The Graduate School and McCormick provide incoming PhD students with full funding, including paid tuition and a monthly stipend. The Graduate School and McCormick provide incoming PhD students with full funding, including paid tuition and a monthly stipend.

Graduate Study
Curriculum & Requirements

The PhD program in applied mathematics at Northwestern includes a combination of coursework, research, and professional development. The coursework is a combination of core applied mathematics topics with special topics courses that are chosen to support your research and personal interests. The core courses include differential equations, mathematical modeling, asymptotic analysis, and numerical methods.

Typically graduate students are not involved in research during their first year, completing only coursework. There are four preliminary exams (given in the first year in the beginning of January) that are based on foundation concepts necessary for more advanced coursework and research.

At the end of the first year of coursework, students choose research advisers and begin research that will lead to their PhD dissertation. Research groups vary in size from a single faculty member and student, to groups involving combinations of multiple faculty, postdocs, and graduate and undergraduate students. Often research is conducted in collaboration with faculty in an applied field outside the department.

Almost all students serve as teaching assistants during their second year of studies. Serving as a teaching assistant gives students the opportunity to develop their teaching and mentoring skills. During the second and part of the third year, students continue taking courses along with their research. Students also take the Qualifying Examination by the end of their second year. After that, they concentrate mainly on research.

The average time for completion of the PhD program is about five years.

Jump to a Section

The following requirements are in addition to, or further elaborate upon, those requirements outlined in the Northwestern University Graduate School policies. These requirements can generally lead to a master's degree after three quarters of study.

Students admitted to the PhD program will satisfy these requirements upon completion of the first year PhD degree program (see below). Additional information is available in the ESAM department's PhD student handbook.

Coursework Requirements

To see a list of coursework requirements for the PhD in engineering sciences and applied mathematics, please see the department’s PhD student handbook.

PhD student handbook

Return to Top

Required Program for first-year PhD Students


ES APPM 420-1
ES APPM 411-1
ES APPM 446-1
ES APPM 421-1


ES APPM 420-2
ES APPM 411-2
Designated Modeling Elective*


Designated Asymptotics Elective
ES APPM 411-3
ES APPM 444-0 or ES_APPM 445-0
Designated Modeling Elective*

*The designated electives will be determined by the department. Reminder: The Responsible Conduct of Research training is also required in the first year.

Return to Top

Responsible Conduct of Research

Responsible Conduct of Research (RCR) training is required by The Graduate School of all first year graduate students and consists of two parts: First is the GEN_ENG 519 course, which must be completed by the end of the Spring Quarter of the first year of study. Please see the PhD student handbook for more details.

Second is a CITI online course that should be completed by December 1 of the first year of study. Learn more about setting up a CITI account

Return to Top


During the first year of study, a passing grade in the written preliminary examinations in differential equations, advanced calculus, complex variables and linear algebra is required. The examinations are given at the advanced undergraduate-beginning graduate level. The preliminary exams are scheduled for the beginning of winter quarter. One retest is possible and will be scheduled for the beginning of spring quarter.

Return to Top

Qualifying Examination

An oral qualifying examination is required for admission to candidacy. The qualifying examination is normally taken at the end of the second year of the program. This oral examination is administered by a faculty committee, including the student's research adviser.

The precise nature of the examination is decided by the student's approved thesis committee. The content of the exam is determined by the research advisor(s) and can include a brief presentation of the proposed thesis research project in addition to questions drawn from course material relevant to the project. The student must identify, in consultation with the research advisor(s), at least three graduate level ESAM courses that are most relevant to the proposed project. The list of courses must be approved by the committee prior to the examination and the student will be expected to answer questions based on those courses. 

Upon passing the qualifying examination, the student is admitted to PhD candidacy. A student must be admitted to candidacy prior to the beginning of the student's third year. If the student does not pass the examination, the faculty committee will determine if and when a retake is warranted.

Return to Top

PhD Dissertation

Original research, defended before the student's doctoral committee.

Return to Top

Thesis Defense

The final examination is on the student's completed doctoral research, presented in lecture style to a faculty committee including the research adviser. Copies of the doctoral dissertation should be given to each member of the examination committee at least two weeks prior to the presentation. Upon passing the final examination, the committee will recommend to the university that the PhD degree be awarded.

Return to Top

Other requirements

Satisfactory progress in the program is determined by department review of examination results, course grades, and faculty recommendations.

Return to Top

requirements for Students entering with BS

Students entering with a BS degree must take at least 20 courses. There are 12 core, required courses, and students may choose their remaining 8 elective courses. Most students take 12 courses, 4 per quarter, during the first year, 6-7 courses in the second year, and 1-2 courses at the beginning of the third year of study. After successful completion of the first year of study, students may receive an MS degree.

Return to Top

Requirements for Students Entering with MS

Students entering with an MS degree must take at least 18 courses. There are 12 core, required courses, and students may choose their remaining 6 elective courses. Most students take 12 courses, 4 per quarter, during the first year, and 6 courses in the second year.