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It will take five years for a typical student to complete a PhD. A student with strong background could complete the program in four years. This work will consist of three stages: taking courses, completing an internship and writing a dissertation.

A minimum of 75 credits of coursework is required. The formal course curriculum is designed to ensure thorough grounding in Mathematics as well as choice for specialization. Advisors will help the student choose a suitable curriculum. This will include selection of electives as well as the suggestion of other courses that may be needed to develop skills critical for the student’s research and career goals, especially quantitative skills. A grade of "B" or higher in all required core courses, and a cumulative GPA of 3.0 or higher must be maintained.

The Applied Experience Component consists of a one-semester (usually summer) paid internship at a private corporation. To steer students into good internships and jobs outside academia, an Advisory Panel will be established, drawn from industry and from faculty from other disciplines with connections and interactions with business and industry.

  • Credit Requirements

    Of the 75 credit hours of required coursework, 27 credits will be made up of the nine core courses. All students must also take four courses (12 credits) from the thesis preparatory courses list. All students must take 25 credits of independent study, seminars and dissertation research courses; at least 15 credits should be Dissertation Research. The remaining 15 credits of the required 75 may be filled by courses from:

    • Any courses from the thesis preparatory courses which are not counted as the four courses above.
    • Courses from the elective list.
    • Courses of level 5000 or higher from Computer Science, Statistics, Physics, Economics or Engineering approved by the Graduate Committee.
    • If a student has a co-advisor from another department, then at least 6 credits must be taken from the other department. The core and thesis preparatory courses and credit are summarized below.
  • Course Sequence

    In the fall semester in which most new graduate students arrive, three core courses, Real Analysis, Ordinary Differential Equations, and Applied Linear Algebra will be offered. A typical new graduate student is required to take these three courses. In this semester, students will also register for Training in Mathematical Exposition (1 credit), for a total of 10 credits.

    In the second semester, students are required to take another three core courses, Complex Analysis, Numerical Methods and Partial Differential Equations.

    No core courses are offered in the summer semester.

    In the fall semester of the second year, students are required to take one more core course, Scientific Computations, among other courses. By so doing, the student has finished all core courses except for the Applied Experience Component, which they must complete after the internship. In the third semester, students will start taking thesis preparatory courses upon approval of the graduate committee, as well as electives. Additional credits will be earned by registering for the independent studies and seminars to do research under the guidance of the advisors.

  • Core Courses
    • MAA 6616 Real Analysis (3)
    • MAA 6406 Complex Analysis (3)
    • MAD 5405 Numerical Methods (3)
    • MAP5316 Ordinary Differential Equations (3)
    • MAP6326 Partial Differential Equations (3)
    • MAS5145 Applied Linear Algebra (3)
    • MAP 5255 Scientific Computations (3)
    • MAT5921 Training in Mathematical Expositions (1)
    • MAT6946 Applied Experience Component (1)
  • Qualifying Examination

    Students must complete a Qualifying Examination to ensure the they suitable background knowledge to conduct research in their chosen area. Consult the Graduate Catalog for more information.

    Analysis Qualifying Exam Syllabus

  • Thesis Preparation Courses
    • MAA 6506 Functional Analysis (3)
    • MAP 6217 Calculus of Variations (3)
    • MAD 6409 Numerical Methods II (3)
    • MAD 7408 Topics in Numerical Analysis (3)
    • MAP 5415 Introduction to Fourier Analysis (3)
    • MAP 6357 Partial Differential Equations II (3)
    • MAP 7359 Topics in Partial Differential Equations (3)
    • MAP 6218 Stochastic Calculus (3)
    • STA 5446 Probability Theory I (3)
    • STA 5447 Probability Theory II (3)
    • STA 6807 Queueing and Statistical Models (3)

For more information, consult the Graduate Catalog.