# 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 methods | Scientific Computing | Specialization 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 Dynamics | B. Fluid Dynamics | C. 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 Methods | Comprehensive Exam in Numerical Analysis and HPC | Oral or Written Exam in Specialization Area |

Seminar Presentation of Thesis Proposal to Dissertation Committee |

Approved Technical Elective Courses | |

IAM 940 | Asymptotic and Perturbation Methods |

ME 812 | Waves in Fluids |

ME 911 | Theory of Hydrodynamic Stability |

*Other | Available with approval |

## Sample Student Programs

### Generic incoming math student

SEMESTER I | SEMESTER 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 Seminar | iv. IAM Seminar |

SEMESTER III | SEMESTER 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 Seminar | iv. IAM Seminar |

### Generic incoming math student choosing Scientific Area A: Nonlinear Dynamics

SEMESTER I | SEMESTER 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 Seminar | iv. IAM Seminar |

SEMESTER III | SEMESTER 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 Seminar | iv. IAM Seminar |

### Generic incoming engineering or physics student

SEMESTER I | SEMESTER 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 Seminar | iv. IAM Seminar |

SEMESTER III | SEMESTER 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 Analysis | iii. Technical (Science/Engr) Elective (E) |

iv. IAM Seminar | iv. IAM Seminar |

### Generic incoming Engineering student choosing Scientific Area B: Fluid Dynamics

SEMESTER I | SEMESTER 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 Seminar | iv. IAM Seminar |

SEMESTER III | SEMESTER 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 Seminar | iv. IAM Seminar |

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