Surveys in Applied Mathematics

Surveys in Applied Mathematics: Essays Dedicated to S.M. Ulam covers the proceedings of the First Los Alamos Symposium on Mathematics in the Natural Sciences. The book focuses on the processes, principles, methodologies, and applications of mathematics in the natural sciences. The selection first offers information on the role of applied mathematics, shape of a curve, and biased versus unbiased estimation. Discussions focus on the James-Stein estimator, automorphic forms and Poincaré series, Poincaré metrics, Schottky space and augmented Schottky space, and Schottky groups and Riemann surfaces. The text then examines algorithms, Whitney numbers of geometric lattices, and continued fraction expansion of algebraic numbers. The book takes a look at bifurcations in reaction-diffusion problems, survey of some finite element methods proposed for treating the Dirichlet problem, and mathematics of quantum fields. Topics include Dirichlet problem, chemical waves and reaction-diffusion equations, and bifurcation theorems. The text then ponders on almost periodic behavior of nonlinear waves, turbulence theory, and renormalization group methods. The selection is a valuable source of information for mathematicians and researchers interested in applied mathematics.

Contributors

Preface

Introduction

On the Role of Applied Mathematics

On the Shape of a Curve

Automorphic Forms for Schottky Groups

Biased Versus Unbiased Estimation

Algorithms

Whitney Numbers of Geometric Lattices

Continued Fraction Expansion of Algebraic Numbers

Random Time Evolution of Infinite Particle Systems

Bifurcations In Reaction-Diffusion Problems

Singular Perturbation

A Survey of Some Finite Element Methods Proposed for Treating the Dirichlet Problem

The Mathematics of Quantum Fields

Renormalization Group Methods

Remarks on Turbulence Theory

On an Explicitly Soluble System of Nonlinear Differential Equations Related to Certain Toda Lattices

Three Integrable Hamiltonian Systems Connected with Isospectral Deformations

Almost Periodic Behavior of Nonlinear Waves

A Constructive Definition of the Real Numbers