Introduction: Data Science and BigData Computing -- Overview of Basic Methods for Data Science -- Relationship and Connectivity of Incomplete Data Collection -- Machine Learning for Data Science: Mathematical or Computational -- Images, Videos, and BigData -- Topological Data Analysis -- Monte Carlo Methods and their Applications in Big Data Analysis -- Feature Extraction via Vector Bundle Learning -- Curve Interpolation and Financial Curve Construction -- Advanced Methods in Variational Learning: Segmentation with Intensity Inhomogeneity -- An On-line Strategy of Groups Evacuation From a Convex Region in the Plane -- A New Computational Model of Bigdata.