Module #11 Finite Difference Methods for SPDEs Introduction to finite difference methods for stochastic partial differential equations (SPDEs)
Module #12 Applications to Finance Pricing options using stochastic numerical methods, risk analysis, and portfolio optimization
Module #13 Applications to Biology Modeling population dynamics, chemical reactions, and biological systems using stochastic numerical methods
Module #14 Applications to Physics Modeling particle systems, diffusion processes, and quantum systems using stochastic numerical methods
Module #15 Markov Chain Monte Carlo (MCMC) Methods Introduction to MCMC methods, importance sampling, and Gibbs sampling
Module #16 Gaussian Processes and Kriging Introduction to Gaussian processes, kriging, and applications to uncertainty quantification
Module #17 Stochastic Collocation Methods Introduction to stochastic collocation methods, advantages, and applications
Module #18 Uncertainty Quantification Introduction to uncertainty quantification, sensitivity analysis, and propagation of uncertainty
Module #19 Multilevel Monte Carlo Methods Introduction to multilevel Monte Carlo methods, advantages, and applications
Module #20 Parallel Computing and Stochastic Numerical Methods Introduction to parallel computing, parallelization of stochastic numerical methods
Module #21 Case Studies:Stochastic Numerical Methods in Engineering Real-world applications of stochastic numerical methods in engineering
Module #22 Case Studies:Stochastic Numerical Methods in Climate Modeling Real-world applications of stochastic numerical methods in climate modeling
Module #23 Case Studies:Stochastic Numerical Methods in Epidemiology Real-world applications of stochastic numerical methods in epidemiology
Module #24 Hands-on Project:Implementing Stochastic Numerical Methods Guided project to implement stochastic numerical methods using programming languages (e.g. Python, MATLAB)
Module #25 Research Trends and Future Directions Overview of current research trends and future directions in stochastic numerical methods
Module #26 Advanced Topics in Stochastic Numerical Methods Special topics in stochastic numerical methods (e.g. stochastic Galerkin methods, polynomial chaos)
Module #27 Stochastic Numerical Methods for Machine Learning Applications of stochastic numerical methods to machine learning and data analysis
Module #28 Final Project:Applying Stochastic Numerical Methods to a Real-World Problem Independent project to apply stochastic numerical methods to a real-world problem
Module #29 Conclusion and Future Work Review of course material, conclusion, and future work
Module #30 Course Wrap-Up & Conclusion Planning next steps in Stochastic Numerical Methods and Applications career
