The first part covers probabilistic models for time series and statistical approaches to analyzing time series data. The second part considers probabilistic models that involve one or more spatial variables.
This course provides a rigorous mathematical and practical foundation in statistical and machine learning theory, bridging formal proofs and real-world engineering applications. Master the mechanics of parametric estimation, hypothesis testing, and uncertainty quantification while exploring the theoretical frameworks of Supervised and Unsupervised Learning, including PAC learning and dimensionality reduction. By grounding these complex concepts in Python-based programming exercises and case studies spanning finance and life sciences, the curriculum ensures you can not only identify and solve complex engineering problems, but also interpret data with the statistical depth required for advanced data science.
This course serves as a blend between microscopic and macroscopic worlds, combining quantum mechanics, classical mechanics, and probability theory to explain how bulk properties like temperature emerge from individual particle dynamics. Beyond its complex mathematical foundations, the curriculum emphasizes a deeply synthetic approach to learning, requiring active discussion and outside research to master applications that span from astrophysics to information theory and biological systems.
This two-part course sequence explores the process of launching and growing a high-tech startup, designed specifically for students in engineering and applied sciences with a strong interest in innovation. The first course introduces key concepts such as opportunity recognition, intellectual property, and early-stage venture development through case studies and guest speakers. The second course builds on this foundation, offering hands-on experience in developing and presenting a full business plan. Topics include market analysis, competitive strategy, financial planning, and startup leadership. The program emphasizes real-world decision-making, team collaboration, and effective communication, culminating in a final presentation to industry experts.
A continuation of introductory quantum theory, covering matrix mechanics, spin, many-particle systems, perturbation theory, and scattering. Applied concepts to physical systems such as atoms, neutrino oscillations, and solids. The course also introduced foundational principles of quantum computing and explored recent developments in quantum technologies.
This course explores how engineering design can address challenges faced by people with disabilities and rehabilitation specialists. Students engage in hands-on design projects, attend lectures, and visit clinical facilities, gaining direct experience with real-world problems. The course includes substantial interaction with clinical faculty and emphasizes practical, human-centered solutions.
This course covers classical mechanics of systems of particles, conservation laws, Lagrangian mechanics, motion in central potentials, and core elements of chaos/non-linear dynamics. Fluid mechanics topics include the assumptions of the fluid approximation, key conservation laws, laminar, creeping, turbulent flow, and special topics like convection, waves, vortices, rotating flows, instabilities, light, and flows as time and interest permit.
This course surveys major algorithms in modern scientific computing, with a focus on continuous problems. Topics include numerical differentiation and integration, numerical linear algebra, root-finding, optimization, Monte Carlo methods, and discretization of differential equations. Basic ideas of error analysis are presented, and regular computer work in class introduces students to software packages (Matlab) and their applications in the natural and social sciences.