Related papers: Topics in Applied Mathematics and Nonlinear Waves
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
This study uses social network analysis and the Classroom Observation Protocol for Undergraduate STEM (COPUS) to characterize six research-based introductory physics curricula. Peer Instruction, Modeling Instruction, ISLE, SCALE-UP,…
Working with letters that represent unknown constants, i.e., parameters, has been historically challenging for students. This is an important skill for their success in many future quantitative settings, and yet it appears this topic is…
The arctic curve, i.e. the spatial curve separating ordered (or `frozen') and disordered (or `temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root-of-unity vertex weights. In these cases…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
This textbook is an introduction to economic networks, intended for students and researchers in the fields of economics and applied mathematics. The textbook emphasizes quantitative modeling, with the main underlying tools being graph…
In the article the problems of the systems of computer mathematics use as a tool for the students learning and research activities support are investigated. The promising ways of providing access to the mathematical software in the…
The following is the very first set of the series in 'Problems and Solutions in a Graduate Course in Classical Electrodynamics'. In each of the sets of the problems we intend to follow a theme, which not only makes it unique but also deals…
The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in…
This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between…
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…
In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the…
This volume contains a selection of papers presented at Linearity/TLLA 2018: Joint Linearity and TLLA workshops (part of FLOC 2018) held on July 7-8, 2018 in Oxford. Linearity has been a key feature in several lines of research in both…
I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent…
These are the notes for an eponymous course given by the authors at the summer school on p-adic arithmetic geometry in Hangzhou.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with…
The numerical simulation of acoustic waves in complex 3D media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this…
The traditional theoretical statistics course which develops the theoretical underpinnings of the discipline (usually following a probability course) is undergoing near-continuous revision in the statistics community. In particular, recent…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…