- Graduate Program Summary
- Fellowships
- Application Process
- MS Degree Requirements
- PhD Degree Requirements
- 1st Year Graduate Program Schedule
- Graduate Program Registration Sequence
Graduate Program Summary
Qualified students with backgrounds in engineering, mathematics, or science are eligible for admission to the Program in Applied Mathematics. Study plans, drawn up to meet the needs of the individual student, encompass courses in mathematical methods and one or more fields of science or engineering where significant applications of mathematics are made. 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 graduate 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 program, send a message to esamgrad@northwestern.edu
All graduate program applications must be submitted online. To apply to the graduate program, follow the online application instructions below.
The department has a deadline of Friday, February 5, 2010 for the receipt of all application materials. Please note that this deadline is different from the deadline published by the graduate school website, which does not apply to our program.
All information about the application process can be found at the Graduate School website. For your convenience, the application steps are summarized below.
Online Application
The online application is a two-step process:
Step 1. Go to the Graduate School website . Click on the "Apply Online" link. Follow the instructions to complete the application. You will be able to indicate your desire to be considered for financial aid. Please note that your application will not be processed until the fee is paid.
Step 2. Send the following required supplementary materials to the department:
- Letters of recommendation (minimum of two)
- Transcripts (from all universities/colleges listed in your application)
- A photocopy of your GRE scores (only general aptitude exam required)
- A photocopy of your TOEFL score (all applicants whose native language is not English)
PLEASE NOTE: Official GRE and TOEFL scores must be sent from the Educational Testing Service (ETS) to the institution code 1565
The department address is:
Graduate Admissions Officer
Department of Engineering Sciences and Applied Mathematics, Technological Institute
Northwestern University
2145 Sheridan Road
Evanston, IL 60208-3125
MS Degree Requirements
The following requirements are in addition to, or further elaborate upon, those requirements outlined in the Northwestern University Graduate School Bulletin.
Admission Qualifications
See PhD Degree Requirements below.
Coursework Requirements
Each candidate for the 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 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 |
| Department Electives (approved) | 5 | |
| Total Required Units: | 12 | |
Other MS Degree Requirements
- Examinations:
- Written preliminary examinations in differential equations, advanced calculus, complex variables, and linear algebra.
- Research/Projects:
- Not required
- Master's Thesis:
- Not required
- Other:
- Satisfactory progress in the program is determined by department review of examination results, course grades, and faculty recommendations
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 | Differential Equations of Mathematical Physics | 2 |
| 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, 2 (approved) | 13 | |
| Total Required Units: | 20 | |
1 Students admitted with an approved MS degree are required to take 11 approved electives.
2A 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.
Other PhD Degree Requirements
- 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 level of advanced undergraduate-beginning graduate. 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 Ph.D. 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 Ph.D. 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 graduate Students
| Fall | Winter | Spring |
|---|---|---|
| 420-1 | 420-2 | Designated Asymptotics Elective3 |
| 411-1 | 411-2 | Designated Analysis Elective3 |
| 446-1 | Numerics Elective2 | 446-2 |
| 421-1 | Designated Modeling Elective1,3 | Designated Modeling Elective1,3 |
1Students supported as a TA in the 1st year should delay the modeling sequence and take the other 3 courses in the required program.
2Numerical Methods for Random Processes 448 and a course on the Numerical Solutions of Elliptic Equations are the Numerics Electives and will be offered in alternate years.
3The designated electives will be determined by the department.
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.
