Mathematics for Physics: A Guided Tour for Graduate Students
by Michael Stone, Paul Goldbart
Publisher: Cambridge University Press 2009
Number of pages: 919
An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics - differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables.
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by T.H. Havelock - Cambridge University Press
Table of contents: Simple groups and group velocity; The velocity of light; The Kelvin method for wave groups; Illustrations of group analysis; Action of a prism upon white light; The flow of energy; Propagation of wavefronts with discontinuities.
by Marios Tsatsos - arXiv
The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can give rise to new descriptions of quantum physics.
by B. Eynard - arXiv.org
This is an introductory course about random matrices. These notes will give the reader a smell of that fascinating tool for physicists and mathematicians that are Random Matrices, and they can give the envy to learn and search more.
by John C. Baez, Mike Stay - arXiv
There is extensive network of analogies between physics, topology, logic and computation. In this paper we make these analogies precise using the concept of 'closed symmetric monoidal category'. We assume no prior knowledge of category theory.