Graduate Programs
Graduate Programs as of 2011-2012
- Graduate Program Summary
- Fellowships
- Application Process
- MS Degree Requirements
- PhD Degree Requirements
- 1st Year PhD Program Schedule
- Graduate Program Registration Sequence
Graduate Programs Summary
The Department offers two graduate programs, an MS program and a PhD program. Qualified students with backgrounds in engineering, mathematics, or science are eligible for admission to either program.
The MS program is designed for students who want a background in basic applied math skills but who are not necessarily interested in pursuing PhD studies. The MS program can be completed in 3 quarters of study and is suitable for students who intend to work in, for example, industrial environments where specialized PhD training is not required.
The PhD program is designed for students who want to pursue research in applied math at the highest level. The PhD program prepares students for independent research, emphasizes flexibility in adapting research areas to current opportunities and is suitable for students interested in teaching at the university/college level or those interested in PhD level research at national and industrial laboratories and other similar environments. PhD students can obtain a Masters degree after successful completion of the first year PhD program.
The applied mathematics faculty is involved in research that utilizes a variety of mathematical methods associated with asymptotic analysis, bifurcation theory, graph theory, numerical analysis, optimal control, ordinary and partial differential equations, probability and statistics, singular perturbations, stability theory, and stochastic processess. These methods are employed in the investigation of problems arising in biomechanics, combustion theory, diffusion processes, fluid mechanics, geophysics, interfacial phenomena, molecular biology, queueing theory, reactor theory, solid mechanics, statistical mechanics, transport theory, and wave phenomena.
Fellowships
First-year PhD students are typically supported by university fellowships, which pay tuition costs and additionally provide a generous monthly stipend to cover living expenses. These fellowships carry no assigned duties, so that students can direct all their efforts toward their studies. After the first year, students are supported by research assistantships, teaching assistantships or other special fellowships.
Application Process
To obtain more information about the programs send a message to esamgrad@northwestern.edu
All graduate program applications must be submitted online. To apply to either graduate program follow the online application instructions below.
The application deadline for Fall admission is Friday, January 13, 2012. The application and all of your materials (including rec. letters, transcripts, scores, etc.) must be in by this date.
All information about the application process can be found at the Graduate School website. For your convenience, the application steps are summarized below.
The application process:
Go to the Graduate School website . Click on the "Apply Online" link. Follow the instructions to complete the application. PhD applicants will be able to indicate their desire to be considered for financial aid. Please note that your application will not be processed until the application fee is paid.
Graduate School Requirements
All applicants receiving an offer of admission must have earned a bachelor’s degree from a regionally accredited institution or the international equivalent(3-year Bachelor’s degrees are acceptable). Applicants that have not earned a bachelor’s degree by their intended quarter of entry will not be permitted to enroll. Applicants who are not United States citizens or permanent residents, or whose native language is not English, must provide evidence of English proficiency (see Certifying English Proficiency). At the minimum, all applicants must submit the following items online:
- application
- Statement of Purpose
- $75 non-refundable application fee, paid via credit card
- official transcripts of all academic work
- two letters of recommendation
- a copy of your GRE scores (only general aptitude exam required)
- a copy of your TOEFL score (all applicants whose native language is not English unless the applicant has a degree from an English-speaking institution)
PLEASE NOTE: Official GRE and TOEFL scores must be sent from the Educational Testing Service (ETS) to the institution code 1565. The minimum TOEFL-IBT score is 90 for the PhD program, and 80 for the MS program.
MS Degree Requirements
The following requirements are in addition to, or further elaborate upon, those requirements outlined in the Northwestern University Graduate School Bulletin. These requirements can generally lead to a Masters Degree after 3 quarters of study. Students admitted to the PhD program will satisfy these requirements upon satisfactory completion of the first year PhD degree program (see below).
Admission Qualifications
- Supplementary Material:
- None specified beyond the requirements outlined in the Admission section of The Graduate Bulletin.
- Undergraduate/Graduate Degree:
- Preference given to majors in mathematics, the physical sciences, or engineering
- Coursework Background:
- Linear algebra, advanced calculus, complex variables, ordinary differential equations and partial differential equations highly desirable
- Relevant Research or Experience:
- Prefer experience with topics mentioned above
- Other:
- Official GRE scores
Coursework Requirements
Each candidate for a MS degree is required to satisfactorily complete an approved program of three full quarters of graduate study.
| Course | Subject | Units |
|---|---|---|
| ES APPM 411-1,2 |
Differential Equations of Mathematical Physics |
2 |
| ES APPM 311-1,2 can be substituted with department permission | ||
| ES APPM 420-1 | Asymptotic and Perturbation Methods in Applied Mathematics | 1 |
| Approved modeling electives | 3 | |
| ES APPM 446-1,2 | Numerical Solution of Partial Differential Equations and designated numerics elective |
3 |
| Additional approved electives, of which up to 2 can be Masters projects (ES APPM 499) |
3 |
|
| Total Required Units: | 12 | |
Other MS Degree Requirements
- Satisfactory progress in the program is determined by department review of course grades, and faculty recommendations. The Graduate School requires all students to maintain at least a B average.
PhD Degree Requirements
Admission Qualifications
- Supplementary Material:
- None specified beyond the requirements outlined in the Admission section of The Graduate Bulletin.
- Undergraduate/Graduate Degree:
- Preference given to majors in mathematics, the physical sciences, or engineering
- Coursework Background:
- Linear algebra, advanced calculus, complex variables, ordinary differential equations and partial differential equations highly desirable
- Relevant Research or Experience:
- Prefer experience with topics mentioned above
- Other:
- Official GRE scores
Coursework Requirements
| Course | Subject | Units |
|---|---|---|
| ES APPM 411-1,2,3 | Differential Equations of Mathematical Physics3 | 3 |
| ES APPM 420-1,2 | Asymptotic and Perturbation Methods in Applied Mathematics | 2 |
| ES APPM 421-1 | Models in Applied Mathematics | 1 |
| ES APPM 446-1,2 | Numerical Solution of Partial Differential Equations | 2 |
| Electives1 (designated2 or approved) | 12 minimum | |
| Total Required Units: | 20 minimum | |
1A maximum of 3 electives from outside the department can be taken after the 1st year of study. Additional outside electives can be requested by petition to the ESAM department.
2There are two designated numerics electives, ES_APPM 445 Iterative Methods for Elliptic Equations and ES_APPM 448 Numerical Methods for Random Processes. There are two designated asymptotics electives, ES_APPM 420-3, the third quarter of Asymptotic and Perturbation Methods in Applied Mathematics and ES_APPM 412-1, Methods of Nonlinear Analysis. Designated numerics electives are offered in alternate years as are designated asymptotics electives.
Other PhD Degree Requirements
- 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 a 3-hour ES_APPM 519 seminar that will be offered in the Winter and Spring 2011 quarters. Information about RCR can be found here.
Second is a CITI online course that must be taken before the beginning of the second year of studies. Information on setting up a CITI account can be found here.
- Examinations:
- 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 upon petition and will be scheduled for the beginning of Spring quarter.
- Qualifying Examination
- An oral qualifying examination is required for admission to candidacy. The qualifying examination is normally taken close to the time when graduate course work is completed. This oral examination is administered by a faculty committee, including the student's research advisor. The precise nature of the examination is decided by the committee. The examination will cover, but not necessarily be limited to, material from advanced courses as well as topics in the proposed field of doctoral research. 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 fourth year. If the student does not pass the examination, the faculty committee will determine if and when a retake is warranted.
- Research/Projects:
- None specified
- PhD Dissertation:
- Original research, defended before student's doctoral committee
- Final Evaluations:
- The final examination is on the student's completed doctoral research, presented in lecture style to a faculty committee including the research advisor. 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.
- Other:
- Satisfactory progress in the program is determined by department review of examination results, course grades, and faculty recommendations
Required Program for 1st year PhD Students
| Fall | Winter | Spring |
|---|---|---|
| ES APPM 420-1 | ES APPM 420-2 | Designated Asymptotics Elective |
| ES APPM 411-1 | ES APPM 411-2 | ES APPM 411-3 |
| ES APPM 446-1 | Designated Numerics Elective | ES APPM 446-2 |
| ES APPM 421-1 | Designated Modeling Elective1 | Designated Modeling Elective1 |
1The designated electives will be determined by the department.
Reminder: ES_APPM 519 seminar (either Winter or Spring quarter) and the CITI online course are also required.
Applied Mathematics Typical Graduate Program Registration Sequence
This description should be applicable to most ES/AM students. If not please see your advisor or contact the department.
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* Those who do not complete in 9 years must enroll in TGS 513 (if not funded) or TGS 500 (if receiving funding or unfunded international student) for the remaining quarters and pay tuition accordingly.
Additional Information
More information about The Graduate School (TGS) including academic services and calendar, a PhD timeline and TGS news can be found on the TGS website here: https://www.tgs.northwestern.edu/dgs_guide/guide/communications/program/
