Mathematical Sciences
Faculty
S. Olson, William Steur Professor and Department Head; Ph.D., North Carolina State University, 2008. Mathematical biology, computational biofluids, scientific computing.
J. Abraham, Professor of Practice and Actuarial Mathematics Coordinator; Fellow, Society of Actuaries, 1991; B.S., University of Iowa, 1980.
A. Arnold, Associate Professor; Ph.D., Case Western Reserve University, 2014. Inverse problems, uncertainty quantification, scientific computing, Bayesian inference, parameter estimation in biological and medical applications.
F. Bernardi, Assistant Professor; Ph.D., University of North Carolina at Chapel Hill, 2018. Smallscale fluid mechanics and microfluidics, solute and particle diffusion and transport, water filtration.
M. Blais, Professor of Teaching; Ph.D., Cornell University, 2006. Mathematical finance, operations research, fintech.
T. Doytchinova, Senior Instructor; M.S., Carnegie Mellon University, 1999.
V. Druskin, Research Professor; Ph.D., Lomonosov Moscow State University, 1984. Inverse problems, physicsinformed artificial intelligence, computational linear algebra, and model order reduction.
J. D. Fehribach, Professor; Ph.D., Duke University, 1985. Partial differential equations and scientific computing, free and moving boundary problems (crystal growth), nonequilibrium thermodynamics and averaging (molten carbonate fuel cells), Kirchhoff graphs.
C. Fowler, Assistant Professor; Ph.D., Columbia University, 2024. Causal inference and personalized medicine for intensive longitudinal or time series data.
D. Ferranti, Assistant Research Professor; Ph.D., Tulane University, 2023.
A. C. Heinricher, Professor; Ph.D., Carnegie Mellon University, 1986. Applied probability, stochastic processes and optimal control theory.
M. Humi, Professor; Ph.D., Weizmann Institute of Science, 1969. Mathematical physics, applied mathematics and modeling, Lie groups, differential equations, numerical analysis, turbulence and chaos.
M. Johnson, Professor of Teaching; Ph.D., Clark University, 2012. Industrial organization, game theory.
K. Kidwell, Assistant Teaching Professor; Ph.D., UT Austin, 2014. Number Theory.
C. J. Larsen, Professor; Ph.D., Carnegie Mellon University, 1996. Variational problems from applications such as optimal design, fracture mechanics, and image segmentation, calculus of variations, partial differential equations, geometric measure theory, analysis of free boundaries and free discontinuity sets.
K. A. Lurie, Professor; Ph.D., 1964, D.Sc., 1972, A. F. Ioffe PhysicalTechnical Institute, Academy of Sciences of the USSR, Russia. Control theory for distributed parameter systems, optimization and nonconvex variational calculus, optimal design.
O. Mangoubi, Assistant Professor; Ph.D., Massachusetts Institute of Technology, 2016. Optimization, Machine Learning, Statistical Algorithms.
W. J. Martin, Professor; Ph.D., University of Waterloo, 1992. Algebraic combinatorics, applied combinatorics, quantum information theory.
A. Nachbin, Harold J. Gay Professor; Ph.D., Courant Institute of Mathematical Sciences, 1989. Waves in fluids, considered as partial differential equations in applications: mathematical modeling, theory and scientific computing.
B. Nandram, Professor; Ph.D., University of Iowa, 1989. Survey sampling theory and methods, Bayes and empirical Bayes theory and methods, categorical data analysis.
R. C. Paffenroth, Associate Professor; Ph.D., University of Maryland, 1999. Large scale data analytics, statistical machine learning, compressed sensing, network analysis.
B. Peiris, Associate Professor of Teaching; Ph.D., Southern Illinois University, Carbondale, 2014. Bayesian Statistics, order restricted inference, metaanalysis.
G. Peng, Assistant Professor; Ph.D., Purdue University, 2014. Partial differential equations with a focus on applications to the sciences.
B. Posterro, Associate Teaching Professor; M.S., Financial Mathematics, Worcester Polytechnic Institute, 2010, M.S. Applied Mathematics, Worcester Polytechnic Institute, 2000.
D. Rassias, Assistant Teaching Professor; Ph.D., Worcester Polytechnic Institute, 2018. Biomedical modeling.
A. Sales, Assistant Professor; Ph.D., University of Michigan, 2013. Methods for causal inference using administrative or highdimensional data, especially in education.
W. C. Sanguinet, Assistant Professor of Teaching; Ph.D., Worcester Polytechnic Institute, 2017. Modeling and numerical analysis with applications in materials science.
M. Sarkis, Professor; Ph.D., Courant Institute of Mathematical Sciences, 1994. Domain decomposition methods, numerical analysis, parallel computing, computational fluid dynamics, preconditioned iterative methods for linear and nonlinear problems, numerical partial differential equations, mixed and nonconforming finite methods, overlapping nonmatching grids, mortar finite elements, eigenvalue solvers, aeroelasticity, porous media reservoir modeling.
B. Servatius, Professor; Ph.D., Syracuse University, 1987. Combinatorics, matroid and graph theory, structural topology, geometry, history and philosophy of mathematics.
H. Servatius, Assistant Teaching Professor; Ph.D., Syracuse University, 1987. Rigidity of graphs, motions in molecules, and tensegrities.
Q. Song, Associate Professor; Ph.D., Wayne State University, 2006. Stochastic analysis, control theory, and financial mathematics.
S. Sturm, Associate Professor; Ph.D., TU Berlin 2010. Stochastic modeling, mathematical finance.
D. Tang, Professor; Ph.D., University of Wisconsin, 1988. Biofluids, biosolids, vulnerable plaque modeling, ventricle models, computational fluid dynamics.
C. S. Thorp, Professor of Practice; M.S., Worcester Polytechnic Institute, 2019. Experimental design, risk management, and statistical quality control.
B. S. Tilley, Professor; Ph.D., Northwestern University, 1994. Freeboundary problems in continuum mechanics, interfacial fluid dynamics, viscous flows, electromagnetic heating, geothermal energy, partial differential equations, mathematical modeling, asymptotic methods.
S. W. Tripp, Assistant Professor of Teaching; Ph.D., Dartmouth University, 2023. Lowdimensional topology and knot homologies.
B. Vernescu, Professor; Ph.D., Institute of Mathematics, Bucharest, Romania, 1989. Partial differential equations, phase transitions and freeboundaries, viscous flow in porous media, asymptotic methods and homogenization.
D. Volkov, Professor; Ph.D., Rutgers University, 2001. Electromagnetic waves, inverse problems, wave propagation in waveguides and in periodic structures, electrified fluid jets.
S. Walcott, Professor; Ph.D., Cornell University, 2006. Mathematical and physical biology.
Z. A. Wagner, Assistant Professor; Ph.D., University of Illinois at UrbanaChampaign, 2018. Machine learning, combinatorics, and graph theory.
F. Wang, Associate Professor; Ph.D., UNC Chapel Hill, 2009. Time series analysis, spatial statistics/spatial econometrics, financial econometrics, and risk management.
G. Wang, Associate Professor and Associate Department Head; Ph.D., Boston University, 2013. Stochastic control, mathematical finance, stochastic analysis, applied probability.
S. Weekes, Professor; Ph.D., University of Michigan, 1995. Numerical analysis, computational fluid dynamics, porous media flow, hyperbolic conservation laws, shock capturing schemes.
M. Wu, Associate Professor; Ph.D., University of California, Irvine, 2012. Mathematical biology, modeling of living systems.
Z. Wu, Professor; Ph.D., Yale University, 2009. Biostatistics, statistical genetics, bioinformatics, statistical signal detection, statistical learning.
Z. Zhang, Associate Professor; Ph.D., Brown University, 2014, Shanghai University, 2011. Numerical analysis, scientific computing, computational and applied mathematics, uncertainty qualification, scientific machine learning.
J. Zou, Associate Professor; Ph.D., University of Connecticut, 2009. Financial time series (especially high frequency financial data), spatial statistics, bio surveillance, high dimensional statistical inference, Bayesian statistics.
Emeritus
P. Christopher, Professor
P. W. Davis, Professor
J. Goulet, Professor
W. J. Hardell, Professor
J. J. Malone, Professor
U. Mosco, Professor
W. B. Miller, Professor
R. Y. Lui, Professor
J. Petrucelli, Professor
D. Vermes, Professor
H. Walker, Professor
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, nonlinear 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.
Programs of Study
The Mathematical Sciences Department offers four programs leading to the degree of master of science, a combined B.S./M.S. program, one program leading to the degree of master of mathematics for educators, and two programs leading to the degree of doctor of philosophy.
Admission Requirements
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. 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 deficiencies may be required to correct them on a noncredit basis. Applicants to the Mathematical Sciences Ph.D. Program should submit GRE Mathematics Subject Test scores if possible; an applicant who finds it difficult to submit a score is welcome to contact the Mathematical Sciences Department Graduate Admissions Committee (maquestions@wpi.edu) to discuss the applicant’s situation.
For the applicants to the Ph.D. Program in Statistics, strong background of undergraduate analysis, linear algebra and probability is assumed; Applicants are strongly recommended to take the GRE Mathematics Subject Test
Candidates for the Master of Mathematics for Educators and Master of Science in 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, linear algebra, and statistics. Students are encouraged to enroll in courses on an ad hoc basis without official program admission. However, (at most) four such courses may be taken prior to admission.
Mathematical Sciences Computer Facilities
Currently, students have access to computer labs, Bloomberg terminals, and a Linux compute machine which features 24 cores driven by a pair of Intel Xeon Silver 4310 processors as well as a pair of NVIDIA Ampere A30 GPU’s each with 2584 cores of computing power. In addition, students have access to Turing, the primary research cluster for computational science across WPI.
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 realworld 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.

M.S. in Applied Statistics Program, Master of Science 
M.S. in Applied Mathematics Program, Master of Science 
Master of Mathematics for Educators (MME), Master of Mathematics for Educators (MME) 
Master of Science in Mathematics for Educators (MMED), Master of Science 
Ph.D. in Mathematical Sciences, Ph.D. 
Ph.D. in Statistics, Ph.D. 
Professional Master of Science in Industrial Mathematics Program, Master of Science
Classes
BCB 504/MA 584: Statistical Methods in Genetics and Bioinformatics
This course provides students with knowledge and understanding of the applications of statistics in modern genetics and bioinformatics. The course generally covers population genetics, genetic epidemiology, and statistical models in bioinformatics. Specific topics include meiosis modeling, stochastic models for recombination, linkage and association studies (parametric vs. nonparametric models, familybased vs. populationbased models) for mapping genes of qualitative and quantitative traits, gene expression data analysis, DNA and protein sequence analysis, and molecular evolution. Statistical approaches include loglikelihood ratio tests, score tests, generalized linear models, EM algorithm, Markov chain Monte Carlo, hidden Markov model, and classification and regression trees. Students may not receive credit for both BCB 4004 and BCB 504.
knowledge of probability and statistics at the undergraduate level
DS/MA 517: Mathematical Foundations for Data Science
The foci of this class are the essential statistics and linear algebra skills required for Data Science students. The class builds the foundation for theoretical and computational abilities of the students to analyze high dimensional data sets. Topics covered include Bayes’ theorem, the central limit theorem, hypothesis testing, linear equations, linear transformations, matrix algebra, eigenvalues and eigenvectors, and sampling techniques, including Bootstrap and Markov chain Monte Carlo. Students will use these techniques while engaging in handson projects with real data.
Some knowledge of integral and differential calculus is recommended.
MA/DS 517: Mathematical Foundations for Data Science
The foci of this class are the essential statistics and linear algebra skills required for Data Science students. The class builds the foundation for theoretical and computational abilities of the students to analyze high dimensional data sets. Topics covered include Bayes’ theorem, the central limit theorem, hypothesis testing, linear equations, linear transformations, matrix algebra, eigenvalues and eigenvectors, and sampling techniques, including Bootstrap and Markov chain Monte Carlo. Students will use these techniques while engaging in handson projects with real data.
Some knowledge of integral and differential calculus is recommended.
MA 500: Basic Real Analysis
MA 501: Engineering Mathematics
A knowledge of ordinary differential equations, linear algebra and multivariable calculus is assumed
MA 502: Linear Algebra
MA 503: Lebesgue Measure and Integration
Basic knowledge of undergraduate analysis is assumed
MA 504: Functional Analysis
MA 503 or equivalent
MA 505: Complex Analysis
knowledge of undergraduate analysis
MA 508: Mathematical Modeling
knowledge of ordinary differential equations and of analysis at the level of MA 501 is assumed
MA 509: Stochastic Modeling
knowledge of basic probability at the level of MA 2631 and statistics at the level of MA 2612 is assumed.
MA 510/CS 522: Numerical Methods
knowledge of undergraduate linear algebra and differential equations is assumed, as is familiarity with MATLAB or a higherlevel programming language
MA 511: Applied Statistics for Engineers and Scientists
Integral and differential calculus
MA 512: Numerical Differential Equations
graduate or undergraduate numerical analysis. Knowledge of a higherlevel programming language is assumed
MA 514: Numerical Linear Algebra
basic knowledge of linear algebra or equivalent background. Knowledge of a higherlevel programming language is assumed
MA 520: Fourier Transforms and Distributions
MA 521: Partial Differential Equations
MA 503 or equivalent
MA 522: Hilbert Spaces and Applications to PDE
MA 524: Convex Analysis and Optimization
MA 525: Optimal Control and Design with Composite Materials I
MA 526: Optimal Control and Design with Composite Materials II
MA 528: Measure Theoretic Probability Theory
MA 500 Basic Real Analysis or equivalent
MA 529: Stochastic Processes
MA 528. MeasureTheoretic Probability Theory, which can be taken concurrently (or, with special permission by the instructor, MA 540)
MA 530: Discrete Mathematics
college math at least through calculus. Experience with recursive programming is helpful, but not required
MA 533: Discrete Mathematics II
MA 535: Algebra
MA 540/4631: Probability and Mathematical Statistics I
knowledge of basic probability at the level of MA 2631 and of advanced calculus at the level of MA 3831/3832 is assumed
MA 541/4632: Probability and Mathematical Statistics II
knowledge of the material in MA 340 is assumed
MA 542: Regression Analysis
knowledge of probability and statistics at the level of MA 311 and of matrix algebra is assumed
MA 543/DS 502: Statistical Methods for Data Science
Statistics at the level of MA 2611 and MA 2612 and linear algebra at the level of MA 2071.
MA 546: Design and Analysis of Experiments
knowledge of basic probability and statistics at the level of MA 511 is assumed
MA 547: Design and Analysis of Observational and Sampling Studies
knowledge of basic probability and statistics, at the level of MA 511 is assumed
MA 548: Quality Control
knowledge of basic probability and statistic, at the level of MA 511 is assumed
MA 549: Analysis of Lifetime Data
knowledge of basic probability and statistics at the level of MA 511 is assumed
MA 550: Time Series Analysis
knowledge of MA 511 is assumed. Knowledge of MA 541 is also assumed, but may be taken concurrently
MA 551: Computational Statistics
Computational statistics is an essential component of modern statistics that often requires efficient algorithms and programing strategies for statistical learning and data analysis. This course will introduce principles and techniques of statistical computing and data management necessary for computationally intensive statistical analysis especially for big data. Topics covered include management of large data (data structure, data query), parallelized data analyses, stochastic simulations (Monte Carlo methods, permutationbased inference), numerical optimization in statistical inference (deterministic and stochastic convex analysis, EM algorithm, etc.), randomization methods (bootstrap methods), etc. Students will use these techniques while engaging in handson projects with real data. Students who have taken the MA590 version of this course cannot also earn credit for MA 551.
No previous programming knowledge/experience is assumed. Some knowledge of probability and statistics, or MA511 equivalent is recommended.
MA 552: DistributionFree and Robust Statistical Methods
knowledge of MA 541 is assumed, but may be taken concurrently
MA 554: Applied Multivariate Analysis
knowledge of MA 541 is assumed, but may be taken concurrently. Knowledge of matrix algebra is assumed
MA 556: Applied Bayesian Statistics
knowledge of MA 541 is assumed
MA 557: Graduate Seminar in Applied Mathematics
This seminar introduces students to modern issues in Applied Mathematics. In the seminar, students and faculty will read and discuss survey and research papers, make and attend presentations, and participate in brainstorming sessions toward the solution of advanced mathematical problems.
MA 559: Statistics Graduate Seminar
MA 560: Graduate Seminar
MA 562 A and B.: Professional Master's Seminar
MA 571: Financial Mathematics I
MA 540, which can be taken concurrently
MA 572: Financial Mathematics II
MA 573: Computational Methods of Financial Mathematics
MA 571 and programming skills at the level of MA 579, which can be taken concurrently
MA 574: Portfolio Valuation and Risk Management
MA 575: Market and Credit Risk Models and Management
knowledge of MA 540 assumed but can be taken concurrently
MA 579: Financial Programming Workshop
Intermediate scientific programming skills
MA 584/BCB 504: Statistical Methods in Genetics and Bioinformatics
knowledge of probability and statistics at the undergraduate level