Related papers: Analytical Methods in Physics
I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…
This volume constitutes the proceedings of the 7th International Workshop on Physics and Computation (PC 2016). The workshop was held on the 14th of July 2016 in Manchester, UK, as a satellite workshop to UCNC 2016, the 15th International…
The past decade has witnessed two important new developments in the study of linear series on algebraic varieties. First, vector bundles have emerged as powerful tools for analyzing linear series on curves and surfaces. More recently, the…
Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
Plan of this report is given below: 1. Motivation from Physical and Mathematical Point of View; 2. Differential Calculi on Finite Groups; 3. Metrics; 4. Lagrangian Field Theory and Symplectic Structure; 5. Scalar Field Theory and Spectral…
To conduct a didactic analysis of the current modality of study of real numbers in the Bachelor's Degree in Mathematics, we rely on the notion of didactic paradigm and employ a novel research methodology within the framework of the…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document…
The papeer presents results of "non-traditional" teaching of basic course of Physics in the first year of study at the Technical University in Zvolen, specifically teaching via interactive method based on an increased focus on problem tasks…
The selection of topics in this text has formed the core of a one semester course in applied mathematics at the Arctic University of Norway that has been running continuously since the 1970s. The class has, during its existence, drawn…
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
These notes grew out of a mini-course given by the second-named author at Casa Matem\'atica Oaxaca in the Fall of 2022. Their purpose is to provide an exposition, directed at graduate students, of the basic properties of complex analytic…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
Based on lectures delivered at (1) the AMS meeting at USC, Nov. 1992 (2) Conference on Quantum Aspects of Black Holes, ITP, UC- Santa %Barbara, %%June 1993. (3) 25th Summer Institute, Ecole Normale Superieure, % Paris, Aug. 1992. To appear…
This is an introduction to $p$-adic geometry and $p$-adic analysis focusing on the theme of $p$-adic period mappings. We follow as closely as possible the development of the classical theory of complex period mappings, blending differential…
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics,…
An introduction to quantum groups and non-commutative differential calculus (Lecture at the III Workshop on Differential Geometry, Granada, September 1994)
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…