Graduate Study

Information for Prospective Graduate Students

Applicants to the IAM Ph.D. program are expected to have a bachelor's degree in mathematics or an appropriate science or engineering field. Applications for the Fall term are due February 15. Inquiries regarding the program may directed to Prof. Greg Chini. If you already have a specific interest in one of our research programs, we can have a faculty member and/or a current graduate student who works in that area get in touch with you. They will be able to tell you about their current research, give a description of living conditions in Durham, and provide information about student activities. If you prefer more general information about the program rather than about a specific research area, this also can be provided by a faculty member and/or a graduate student. Campus visits are encouraged; please contact April Flore for more information.

The program generally provides financial support to incoming graduate students in the form of teaching assistantships (TAs). Most students are supported as research assistants in the summers. Research assistantships (RAs) become the dominant source of support as students progress in the program.

Application materials for graduate study at UNH can be obtained online at the Graduate School. Select "Math, Applied" on the application page for the IAM program.

Curriculum

Synopsis: The essence of modern applied mathematics is the interplay between mathematical analysis, numerical computation and scientific/engineering specialization. Thus, the IAM curriculum is designed to provide applied mathematics graduate students with advanced training in these three broad, inter-related topics: (1) Mathematical Methods, (2) Scientific Computing, and (3) a Scientific or Engineering Area of Specialization. In addition to completing 9 core courses (27 cr. hrs), IAM students will take a minimum of 3 technical electives (9 cr. hrs). The core curriculum is summarized in the table below; the electives must be selected from an approved list of IAM courses. Students also will be required to regularly participate in an IAM Seminar Series. Additional coursework, generally at the 800 level, may be required in order to help prepare students for the program.

Core Courses
Mathematical methodsScientific ComputingSpecialization Area
Mathematical Methods
PHYS 931
High-Performance Computing
IAM 951
Select one 2-course
sequence in A,B,or C
Graduate ODEs
IAM 830
Numerical Linear Algebra
IAM 961
A. Nonlinear Dynamics
Graduate PDEs
IAM 932
Numerical ODEs & PDEs
IAM 962
B. Fluid Dynamics
Applied Functional Analysis
IAM 933
 C. Plasma Physics

The scientific focus areas proposed below satisfy the following two criteria: (1) each involves the application of sophisticated analytical and computational methods; (2) each is adequately staffed by UNH IAM faculty, so that core courses and technical electives may be regularly offered in these areas. IAM faculty may propose similar sequences in other areas when the above two criteria can be met.

Specialization Areas
A. Nonlinear DynamicsB. Fluid DynamicsC. Plasma Physics
Nonlinear Dynamics and Chaos
MATH 847
Foundation of Fluid Dynamics
ME 807
Magnetohydrodynamics
PHYS 953
Spatiotemporal Dynamics
IAM 950
Incompressible Flow
ME 909
Plasma Physics
PHYS 951
3-Part Ph.D. Qualifying Exam
Comprehensive Exam in Mathematical MethodsComprehensive Exam in Numerical Analysis and HPCOral or Written Exam in Specialization Area
Seminar Presentation of Thesis Proposal to Dissertation Committee
Approved Technical Elective Courses
IAM 940Asymptotic and Perturbation Methods
ME 812Waves in Fluids
ME 911Theory of Hydrodynamic Stability
*OtherAvailable with approval

Sample Student Programs

Generic incoming math student

SEMESTER ISEMESTER II
i. Applied Functional Analysis (C)i. High-Performance Computing (C)
ii. Numerical Analysis I - Linear Algebra (C)ii. Numerical Analysis II – ODEs & PDEs (C)
iii. ODEs (C)iii. PDEs (C)
iv. IAM Seminariv. IAM Seminar
SEMESTER IIISEMESTER IV
i. Science & Engr Specialization Course (C)i. Technical (Math) Elective (E)
ii. Mathematical Methods I (C)ii. Science & Engr Specialization Course (C)
iii. Technical (Math) Elective (E)iii. Technical (Science/Engr) Elective (E)
iv. IAM Seminariv. IAM Seminar

Generic incoming math student choosing Scientific Area A: Nonlinear Dynamics

SEMESTER ISEMESTER II
i. Applied Functional Analysis (C)i. High-Performance Computing (C)
ii. Numerical Analysis I - Linear Algebra (C)ii. Numerical Analysis II – ODEs & PDEs (C)
iii. ODEs (C)iii. PDEs (C)
iv. IAM Seminariv. IAM Seminar
SEMESTER IIISEMESTER IV
i. Nonlinear Dynamics & Chaos (C)i. Asymptotic Methods (E)
ii. Mathematical Methods I (C)ii. Hamiltonian Dynamics (C)
iii. Computational PDEs or Spectral Methods (E)iii. Nonlinear Control Theory (E)
iv. IAM Seminariv. IAM Seminar

Generic incoming engineering or physics student

SEMESTER ISEMESTER II
i. Science & Engr Specialization Course (C)i. Science & Engr Specialization Course (C) or High-Performance Computing (C)
ii. Numerical Analysis I - Linear Algebra (C)ii. Numerical Analysis II – ODEs & PDEs (C)
iii. ODEs (C)iii. PDEs (C)
iv. IAM Seminariv. IAM Seminar
SEMESTER IIISEMESTER IV
i. Science & Engr Specialization Course (C) or High-Performance Computing (C)i. Technical (Math) Elective (E)
ii. Mathematical Methods I (C)ii. Technical (Math) Elective (E)
iii. Applied Functional Analysisiii. Technical (Science/Engr) Elective (E)
iv. IAM Seminariv. IAM Seminar

Generic incoming Engineering student choosing Scientific Area B: Fluid Dynamics

SEMESTER ISEMESTER II
i. Intermediate Fluid Dynamics (C)i. Incompressible Flow (C)
ii. Numerical Analysis I - Linear Algebra (C)ii. Hamiltonian Dynamics (C)
iii. ODEs (C)iii. PDEs (C)
iv. IAM Seminariv. IAM Seminar
SEMESTER IIISEMESTER IV
i. Waves in Fluids (E)i. Asymptotic Methods (E)
ii. High-Performance Computing (C)ii. Numerical Analysis II – ODEs & PDEs (C)
iii. Mathematical Methods I (C)iii. Applied Functional Analysis (C)
iv. IAM Seminariv. IAM Seminar