  Modern scientific computational methods are undergoing a transformative
change; big data and statistical learning methods now have the potential to
outperform the classical first-principles modeling paradigm. This book bridges
this transition, connecting the theory of probability, stochastic processes,
functional analysis, numerical analysis, and differential geometry. It
describes two classes of computational methods to leverage data for modeling
dynamical systems. The first is concerned with data fitting algorithms to
estimate parameters in parametric models that are postulated on the basis of
physical or dynamical laws. The second class is on operator estimation, which
uses the data to nonparametrically approximate the operator generated by the
transition function of the underlying dynamical systems.
  This self-contained book is suitable for graduate studies in applied
mathematics, statistics, and engineering. Carefully chosen elementary examples
with supplementary MATLAB codes and appendices covering the relevant
prerequisite materials are provided, making it suitable for self-study.
