Requirements for the M.S. Degree in Applied Mathematics and Statistics

In addition to the minimum Graduate School requirements, the following are required:

**A. Course Requirements**

The M.S. degree in the Department of Applied Mathematics and Statistics requires the satisfactory completion of a minimum of 30 graduate credits in letter-graded (A,B,C,F) graduate courses, with some specializations requiring up to 36 credits.

All credits in satisfaction of the degree must be at the graduate level. The department may impose additional requirements as described below. In addition, the cumulative grade point average for all courses taken must be B or higher, and at least 18 credits of all courses taken must carry a grade of B or above, and the grade point average over all core (nonelective) requirements must be 3.0 or higher.

The student pursues a program of study planned in consultation with an academic advisor. The program and any subsequent modifications require approval by the graduate program director.

*Core Requirements for the M.S. Degree*

1. Computational Applied Mathematics

AMS 501 Differential Equations and Boundary Value Problems

AMS 503 Applications of Complex Analysis

AMS 510 Analytical Methods for Applied Mathematics and Statistics

AMS 526 Numerical Analysis I

AMS 527 Numerical Analysis II

AMS 528 Numerical Analysis III

AMS 595 Fundamentals of Computing (1 credit)

Four elective courses (12 credits total) chosen in consulation with advisor

2. Computational Biology

AMS 507 Introduction to Probability

AMS 510 Analytical Methods for Applied Mathematics and Statistics

MCB 520 Graduate Biochemistry OR

CHE 541 Biomolecular Structure and Analysis

AMS 531 Laboratory Rotations in Computational Biology (two semesters, 0 credit)

AMS 532 Journal Club in Computational Biology (two semesters, 0 credit)

AMS 533 Numerical Methods and Algorithms in Computational Biology

AMS 535 Intro to Computational Structural Biology & Drug Design

AMS 537 Biological Networks & Dynamics

AMS 539 Introduction to Physical & Quantitative Biology (0 credit)

CSE 549 Computational Biology

Three elective courses (9 credits total) chosen in consultation with advisor

3. Operations Research

AMS 510 Analytical Methods for Applied Mathematics and Statistics

AMS 507 Introduction to Probability

AMS 540 Linear Programming

AMS 550 Stochastic Models

AMS 553/CSE 529 Simulation and Modeling

One course in statistics (AMS 570 - 586)

AMS 595 Fundamentals of Computing (1 credit)

Four elective courses (12 credits total) chosen from AMS 542-556; one of these may be substituted by an additional statistics course (AMS 570-586), and one may be substituted by a quantitative finance course (AMS 511-523)

4. Statistics

AMS 510 Analytical Methods for Applied Mathematics and Statistics

AMS 507 Introduction to Probability

AMS 570 Mathematical Statistics I

AMS 572 Exploratory Data Analysis

AMS 573 Design & Analysis of Categorical Data

AMS 578 Regression Theory

AMS 582 Design of Experiments

AMS 597 Statistical Computing

Two elective courses (6 credits total) chosen in consultation with advisor

5. Quantitative Finance

AMS 507 Introduction to Probability

AMS 510 Analytical Methods for Applied Mathematics and Statistics

AMS 511 Foundations of Quantitative Finance

AMS 512 Capital Markets & Portfolio Theory

AMS 513 Financial Derivatives and Stochastic Calculus

AMS 514 Computational Finance

AMS 516 Statistical Methods in Finance

AMS 517 Quantitative Risk Management

AMS 518 Advanced Stochastic Models, Risk Assessment & Portfolio Optimization

AMS 572 Data Analysis I

FIN 539 Investment Analysis

One elective course (3 credits total) chosen in consultation with advisor

*Elective Requirements for the M.S. Degree*

Unless otherwise specified, any graduate-level AMS or other graduate-level courses in a related discipline approved by the graduate program director may be used to satisfy the credit requirement beyond the core course requirement.

**B. Final Recommendation**

Upon the fulfillment of the above requirements, the faculty of the graduate program will recommend to the dean of the Graduate School that the Master of Science degree be conferred or will stipulate further requirements that the student must fulfill.

**C. Time Limit**

All requirements for the Master of Science degree must be completed within three years of the student’s first registration as a full-time graduate student.

Requirements for the Ph.D. Degree in Applied Mathematics and Statistics

**A. Course Requirements**

The course of study prescribed for the M.S. degree provides basic guidelines for doctoral study. The student pursues a program of study planned in consultation with an academic advisor. The program and any subsequent modifications require approval of the graduate program director.

**B. Qualifying Examination**

A student must pass a two-part qualifying examination to be allowed to continue toward the Ph.D. degree. Each component of the qualifying examination is given twice a year at the beginning and the end of the Spring semester and is designed to test the student’s preparation to do research in applied mathematics. Each student must demonstrate competency in linear algebra and analysis and in-depth knowledge in one of the following areas:

Computational Applied Mathematics

Computational Biology

Operations Research

Quantitative Finance

Statistics

**C. Research Advisor**

After completion of at least one year of full-time residence and prior to taking the preliminary examination, the student must select a research advisor who agrees to serve in that capacity.

**D. Preliminary Examination**

This is an oral examination administered by a committee and given to the student when he or she has developed a research plan for the dissertation. The plan should be acceptable to the student’s research advisor.

**E. Mathematical Writing Requirement**

The mathematical writing requirement is associated with the preliminary oral examination. The student must submit a document, typically 20 to25 double-spaced pages long, containing the research plan for the dissertation, including a wellreferenced synopsis of the relevant background literature, as well as a summary of research work accomplished to date. It must be given to the members of the Preliminary Examination committee at least one week before the oral presentation.

The document must be approved for satisfactory written style and use of technical English as well as for intellectual content; this will be assessed by the Preliminary Examination Committee, who is appointed by the graduate program director. International students may need extensive writing assistance from the ESL Tutoring Center established to provide exactly this kind of technical writing tutorial support.

Tutorial assistance in writing, if needed, will also be provided to native students.

**F. Advancement to Candidacy**

After successfully completing all requirements for the degree other than the dissertation, the student is eligible to be recommended for advancement to candidacy. This status is conferred by the dean of the Graduate School upon recommendation from the graduate program director.

**G. Dissertation**

The most important requirement of the Ph.D. degree is the completion of a dissertation, which must be an original scholarly investigation. The dissertation must represent a significant contribution to the scientific literature and its quality must be comparable with the publication standards of appropriate and reputable scholarly journals.

**H. Dissertation Defense**

The student must defend the dissertation before an examining committee. On the basis of the recommendation of this committee, the Department of Applied Mathematics and Statistics will recommend acceptance or rejection of the dissertation to the dean of the Graduate School. All requirements for the degree will have been satisfied upon successful defense of the dissertation. There must be at least one year between advancing to candidacy and scheduling a dissertation defense.

**I. Minimum Residence**

At least two consecutive semesters of full-time study are required.

**J. Time Limit**

All requirements for the Ph.D. degree must be completed within seven years after the completion of 24 graduate credits in the program. The time limits for the qualifying and preliminary examinations and advancement to candidacy are described in the departmental *Graduate Student Handbook.*

**K. Teaching Requirement**

One academic year long teaching experience required.