The Department of Mathematical Sciences is a leader in the field of algebraic cryptography and is home to the internationally recognized Algebra and Cryptology Center (ACC).
The Department has research strengths in the areas of group theory, stochastic modeling, mathematical models of risk, optimization and control under uncertainty and risk, statistical learning, numerical analysis, partial differential equations (PDEs) and reliability theory.
Recent research themes include risk-averse learning and control for distributed dynamical systems, theory of interpretations and applications to algebra, algebraic geometry in nilpotent groups, new types of computational complexity, quadratic equations in groups, inverse problems in electrohydrodynamics (EHD), randomized local model reduction, random packing models, dense weighted networks, Bayesian models for high-dimensional time series, reliability of complex engineering systems, and uncertainty quantification of combustion processes, to name just a few. Faculty members are supported by major government funding agencies and collaborate with Stevens Institute for Artificial Intelligence (SIAI), the Center for Research toward Advancing Financial Technologies (CRAFT) and the Center for Quantum Science and Engineering.
The Department hosts weekly seminars on mathematical cryptology, has co-organized a series of workshops on optimization of stochastic systems, and encourages research and research-related activities by faculty and students at all levels. The Stevens Math Club welcomes undergraduates of all majors and serves as a platform for discussing and solving challenging mathematical problems. It also prepares Stevens undergraduates for the annual Putnam Mathematical Competition organized and supported by the Mathematical Association of America (MAA). Master’s students are encouraged to elect a thesis in mathematics and pursue further studies in our mathematics doctoral program, which focuses on research with the main aim of producing significant mathematical results.
“It is important to engage students in substantive research. They are interested in what they can do with their studies after they graduate and seeing the implementation of theoretical research is very appealing.” - Dr. Darinka Dentcheva
“Everything in the field of cryptographic mathematics is wide open, presenting challenging and exciting opportunities for researchers such as myself and offering an exceptional chance for students to participate in this groundbreaking field.” - Dr. Alexei Miasnikov
Risk and Decision-Making
Models of risk aim at capturing the impact of low-probability but high-cost events. While those models enjoy much attention in mathematical finance, one could trace their origin to the works of Lorenz, Von Neumann and Morgenstern, Markowitz, and Choquet. We are engaged in developing the theory and methods of optimization and control under uncertainty and risk, in solving the exciting mathematical challenges arising in these areas, as well as in their applications to relevant practical problems in cooperation with colleagues and industry representatives. Stochastic optimization and control are of great importance to the decision processes in business, medicine, military problems, energy production and distribution, insurance, environmental protection, and many others. The Department has co-organized a series of Rutgers-Stevens workshops on optimization of stochastic systems and continues to be at the forefront of this extremely important and thriving research area.
Algebra and Cryptology
The Algebra and Cryptology Center (ACC) investigates new techniques from computational algebra and their applications to practical problems in cryptography and cryptanalysis. For example, the standard notion of complexity is “what happens in the worst case for inputs of a given size” but the relevant notion for cryptography is “what happens with overwhelming probability as the size of the inputs becomes very large”. The center develops mathematical algorithms in application to security in quantum computing systems — an integral blending of computer science and mathematics embracing principles of quantum mechanics. Post-quantum cryptography is one of the rapidly evolving research areas being actively pursued by the ACC faculty. The center also conducts world-class research in computational, combinatorial, and geometric group theory and hosts a weekly seminar, open to the public and featuring scholars from around the globe.
Research on Innovative Educational Technologies
The Department has spearheaded numerous research-backed educational initiatives, including major reforms to teaching calculus, that were supported by the NSF-funded Foundations Project and led to a series of Stevens conferences on mathematics education. One of such recent major initiatives, supported by yet another NSF grant, aims to study the impact of community engagement on STEM (Science, Technology, Engineering, and Mathematics) undergraduates, who as part of their university curricula, lead mathematics enrichment activities for elementary school students via the Math Circle. This initiative serves the national interest by fostering partnerships between higher education and local communities to improve K-12 mathematics education while developing teaching, leadership, and communication skills of undergraduates majoring in STEM fields. Faculty members have also been involved in research and development of a novel educational platform that has been adopted by mathematics departments across the nation.