Course names are capitalized when one is referring to a specific course title, the actual name of the course.
Ex. I am taking Physics 102 Ex. My favorite class is American History during fourth period.
Course names are not capitalized when referring to the SUBJECT studied in a certain course.
Ex. I think that math is a littler harder this year. (Your actual math class might be Probability and Statistics, that would be capitalized) Ex. My business class was really difficult. (You would capitalize "Modern Business Organization, not just "business".
letters
Yes of course. All personal names are capitalised
Yes, names of countries are capitalized.
No, the names of most herbs are not capitalized
Yes, protein names are typically capitalized in scientific writing.
In general, "course" should not be capitalized unless it is part of a title or at the beginning of a sentence.
No, but the names of individual languages are capitalized.
"Roman" should be capitalized, but "goddess" should not me. The names of Roman goddesses are proper nouns and should be capitalized.
Yes, gene names are typically capitalized in scientific research papers.
No, generic drug names should not be capitalized in medical writing.
No, I read an article about scarlet fever, and it was not capitalized.
Yes, names should always be capitalized.
No it is not as it is not a trade name. Only trade names of medications are capitalized.