Step-by-Step BS to PhD Math/Physics
by Alex Alaniz
Publisher: UC Riverside 2013
Number of pages: 323
These are step-by-verifiable-step notes which are designed to help students with a year of calculus based physics who are about to enroll in ordinary differential equations go all the way to doctoral foundations in either mathematics and more so in physics with much reduced mystery. Abstract algebra, topology (local and global) folds into a useful, intuitive toolset for ordinary differential equations and partial differential equations, be they linear or nonlinear.
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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.
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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.
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