A student in the applied mathematics program must demonstrate knowledge of scientific computing, mathematical modeling, and differential equations. Students must take 36 credit hours of approved courses with a grade average of B or better. For students entering with a master’s degree in a mathematical subject compatible with our program, as determined by the graduate committee, this requirement is reduced to 18 credit hours of approved courses. This includes taking qualifying examinations in the areas of computational mathematics and mathematical modeling, and taking certain courses in these areas, as specified below.

Qualifying Examination

Each student will be required to take two written qualifying exams in numerical analysis and modeling. Syllabi for the exams are available to students. Exams will be offered twice a year, usually in January and May. Students may attempt each exam up to two times. Under normal circumstances, students are expected to have passed both exams by the end of their fifth semester.

Area Exam

Each student will be required to pass an oral area examination showing knowledge of the background and literature in the chosen area of specialization. The exam will be administered by the student’s advising committee, chaired by the research advisor. The exam should normally take place within one year after final passage of the qualifying examinations and at least one year before the defense takes place. A student may retake the area exam once.

A written syllabus, with a list of the papers for which the student will be responsible, should be prepared and agreed upon by the student and advising committee at least two months before the exam takes place, at which time a specific date and time for the exam should be decided. Both the syllabus and the scheduled date of the exam should then be reported to the graduate committee. Once the syllabus and exam date have been reported to the graduate committee, the student will advance to PhD candidacy.

Course requirements

MATH 431	Introduction to Numerical Analysis I	3
MATH 432	Numerical Differential Equations	3
or MATH 433	Numerical Solutions of Nonlinear Systems and Optimization
MATH 441	Mathematical Modeling	3
MATH 435	Ordinary Differential Equations	3
or MATH 445	Introduction to Partial Differential Equations
Approved Courses *		24
Total Credit Hours		36

 

*	Must include at least 9 credit hours of MATH courses and at least 9 credit hours of non-MATH courses.

Applied Mathematics PhD students are subject to the same breadth requirements as students pursuing the MS degree in Applied Mathematics (see above). For students entering with a master’s degree, this can be modified, as described below.

A student with a master’s degree in a mathematical subject compatible with our program, as determined by the graduate committee, must take 18 credit hours of approved courses, which must include at least 6 credit hours of courses offered outside the Department of Mathematics, Applied Mathematics, and Statistics and at least 9 credit hours offered by the Department of Mathematics, Applied Mathematics, and Statistics. The graduate committee will determine which of the specific course requirements stated above have been satisfied by the master’s coursework.

Sample study plans for students with concentrations in scientific computing, imaging, mathematical biology, and stochastics follow. Alternate study plans may also be approved by the graduate committee.