MA 590: Computational Statistics – Professor Fangfang Wang
(offered Fall 2021)
Computational statistics is an essential component of modern statistics that often requires efficient algorithms and programing strategies for statistical learning and data analysis. This course will introduce principles and techniques of statistical computing necessary for computationally intensive statistical analysis. Topics covered include stochastic simulations (Monte Carlo methods, inversion method, rejection sampling, Monte Carlo integration, importance sampling, etc.), numerical methods for optimization and their application to statistical estimation (deterministic and stochastic analyses, EM algorithm, etc.), randomization methods for statistical inference (permutation tests, bootstrap, and jackknife), etc. Students will learn how to implement these techniques by engaging in hands-on projects with real data.
MA 590: Nonlinear elasticity: theory and applications – Professor Min Wu
(offered Spring 2022)
Both geometry and functional analysis play essential roles in nonlinear elasticity. This entry-level graduate course discusses nonlinear elasticity focusing on differential geometry and its application in biomechanics and material sciences concerning soft elastic materials. We prepare the class in the mind of math, physics, and engineering students who have solid experience in Multivariable Calculus and Linear Algebra. No prior exposure to (bio)mechanics/physics is needed. For learning outcomes, we hope the students can understand the geometrical and mechanical behavior of soft elastic materials both computationally and physically.
We divide the topics into 3D and 2D-shell nonlinear elasticity. For 3D bodies, we cover the motions of simple bodies; vector fields, one-forms, and pull backs; the deformation gradient; tensors, two-point tensors, and the covariant derivative; flows and Lie derivatives; the master balance law; the stress tensor and balance of momentum, balance of energy; the principle of virtual work; constitutive theory; linearization of nonlinear elasticity; boundary value problems and application to swelling gels and growing biological tissues. For 2D shells, we cover the regular surfaces and curvatures; vector and tensor field, stress and strain on the regular surfaces; boundary value problems on the surface and application to cell wall mechanics.