A mathematics PhD may refer to several different degrees with diverse areas of focus. The most common doctorates awarded in this field are in mathematics, applied mathematics, statistics, or mathematics education. Each of these has different doctoral study areas and they may have slightly diverse requirements for program application. In any of these subfields, earning a doctorate is challenging and will require a number of preparatory steps.
Most people who seek a mathematics PhD of any kind have earned or will earn an undergraduate degree prior to being admitted to a program. Some schools may prefer masters’ students only, but many schools do admit students with only bachelor’s degrees. In virtually all cases, students have gotten a degree in a mathematics field, though a few people with strong skills and prerequisite courses in math might be able to apply without this, provided they have some type of four-year degree.
A number of doctoral programs require that students take the Graduate Record Exam (GRE) general and subject test, and some schools lean heavily on subject test scores to determine what students they’ll admit. Students also need strong grades in mathematics courses, a good overall GPA, letters of recommendation and an impressive personal statement. Schools prefer studies in foreign languages, particularly languages like Russian, and they often make proving competency in a language part of mathematics PhD requirements.
In many straight mathematics PhD programs, there are several qualifying examinations students will need to take to stay in school. One of these usually occurs the first year of studies, and then students may take additional examinations, both oral and written, in the second and third years of study. Courses taken should help prepare students for these exams, and they may have opportunities to retake them, in some cases. Usually, successful exam completion is essential to progressing in a program, and all exams must be passed before a student is advanced to doctoral candidacy and can start work on a dissertation. Different PhDs in math education or statistics may not have as many examination requirements.
Typically, students don’t begin dissertation work until the third or fourth year of school, and these dissertations are extensive and may take considerable time to complete. It’s unusual for students to finish a mathematics PhD of any kind in less than four years, and many students take five to seven years to complete their work. There are also core and elective courses students take as part of fulfilling unit requirements. The PhD is only earned once all program requirements are met, and after a student’s dissertation has been approved by members of the faculty.
