BIOE 210: Linear Algebra for Biomedical Data Science
Undergraduate/Graduate course, University of Illinois at Urbana-Champaign, Department of Bioengineering, 2025
Teaching
BIOE 210 is a core course required for all bioengineering undergraduates. The goal is to introduce students to essential analytical and computational tools from linear algebra. In addition to describing vector and matrix arithmetic, students will solve systems of linear equations and explore linear regression. These methods can be applied to analyze large, multivariable datasets to quantify relationships between variables; decompose complex datasets into simpler representations; solve common problems in classification and image processing; and visualize high-dimensional data spaces. Course topics include definitions of vector spaces; solvability; rank; basis; linear transformation matrices; and vector & matrix decompositions (eigenanalysis, SVD, PCA). The course focuses on mathematical and computation aspects of problem solving, and consequently requires students to access Matlab
BIOE 485: Computational Mathematics for Machine Learning and Imaging
Undergraduate/Graduate course, University of Illinois at Urbana-Champaign, Department of Bioengineering, 2024
Covers fundamental mathematical and computational methods needed to implement computational imaging and machine learning solutions. Topics : probability theory, matrix decompositions, vector calculus, stochastic sampling methods, numerical optimization-based formulations of inverse problems, first order deterministic and stochastic gradient-based methods, quasi-Newton and Hessian free methods