Numerical Methods for Science and Statistics

Catalog description

Robust, scalable data analysis is built on numerical methods. This course develops the theoretical and computational machinery needed to turn mathematical and statistical models into reliable and efficient scientific tools. Core topics include floating-point error and conditioning; numerical linear algebra (least squares, factorizations, iterative solvers, SVD/eigenvalue problems, and randomized methods); interpolation and approximation; numerical differentiation and integration (quadrature); and ordinary differential equations (initial-value problems, stability, stiffness). Applications emphasize life-science and statistical workflows and #8212;e.g., regression and GLMs, PCA/SVD for high-throughput assays, mixed models/REML, and epidemiological and biochemical ODE models. Emphasis is on accuracy, stability, and practical performance on real datasets. Students will analyze and implement fundamental numerical approaches underlying modern scientific methods. This course is aimed at graduate students and advanced undergraduates in Computational Biology, Statistics / Data Science, Machine Learning, ECE, Bioengineering, and related fields seeking a rigorous, implementation-focused treatment of numerical methods with direct scientific applications. Prerequisites: ( 02-120 or 15-112 ) and 21-122 and ( 21-241 or 21-242 )