Surveys in applied mathematics : essays dedicated to S.M. Ulam ; [proceedings of the First Los Alamos Symposium on Mathematics in the Natural Sciences

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. Content: Inside Front Cover, Page ii Front Matter, Page iii Copyright, Page iv Dedication, Page v CONTRIBUTORS, Pages ix-x PREFACE, Page xi, N. Metropolis, Steven A. Orszag, Gian-Carlo Rota INTRODUCTION, Pages xiii-xv On the Role of Applied Mathematics, Pages 1-22, C.C. LIN On the Shape of a Curve, Pages 23-38, RAOUL BOTT Automorphic Forms for Schottky Groups, Pages 39-68, LIPMAN BERS Biased Versus Unbiased Estimation, Pages 69-87, BRADLEY EFRON Algorithms, Pages 89-101, D.J. KLEITMAN Whitney Numbers of Geometric Lattices, Pages 103-116, KENNETH BACLAWSKI Continued Fraction Expansion of Algebraic Numbers, Pages 117-122, R.D. RICHTMYER Random Time Evolution of Infinite Particle Systems, Pages 123-127, FRANK SPITZER Bifurcations in Reaction–Diffusion Problems, Pages 129-141, LOUIS N. HOWARD Singular Perturbation, Pages 143-155, J.D. COLE A Survey of Some Finite Element Methods Proposed for Treating the Dirichlet Problem, Pages 157-166, JAMES H. BRAMBLE The Mathematics of Quantum Fields, Pages 167-178, JAMES GLIMM Renormalization Group Methods, Pages 179-195, KENNETH G. WILSON Remarks on Turbulence Theory, Pages 197-223, ROBERT H. KRAICHNAN On an Explicitly Soluble System of Nonlinear Differential Equations Related to Certain Toda Lattices, Pages 225-234, M. KAC, PIERRE VAN MOERBEKE Three Integrable Hamiltonian Systems Connected with Isospectral Deformations, Pages 235-258, J. MOSER Almost Periodic Behavior of Nonlinear Waves, Pages 259-270, PETER D. LAX The Real Numbers as a Wreath Product, Pages 271-297, F. FALTIN, N. METROPOLIS, B. ROSS, G.-C. ROTA Edited By N. Metropolis, S. Orszag, G.-c. Rota. Includes Bibliographical References.