In this textbook basic mathematical models used in Big Data Analytics are presented and
application-oriented references to relevant practical issues are made. Necessary mathematical
tools are examined and applied to current problems of data analysis such as brand loyalty
portfolio selection credit investigation quality control product clustering asset pricing
etc. - mainly in an economic context. In addition we discuss interdisciplinary applications to
biology linguistics sociology electrical engineering computer science and artificial
intelligence. For the models we make use of a wide range of mathematics - from basic
disciplines of numerical linear algebra statistics and optimization to more specialized game
graph and even complexity theories. By doing so we cover all relevant techniques commonly used
in Big Data Analytics.Each chapter starts with a concrete practical problem whose primary aim
is to motivate the study of a particular Big Data Analytics technique. Next mathematical
results follow - including important definitions auxiliary statements and conclusions arising.
Case-studies help to deepen the acquired knowledge by applying it in an interdisciplinary
context. Exercises serve to improve understanding of the underlying theory. Complete solutions
for exercises can be consulted by the interested reader at the end of the textbook for some
which have to be solved numerically we provide descriptions of algorithms in Python code as
supplementary material.This textbook has been recommended and developed for university courses
in Germany Austria and Switzerland.
