Re: Mathematical Physics By H.k Dass Pdf Free Download
Brian
Professor Das' research is in the area of theoretical high-energy physics. His research has focused on questions of symmetry in the fundamental laws of nature. In recent years, he has worked extensively on nonlinear integrable systems -- systems which in spite of their complicated appearance can be exactly solved. He has also been working on finite temperature field theories, generalization of the Standard Model to incorporate CP violation, and problems in quantum field theory and string theory.
My mathematical research started out with applying ideas from statistical physics (thermodynamic formalism) to study dynamical systems in one real variable that had chaotic attractors called Cantor sets [who was Georg Cantor?]. I went on to study holomorphic dynamics and the beautiful fractals associated with the names of Julia and Mandelbrot, and the related but very different limit sets of Fuchsian and Kleinian groups that tesselate hyperbolic space. [Look for Maurits Escher's Circle Limits to get an idea of how to visualize these in two dimensions.] For a few low-dimensional examples of such spaces: think of the surface of a coral reef, your lungs, or even some kale. Other good examples are trees (graphs with no loops) in neural networks like the web or in your brain. Following my PhD thesis, I worked on generalizing various aspects of this theory to different scenarios where there is a presence of negative curvature, which lead to a monograph published by the American Mathematical Society.
Much of my current research focuses on areas of number theory that share boundaries with dynamical systems and fractal geometry. In particular, the theory of Diophantine approximation [who was Diophantus?], which involves studying complicated irrational numbers that are algebraic (e.g. the square root of two) or transcendental (e.g. pi) through much simpler numbers, namely fractions (e.g. 99/70 or 355/133). You may be surprised that this branch of esoteric pure/theoretical mathematics plays a surprising role in studying the stability of planetary systems [e.g. look up KAM theory]! If so, read Eugene Wigner's essay on The Unreasonable Effectiveness of Mathematics in the Natural Sciences, as well as The Usefulness of Useless Knowledge by Abraham Flexner, founder of the Institute for Advanced Study in Princeton, NJ.
I also have interests in the history of mathematics, both in itself and also as part of the broader history of culture and ideas. For a taste, try Jacqueline Stedall's excellent The History of Mathematics: A Very Short Introduction.
I serve as an editor for Complex Analysis and Operator Theory (CAOT), which is a Springer Nature journal devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Papers should be submitted via the Online Manuscript Submission, Review and Tracking System of the journal.
"Mathematical Physics" has been written to provide the readers a clear understanding of the mathematical concepts which are an important part of modern physics. The textbook contains 49 chapters on all major topics in an exhaustive endeavour to cover syllabuses of all major universities. Some of the important topics covered in these chapters are Vectors, Integration, Beta and Gamma functions, Differential Equations, Complex Numbers, Matrix and Determinants, and the Laplace transforms.
Applications are invited from students interested in doing M.Sc. or Ph.D. in Theoretical Physics at the Department of Physics and Astronomy, University of Lethbridge, Alberta, Canada, under the supervision of Dr. Saurya Das, to work on Quantum Gravity, Cosmology and related areas, starting January 2015.
Applicants must have B.Sc., M.Sc. or equivalent in Physics/Theoretical Physics, and have an excellent grasp of its fundamental areas. Knowledge of advanced topics, such as general relativity and quantum field theory, and familiarity with computation and computational softwares such as Mathematica, Matlab, GRTensor etc will be an asset.
Please send your Statement, CV, Transcripts (scanned/electronic copies are fine), and arrange to send at least three letters of reference directly to saurya.das[AT]uleth.ca . Complete applications will be reviewed as and when they are received, until the positions are filled. Graduate students are supported by a combination of teaching and research assistantships, which is generally sufficient to cover tuition and living expenses. Information about Lethbridge, the department, research areas and its graduate program and can be found in:
-astronomy
-astronomy/physics-grad-students
Another set of ideas in spectral geometry concerns withdifferent types of trace formulaeand applications to number theory, quantum physics, and quantum chaos.In some sense this even goes back to the very origins of the Weyl's lawin quantum mechanics and in deriving Planck's radiation formula [1,9].Time permitting, this will be touched in some detail in this course.
Graduate students and faculty working in Riemannian geometry,symplectic geometry, geometric analysis and PDE's, mathematical andtheoretical physics, number theory, and noncommutative geometry shouldnd this material quite relevant and useful.