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 David Ellwood, at al. - American Mathematical Society
Mathematical gauge theory studies connections on principal bundles. The book provides an introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds.
by Albert Tarantola - Springer
Reviews Lie groups, differential geometry, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. The theory of heat conduction and the theory of linear elastic media are studied in detail.
by Eric L. Michelsen - UCSD
This text covers some of the unusual or challenging concepts in graduate mathematical physics. This work is meant to be used with any standard text, to help emphasize those things that are most confusing for new students.
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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.