This textbook provides students with a solid introduction to the techniques of approximation
commonly used in data analysis across physics and astronomy. The choice of methods included is
based on their usefulness and educational value their applicability to a broad range of
problems and their utility in highlighting key mathematical concepts. Modern astronomy reveals
an evolving universe rife with transient sources mostly discovered - few predicted - in
multi-wavelength observations. Our window of observations now includes electromagnetic
radiation gravitational waves and neutrinos. For the practicing astronomer these are highly
interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle
physics and data-analysis.The book is organized to be largely self-contained starting from
basic concepts and techniques in the formulation of problems and methods of approximation
commonly used in computation and numerical analysis. This includes root finding integration
signal detection algorithms involving the Fourier transform and examples of numerical
integration of ordinary differential equations and some illustrative aspects of modern
computational implementation. Some of the topics highlighted introduce the reader to selected
problems with comments on numerical methods and implementation on modern platforms including
CPU-GPU computing.Developed from lectures on mathematical physics in astronomy to advanced
undergraduate and beginning graduate students this book will be a valuable guide for students
and a useful reference for practicing researchers. To aid understanding exercises are included
at the end of each chapter. Furthermore some of the exercises are tailored to introduce modern
symbolic computation.
