Education in the United States is mainly provided by the public sector, with control and funding coming from three levels: state, local, and federal, in that order. The common requirements to study at a higher education level in United States will include your admissions essay (also known as the statement of purpose or personal statement), transcript of records, recommendation/reference letters, language tests

The PhD is a doctoral degree, specifically called a "doctor of philosophy" degree. This is misleading because PhD holders are not necessarily philosophers (unless they earned their degree in philosophy!). That said, PhD recipients are able to engage in thought experiments, reason about problems, and solve problems in sophisticated ways.