Proper nouns and formal names of departments and individuals are capitalized. In text, academic degrees when used in a general sense are not capitalized. (That campus offers bachelor's and master's degrees.) You can also use "bachelor's" and "master's" on its own, but do not capitalize.

Which is correct masters or master's?

The correct way to spell master's degree is with the apostrophe. The s in master's indicates a possessive (the degree of a master), not a plural. If you're speaking of a specific degree, you should capitalize master and avoid creating a possessive: Master of Science. The same rules apply to a bachelor's degree.

When should master's be capitalized?

Academic degrees are capitalized only when the full name of the degree is used, such as Bachelor of Arts or Master of Science. General references, such as bachelor's, master's, or doctoral degree, are not capitalized.