Topics in Physical Mathematics (PDF)

From the reviews:

“Topics in physical mathematics is a quite unique account of some of the mathematical background necessary for a beginner entering the field. … the book offers an introduction and overview of some of the remarkable results that have been obtained in the first three decades of research in ‘physical mathematics’. … will be quite useful as a reference and overview of particular subfields within ‘physical mathematics’. I can also … recommending it to a beginning graduate student wishing to quickly fill some gaps of knowledge.” (Johannes Walcher, Mathematical Reviews, Issue 2011 f)

“Reading this book will bring a real pleasure to all mathematically inclined Young physicists having the necessary mathematical luggage in their minds. … it will bring the reader to feel the real correspondence between the real harmony in the physical world and the remarkable mathematical harmony among the various algebraic, geometric and topological structure.” (Stoil Donev, Journal of Geometry and Symmetry in Physics, Vol. 22, 2011)

“The book covers a large subset of today’s mathematics, especially focusing on stuff that has been very active and in vogue for the last half century or so. … The audience of the book … will consist of graduate students and researchers. … I certainly enjoyed it; all in all, reading this book was a fun … .” (Gizem Karaali, The Mathematical Association of America, August, 2012)