Candidates for the Ph.D. degree in the Department of Mathematical Sciences must pass a qualifying examination, three comprehensive written examinations, a basic mathematical reading knowledge test in a language other than English, a comprehensive oral examination, and a final oral doctoral thesis examination. These are briefly described below. For more information, see the Mathematics Graduate Student Handbook.
Qualifying examination:
Every student admitted to the Ph.D. program must complete the Ph.D. oral qualifying examination. Its purpose is to determine the areas in which the student shows strength or weakness, as well as the ability to assimilate subject matter presented at the graduate level. Students who complete their mathematics master's degree at NMSU may request at the time of applying for their master's oral final examination that the Master's examination also fulfill the Ph.D. qualifying examination requirement. In all other cases, towards the end of the student's first semester in the Ph.D. program, the student and his/her adviser will convene an oral examination with three examiners, the examiners being the adviser and some of the student's current or past instructors.
Comprehensive examinations:
Candidates for the Ph.D. degree must pass written comprehensive examinations in three of the seven areas of algebra, complex analysis, differential equations, logic and foundations, real analysis, statistics and topology.
To ensure adequate breadth, a combination of three comprehensive examinations is admissible only if it includes at least one of algebra and topology, and at least one of complex analysis and real analysis.
The seven examinations are based on the following comprehensive examination sequence courses: Algebra (MATH 581, MATH 582), Complex Analysis (MATH 591, MATH 592), Differential Equations (MATH 531, MATH 532), Logic and Foundations (MATH 557, MATH 585), Real Analysis (MATH 593, MATH 594), Statistics (STAT 562, STAT 571), and Topology (MATH 541, MATH 542).
Course requirements:
Ph.D. students must first pass the three one-year sequences needed to prepare for three written comprehensive exams. Before graduation, a student must pass a total of four comprehensive exam sequences, but needs to take the comprehensive examinations in only three of them. Together, the four sequences must include three of the four sequences in Algebra, Complex Analysis, Real Analysis, and Topology. In addition, a student must pass four more (one-semester) regular MATH/STAT courses (not individualized study) above MATH/STAT 529.
A student may pass any of the four comprehensive examination sequences before enrolling as a Ph.D. student, but the four additional courses have to be passed after enrolling as a Ph.D. student.
The following individualized study courses will not count towards the course requirements: MATH/STAT 540, MATH/STAT 598, MATH 599, MATH 600, MATH 700.
Students and advisers are encouraged to consider further courses beyond this minimum.
Foreign language examination:
The department requires that each Ph.D. student passes a basic mathematical reading knowledge exam in a language, other than English, relevant to the student's research interests. This exam is coordinated by the student's adviser and consists of the open-dictionary written translation into English of a mathematical text of interest to the student. Fulfillment of this requirement is needed in order to be admitted to the oral part of the Ph.D. comprehensive examination.