing to work with me, you must get admitted to Courant's Ph.D. program in Mathematics first, through the general admission procedures.