The correct spelling of the phrase "study at coarse" is actually "study at a course." The error likely stems from confusion between the homophones "coarse" and "course." "Coarse" has the IPA phonetic transcription of /kɔːs/, which means rough or heavy in texture. Whereas "course" has the IPA phonetic transcription of /kɔːs/, which refers to a path or direction. It's important to pay attention to small differences in spelling and pronunciation to avoid miscommunication.