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Introductory statistical methods for students in the applied sciences and engineering. Random variables and probability distributions; the concept of random sampling, including random samples, statistics, and sampling distributions; the Central Limit Theorem; parameter estimation; confidence interva...

Topics in combinatorial mathematics that find frequent application in computer science, engineering, and general applied mathematics. Course focuses on graph theory on one hand, and enumeration on the other. Specific topics include graph matching and graph coloring, generating functions and recurren...

Abstracting the essential components and mechanisms from a natural system to produce a mathematical model, which can be analyzed with a variety of formal mathematical methods, is perhaps the most important, but least understood, task in applied mathematics. This course approaches a number of problem...

Abstracting the essential components and mechanisms from a natural system to produce a mathematical model, which can be analyzed with a variety of formal mathematical methods, is perhaps the most important, but least understood, task in applied mathematics. This course approaches a number of problem...

This course provides an introduction to basic mathematical ideas and computational methods for optimization. Topics include linear programming, integer programming, branch-and-bound, branch-and-cut, as well as first-order gradient-based methods with an emphasis on modeling and data science applicati...

Introduction to methods for developing accurate approximate solutions for problems in the sciences that cannot be solved exactly, and integration with numerical methods and solutions. Topics include: dimensional analysis, algebraic equations, complex analysis, perturbation theory, matched asymptotic...

This course serves as an introduction to partial differential equations (PDE) and their applications across the sciences. The course will familiarize students with the process of starting with a model, deriving the appropriate PDE, and solving it. Examples include wave equations, diffusion equations...

This course begins with a solid foundation in classical power system engineering, covering the basic operation and control of electric grids. It then explores the grid’s transformation into a data-rich, power electronically interfaced system. It introduces modern AI-driven approaches for forecasting...

This course explores the science and design of materials. How do we classify materials? Why do we build with certain materials? What are the energy, health, and societal implications of materials? And what does the future of materials look like? The goal of this course is to enable students to under...