The goal of this book is to expose the reader to the indispensable role that
mathematics---often very abstract---plays in modern physics. Starting with the notion of vector
spaces the first half of the book develops topics as diverse as algebras classical orthogonal
polynomials Fourier analysis complex analysis differential and integral equations operator
theory and multi-dimensional Green's functions. The second half of the book introduces groups
manifolds Lie groups and their representations Clifford algebras and their representations
and fiber bundles and their applications to differential geometry and gauge theories. This
second edition is a substantial revision of the first one with a complete rewriting of many
chapters and the addition of new ones including chapters on algebras representation of
Clifford algebras and spinors fiber bundles and gauge theories. The spirit of the first
edition namely the balance between rigor and physical application has been maintained as is
the abundance of historical notes and worked out examples that demonstrate the unreasonable
effectiveness of mathematics in modern physics. Einstein has famously said The most
incomprehensible thing about nature is that it is comprehensible. What he had in mind was
reiterated in another one of his famous quotes concerning the question of how ... mathematics
being after all a product of human thought is so admirably appropriate to the objects of
reality. It is a question that comes to everyone's mind when encountering the highly abstract
mathematics required for a deep understanding of modern physics. It is the experience that
Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the
natural sciences. Some praise for the previous edition: PAGEOPH [Pure and Applied Geophysics]
Review by Daniel Wojcik University of Maryland This volume should be a welcome addition to any
collection. The book is well written and explanations are usually clear. Lives of famous
mathematicians and physicists are scattered within the book. They are quite extended often
amusing making nice interludes. Numerous exercises help the student practice the methods
introduced. ... I have recently been using this book for an extended time and acquired a liking
for it. Among all the available books treating mathematical methods of physics this one
certainly stands out and assuredly it would suit the needs of many physics readers.
ZENTRALBLATT MATH Review by G.Roepstorff University of Aachen Germany ... Unlike most
existing texts with the same emphasis and audience which are merely collections of facts and
formulas the present book is more systematic self-contained with a level of presentation
that tends to be more formal and abstract. This entails proving a large number of theorems
lemmas and corollaries deferring most of the applications that physics students might be
interested in to the example sections in small print. Indeed there are 350 worked-out examples
and about 850 problems. ... A very nice feature is the way the author intertwines the formalism
with the life stories and anecdotes of some mathematicians and physicists leading at their
times. As is often the case the historical view point helps to understand and appreciate the
ideas presented in the text. ... For the physics student in the middle of his training it will
certainly prove to be extremely useful. THE PHYSICIST Review by Paul Davies Orion Productions
Adelaide Australia I am pleased to have so many topics collected in a single volume. All the
tricks are there of course but supported by sufficient rigour and substantiation to make the
dedicated mathematical physicist sigh with delight. EMS [EUROPEAN MATHEMATICAL SOCIETY]
NEWSLETTER This book is a condensed exposition of the mathematics that is met in most parts of
physics. The presentation attains a very good balance between the formal introduction of
concepts theorems and proofs on one hand and the applied approach on the other with many
examples fully or partially solved problems and historical remarks. An impressive amount of
mathematics is covered. ... This book can be warmly recommended as a basic source for the study
of mathematics for advanced undergraduates or beginning graduate students in physics and
applied mathematics and also as a reference book for all working mathematicians and
physicists.
