Introduction to Mathematical Physics
by Alex Madon
Publisher: Wikibooks 2010
The goal of this book is to propose an ensemble view of modern physics. The coherence between various fields of physics is insured by following two axes: a first axis is provided by the universal mathematical language; the second axis followed along this book is the study of the N body problem.
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by B. Eynard
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 Vojkan Jaksic - McGill University
The subject of these lecture notes is spectral theory of self-adjoint operators and some of its applications to mathematical physics. The main theme is the interplay between spectral theory of self-adjoint operators and classical harmonic analysis.
by Ernesto Estrada - arXiv
Text consisting of some of the main areas of research in graph theory applied to physics. It includes graphs in condensed matter theory, such as the tight-binding and the Hubbard model. It follows the study of graph theory and statistical physics...
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The book covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems.