Explore randomized methods for quantum many-body problems in this comprehensive tutorial presented by Robert Webber at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Delve into the challenges of eigenstate calculations for quantum many-body systems and discover how quantum Monte Carlo (QMC) approaches can push the boundaries of scientific understanding. Learn about variational Monte Carlo (VMC) and full configuration interaction quantum Monte Carlo (FCIQMC) algorithms, using quantum spin systems as illustrative examples. Gain insights into matrices, tensor product wave functions, electronic structure, raising and lowering operators, power method, convergence, subspace iteration, historical estimator, compression operator, limitations, and Monte Carlo techniques. Enhance your understanding of advanced quantum mechanics and its mathematical foundations in this in-depth, 75-minute presentation.