Course Objective: Based on the fundamentals of numerical computation and optimization methods, this course will further introduce advanced content on numerical differential equations and optimization methods with applications. In addition, students are expected to be able to use the theory and algorithms to solve at least one of the actual problems in computational and applied mathematics. Therefore, this course emphasizes the practice and programming of problems, and each student must complete and demonstrate a research topic on scientific computing.

General Information: This course will cover the following topics of scientific computing:

• Numerical methods for PDEs with applications to variational image processing

• Principal component pursuit problem for low-rank textures

• Sparse representation and dictionary learning

• Projection methods for the incompressible Navier-Stokes equations

• Some selected topics in data science: dimensionality reduction, support vector machine, etc.

Course Transparency Set: (in PDF)