Applied Mathematics
Master of Science in Applied Mathematics Program
This program gives students a broad background in mathematics, placing an emphasis on areas with the highest demand in applications: numerical methods and scientific computation, mathematical modeling, discrete mathematics, mathematical materials science, optimization and operations research. In addition to these advanced areas of specialization, students are encouraged to acquire breadth by choosing elective courses in fields such as computer science, mechanical engineering and electrical and computer engineering, complementing their studies in applied mathematics. Students have a choice of completing their master's thesis or project in cooperation with one of the department's established industrial partners. The program provides a suitable foundation for the pursuit of a Ph.D. degree in applied mathematics or a related field, or for a career in industry immediately after graduation.
Master of Science in Applied Statistics Program
This program gives graduates the knowledge and experience to tackle problems of statistical design, analysis and control likely to be encountered in business, industry or academia. The program is designed to acquaint students with the theory underlying modern statistical methods, to provide breadth in diverse areas of statistics and to give students practical experience through extensive application of statistical theory to real problems. Of particular note are the statistical consulting course, which develops interpersonal and statistical consulting skills, and the master's project, which involves the solution of a large-scale real-world problem, often originating in industry, business or government.
Through the selection of elective courses, the student may choose a program with an industrial emphasis or one with a more theoretical emphasis.
Professional Master of Science in Financial Mathematics Program
This program offers an efficient, practiceoriented track to prepare students for quantitative careers in the financial industry, including banks, insurance companies, and investment and securities firms. The program gives students a solid background and sufficient breadth in the mathematical and statistical foundations needed to understand the cutting edge techniques of today and to keep up with future developments in this rapidly evolving area over the span of their careers. It also equips students with expertise in quantitative financial modeling and the computational methods and skills that are used to implement the models. The mathematical knowledge is complemented by studies in financial management, information technology and/or computer science.
The bridge from the academic environment to the professional workplace is provided by a professional master's project that involves the solution of a concrete, real-world problem directly originating from the financial industry. Students are encouraged to complete summer internships at financial firms. The department may help students to find suitable financial internships through the industrial connections of faculty affiliated with the Center for Industrial Mathematics and Statistics. Graduates of the program are expected to start or advance their professional careers in such areas as financial product development and pricing, risk management, investment decision support and portfolio management.
Professional Master of Science in Industrial Mathematics Program
This is a practice-oriented program that prepares students for successful careers in industry. The graduates are expected to be generalized problem- solvers, capable of moving from task to task within an organization. In industry, mathematicians need not only the standard mathematical and statistical modeling and computational tools, but also knowledge within other areas of science or engineering. This program aims at developing the analysis, modeling and computational skills needed by mathematicians who work in industrial environments. It also provides the breadth required by industrial multidisciplinary team environments through courses in one area of science or engineering, e.g., physics, computer science, mechanical engineering, and electrical and computer engineering.
The connection between academic training and industrial experience is provided by an industrial professional master's project that involves the solution of a concrete, real-world problem originating in industry. The department, through the industrial connections of the faculty affiliated with the Center for Industrial Mathematics and Statistics (CIMS), may help students identify and select suitable industrial internships. Graduates of the program are expected to start or advance their professional careers in industry.
Combined B.S./Master's Program
This program allows a student to work concurrently toward bachelor and master of science degrees in applied mathematics, applied statistics, financial mathematics and industrial mathematics.
Master of Mathematics for Educators
This is a 30-credit evening program designed primarily for secondary school mathematics teachers. Courses offer a solid foundation in areas such as geometry, algebra, modeling, discrete math and statistics, while also including the study of modern applications. Additionally, students develop materials, based on coursework, which may be used in their classes. Technology is introduced when possible to give students exposure for future consideration. Examples include Geometer's Sketchpad; Maple for algebra, calculus and graphics; Matlab for analysis of sound and music; and the TI CBL for motion and heat.
For teachers in the Massachusetts public schools, WPI may grant a professional license upon completion of the MME degree.
Doctor of Philosophy in Mathematical Sciences Program
The goal of this program is to produce active and creative problem solvers, capable of contributing in academic and industrial environments. One distinguishing feature of this program is a 9-credit-hour project to be completed under the guidance of an external sponsor, e.g., from industry or a national research center. The intention of this project is to connect theoretical knowledge with relevant applications and to introduce the candidate to potential employers.
Mathematical Sciences Computer Facilities
The Mathematical Sciences Department makes available the use of up-to-date computing equipment in the programs that is offers.
Current facilities include a mixed environment of approximately 85 Windows, Linux/Unix and Macintosh workstations utilizing the latest in single- and dual- processor 32 and 64 bit technology. Access is available to our supercomputer, and 16 CPU SGI Altix 350. The Mathematical Sciences Department also has 3 state- ofthe- art computer labs one each dedicated to the Calculus, Statistics, and Financial studies programs.
The department is continually adding new resources to give our faculty and students the tools they need as they advance in their research and studies.
Center for Industrial Mathematics and Statistics (CIMS)
The Center for Industrial Mathematics and Statistics was established in 1997 to foster partnerships between the university and industry, business and government in mathematics and statistics research.
The problems facing business and industry are growing ever more complex, and their solutions often involve sophisticated mathematics. The faculty members and students associated with CIMS have the expertise to address today's complex problems and provide solutions that use relevant mathematics and statistics.
The Center offers undergraduates and graduate students the opportunity to gain real-world experience in the corporate world through projects and internships that make them more competitive in today's job market. In addition, it helps companies address their needs for mathematical solutions and enhances their technological competitiveness.
The industrial projects in mathematics and statistics offered by CIMS provide a unique education for successful careers in industry, business and higher education.
Degree Requirements For the M.S. in Applied Mathematics
The master's program in applied mathematics is a 30-credit-hour program. The student's program must include at least seven MA courses numbered 503 or higher. Among these must be MA 503, MA 510, and either MA 535 or MA 530. In addition, students are required to complete a Capstone Experience, which can be satisfied by one of the following options:
The master's thesis is an original piece of mathematical research work which focuses on advancing the state of the mathematical art. The master's project consists of a creative application of mathematics to a real-world problem. It focuses on proble definition and solution using mathematical tools.
The remaining courses may be chosen from the graduate offerings of the Mathematical Sciences Department. Upper-level undergraduate mathematics courses or a two-course graduate sequence in another department may be taken for graduate credit, subject to the approval of the departmental Graduate Committee. Candidates are required to successfully complete the graduate seminar MA 560.
For the M.S. in Applied Statistics
The master's program in applied statistics is a 30-credit-hour program. Courses taken must include MA 540, MA 541, MA 546, MA 547, 3 credits of MA 559 and at least three additional departmental statistics offerings: MA 509 and courses numbered 542 through 556. In addition the student must complete a Capstone Experience, which can be satisfied by one of the following options:
Upper-level undergraduate courses may be taken for graduate credit subject to the approval of the departmental Graduate Committee.
For the M.S. in Financial Mathematics
The Professional Master's Degree Program in Financial Mathematics is a 30- credithour program including a 3-credit-hour professional M.S. project originating from the financial industry. Students must take foundation courses MA 503 and MA 540, at least three from the four core financial mathematics courses MA 571, MA 572, MA 573 and MA 574, and two additional electives chosen from the graduate courses offered by the Mathematical Sciences Department.
A 6-credit block has to be completed in one of the following complementary areas outside of the Mathematical Sciences Department: financial management (e.g., from ACC 501, FIN 502 or FIN 509), information technology (e.g., from MIS 571, MIS 573 or MIS 578) or computer science (e.g., from CS 504, CS 531, CS 534, CS 542 or CS 552). Students with a degree or substantial work experience in one of the above complementary areas can substitute them with other courses subject to prior approval by the Graduate Committee. B.S./Master's students can count undergraduate credits for MA 4213, MA 4235, MA 4237, MA 4473 or MA 4632 toward electives and suitable undergraduate courses toward the complementary area requirement.
Students shall participate in the Professional Master's Seminars MA 562A and MA 562B. The Professional M.S. Project MA 598 involves solving a real-life problem originating in the financial industry. A student's Plan of Study and the topic of the master's project shall be approved by the Graduate Committee.
For the M.S. in Industrial Mathematics
The Professional Master's Degree Program in Industrial Mathematics is a 30- credithour program. Students must complete four foundation courses: MA 503, MA 510 and two courses out of MA 508, MA 509 and MA 530. Students must also complete a 12-credit-hour module composed of two courses within the department and a sequence of two courses from one graduate program outside the Mathematical Sciences Department. The department offers a wide selection of modules to suit students' interest and expertise.
In addition, students are required to complete a 3-credit-hour elective from the Mathematical Sciences Department and a 3-credit-hour master's project on a problem originating from industry. Candidates are required to successfully complete the Professional Master's Seminars MA 562A and MA 562B. The Plan of Study and the project topic need prior approval of the Graduate Committee.
Examples of Modules for the M.S. Degree in Industrial Mathematics
The courses comprising the 12-credit module should form a coherent sequence that provides exposure to an area outside mathematics and statistics, providing at the same time the mathematical tools required by that particular area. Examples of typical modules are:
For the Combined B.S./Master's Programs in Applied Mathematics and Applied Statistics
A maximum of four courses may be counted toward both the undergraduate and graduate degrees. All of these courses must be 4000-level or above, and at least one must be a graduate course. Three of them must be beyond the 7 units of mathematics required for the B.S. degree.
Acceptance into the program means that the candidate is qualified for graduate school and signifies approval of the four courses to be counted for credit toward both degrees. However, in order to obtain both undergraduate and graduate credit for these courses, grades of B or better have to be obtained.
For the Master of Mathematics for Educators (M.M.E.)
Candidates for the master of mathematics for educators must successfully complete 30 credit hours of graduate study, including a 6-credit-hour project (see MME 592, MME 594, MME 596). This project will typically consist of a classroom study within the context of a secondary mathematics course and will be advised by faculty in the Mathematical Sciences Department. Typically, a student will enroll in 4 credit hours per semester during the fall and spring, with the remaining credit hours taken in the summer. Students may complete the degree in as little as slightly over two years by taking two course per semester, 3 semesters per year.
For the Ph.D.
The course of study leading to the Doctor of Philosophy in Mathematical Sciences requires the completion of at least 60 credit hours beyond the master's degree, of which at least 30 credit hours must be directed toward independent research. The research preparation phase consists of:
Mathematical Sciences Ph.D. Project
As part of the research preparation phase, the student is encouraged to go off campus to complete a project sponsored by industry, national research laboratories or other approved external organizations. The project shall be in an area involving an application of mathematics or statistics. The scope of the project shall be equivalent to 9 credit hours of coursework. In the event that the student is unable to secure sponsorship through an off-campus organization, the student is required to complete an on-campus project in a department other than mathematical sciences.
Plan of Study
Within the first year of enrollment, each student is expected to choose a specialization with his or her advisor. A Plan of Study must be submitted to and approved by the departmental Graduate Committee.
General Comprehensive Examination
In order to be admitted to candidacy, the student must take the general comprehensive examination at the beginning of the first year of study if entering with a master's degree, and no later than the beginning of the second year of study if entering with a bachelor's degree.
Admission to Candidacy
Admission to Ph.D. candidacy is granted when the student has passed the general comprehensive examination and has received approval of an application for admission to candidacy summarizing the student's planned course of study.
Ph.D. Preliminary Examination
Before registering for Ph.D. dissertation credits the candidate must pass the Ph.D. preliminary examination. This examination, which has both written and oral components, should be taken sometime during the second or third year after being admitted as a Ph.D. candidate.
Ph.D. Dissertation Proposal
At least six months prior to completion of the Ph.D. dissertation, the candidate must present a formal seminar to the public describing the proposed dissertation research project. A formal written research proposal must be submitted two weeks before the presentation.
Ph.D. Final Examination
With the dissertation and the other requirements of the program completed, the student is ready for the final oral defense. The student's Ph.D. Thesis Committee will determine by majority vote whether or not the student passes.
Ph.D. Thesis Committee
The student's Dissertation Advisor chairs the Ph.D. Thesis Committee. Under the direction of the advisor, the student selects the rest of the Ph.D. Thesis Committee. The committee must have at least five members. It should be made up of members of the mathematical sciences faculty and at least one faculty member from another department, or one person from outside WPI who is a recognized expert in the area of the student's dissertation. This committee will participate in the Ph.D. dissertation proposal and the Ph.D. final examination. It is required that the committee be selected prior to the Ph.D. preliminary examination.
Admission Requirements
A bachelor's degree is required for admission to all M.S. programs. A basic knowledge of undergraduate analysis, linear algebra and differential equations is assumed for applicants to the master's programs in applied mathematics and industrial mathematics. A strong background in mathematics, which should include courses in undergraduate analysis and linear algebra, is assumed for applicants to the master's program in financial mathematics. Typically, an entering student in the master of science in applied statistics program will have an undergraduate major in the mathematical sciences, engineering or a physical science; however, individuals with other backgrounds will be considered. In any case, an applicant will need a strong background in mathematics, which should include courses in undergraduate analysis and probability. Students with serious de- ficiencies may be required to correct them on a noncredit basis.
Candidates for the master of mathematics for educators degree must have a bachelor's degree and must possess a background equivalent to at least a minor in mathematics, including calculus and either teacher certification in mathematics or science or a full-time teaching position in one of these disciplines. Students are encouraged to enroll in courses on an ad hoc basis without official program admission. However, these students will not be eligible for any financial aid and must pay full tuition for each course. A typical student would complete the program in two years, taking one course each semester. However, the program can accommodate other completion schedules as well.
Research Interests
Active areas of research in the Mathematical Sciences Department include applied and computational mathematics, industrial mathematics, applied statistics, scientific computing, numerical analysis, ordinary and partial differential equations, non-linear analysis, electric power systems, control theory, optimal design, composite materials, homogenization, computational fluid dynamics, biofluids, dynamical systems, free and moving boundary problems, porous media modeling, turbulence and chaos, mathematical physics, mathematical biology, operations research, linear and nonlinear programming, discrete mathematics, graph theory, group theory, linear algebra, combinatorics, applied probability, stochastic processes, time series analysis, Bayesian statistics, Bayesian computation, survey research methodology, categorical data analysis, Monte Carlo methodology, statistical computing, survival analysis and model selection.
Faculty
- B. Vernescu
- Professor and Head; Ph.D. Institute of Mathematics, Bucharest, Romania
- J. Abraham
- Actuarial Mathematics Coordinator, Fellow, Society of Actuaries
- M. Blais
- Visiting Assistant Professor; Ph.D., Cornell University
- I. Blank
- Assistant Professor; Ph.D., Courant Institute of Mathematical Sciences
- C. G. Burgos
- Visiting Assistant Professor; Ph.D., University of the Philippines
- F. Catrina
- Visiting Assistant Professor; Ph.D., Utah State University
- P. R. Christopher
- Professor; Ph.D., Clark University
- P. W. Davis
- Professor; Ph.D., Rensselaer Polytechnic Institute
- W. Farr
- Associate Professor; Ph.D., University of Minnesota
- J. D. Fehribach
- Associate Professor; Ph.D., Duke University
- J. Goulet
- Coordinator, Master of Mathematics for Educators Program; Ph.D., Rensselaer Polytechnic Institute
- A. C. Heinricher
- Professor; Ph.D., Carnegie Mellon University
- M. Humi
- Professor; Ph.D., Weizmann Institute of Science
- C. J. Larsen
- Associate Professor; Ph.D., Carnegie Mellon University
- R. Y. Lui
- Professor; Ph.D., University of Minnesota
- K. A. Lurie
- Professor; Ph.D., A. F. Ioffe Physical-Technical Institute, Academy of Science, USSR
- W. J. Martin
- Associate Professor and Associate Department Head; Ph.D., University of Waterloo
- U. Mosco
- , H. J. Gay Professor; Libera Docenza, University of Rome
- B. Nandram
- Professor; Ph.D., University of Iowa
- J. D. Petruccelli
- Professor; Ph.D., Purdue University
- L. Roman
- Visiting Assistant Professor; Ph.D., University of Minnesota
- M. Sarkis
- Associate Professor; Ph.D., Courant Institute of Mathematical Sciences
- B. Servatius
- Professor; Ph.D., Syracuse University
- A. W. Swift
- Visiting Assistant Professor; Ph.D., George Washington University
- D. Tang
- Professor; Ph.D., University of Wisconsin
- D. Vermes
- Associate Professor; Ph.D., University of Szeged, Hungary
- D. Volkov
- Assistant Professor; Ph.D., Rutgers University
- H. F. Walker
- Professor; Ph.D., Courant Institute of Mathematical Sciences
- S. Weekes
- Associate Professor; Ph.D., University of Michigan
- J. Wilbur
- Assistant Professor; Ph.D., Purdue University
- J. S. Williford
- Visiting Assistant Professor; Ph.D., University of Delaware
- E. Yablonski
- Visiting Assistant Professor; Ph.D., The Ohio State University
- V. Yakovlev
- Research Associate Professor; Ph.D., Institute of Radio Engineering and Electronics, Russian Academy of Sciences
Emeritus
- G. C. Branche
- Professor
- E. R. Buell
- Professor
- V. Connolly
- Professor
- W. J. Hardell
- Professor
- J. J. Malone
- Professor
- B. C. McQuarrie
- Professor
- W. B. Miller
- Professor
Last modified: June 05, 2007 12:02:29