Understanding Mathematical Concepts in Physics

Prof. Sanjeev Dhurandhar has published over hundred papers in top international journals such as Physical Reviews, MNRAS, Classical & Quantum Gravity, and also a review article (coauthored with M. Tinto) in Living Reviews published by Springer. About three quarters of the publications are on gravitational waves, mainly on their data analysis, and the rest are on various aspects of general relativity. Recently, he has published a book (Springer) entitled General Relativity and Gravitational Waves: Essentials of theory and Practice co-authored with Prof. Sanjit Mitra.  The author ledthe gravitational wave group at IUCAA from 1989 to 2011 until he superannuated. He has taught the Mathematical Physics course at IUCAA at graduate level to physics students for decades and also in the mathematics & physics department of Pune University in the1980s. He has also given courses on differential geometry, probability theory etc. during his career at IUCAA. He holds a Master’s degree in mathematics (he switched to physics for his Ph. D.).The author is a recipient of several prestigious awards which include the Vijnan Bhushan Firodia Award for Outstanding Contributions to Science, the Meghnad Saha Memorial Gold Medal (The Asiatic Society, Kolkata, India) for Outstanding Contributions to Physics, Milners breakthrough prize (Milners Foundation U.S.A.) awarded for the detection of gravitational waves (shared with the Ligo Science Collaboration), etc. He is a fellow of the American Physical Society (APS), the three prestigious Indian academies: (i) Indian National Science Academy, Delhi, (ii) the Indian Academy of Sciences, Bangalore, and (iii) National Academy of Sciences India, Allahabad.

• Dedication.- Preface.- Topology.- Hilbert Spaces.- Fourier Analysis.- Complex analysis: hands on.- Understanding differential equations: geometrical insights and general analysis.- Solving Differential Equations.- Differential Geometry and Tensors.- Representations of the rotation group and Lie groups.- Probability and Random Variables.- Probability distributions in physics.- The statistical detection of signals in noisy data.- Bibliography.