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.
