The Princeton Companion to Applied Mathematics is out at last

For those readers anxiously awaiting the publication of The Princeton Companion to Applied Mathematics, the day has come. The book can be purchased either from Princeton University Press or It is a companion to the prize-winning volume Princeton Companion to Mathematics, edited by Timothy Gowers, June Barrow-Green and Imre Leader, which was reviewed by one of us for Siam Review, November 2009.

This book is decidedly not an easy read for a weekend at the cabin. For one thing, at 994 pages and 2.3 kg (5.0 pounds), it is a hefty volume to carry around. It also is not a tutorial or beginning-level introduction. But as an encyclopedic overview of modern applied mathematics, it has no peer.

The editor of this work is Nicholas J. Higham, a well-known numerical analyst at the University of Manchester in the U.K. Higham was assisted in the monumental job of assembling this work by Mark Dennis, Paul Glendinning, Paul Martin, Fadil Santosa and Jared Tanner, whose collective expertise covers many facets of modern applied mathematics. Behind these editors is a veritable army of experts, 165 by our count, who together with the editors authored the individual articles.

The 186 articles are organized into eight topic areas. Here are the eight topic areas, with a sample of the specific topic articles in each area:

  1. Introduction to Applied Mathematics
    • What Is Applied Mathematics?
    • Goals of Applied Mathematical Research
  2. Concepts
    • Chaos and Ergodicity
    • The Fast Fourier Transform
    • Graph Theory
    • Orthogonal Polynomials
  3. Equations, Laws and Functions of Applied Mathematics
    • The Black-Scholes Equation
    • Einstein’s Field Equations
    • The Gamma Function
    • The Navier-Stokes Equations
  4. Areas of Applied Mathematics
    • Calculus of Variations
    • Numerical Linear Algebra and Matrix Analysis
    • Continuous Optimization (Nonlinear and Linear Programming)
    • Data Mining and Analysis
    • Fluid Dynamics
    • Signal Processing
    • General Relativity and Cosmology
  5. Modeling
    • Mathematical Biomechanics
    • Financial Mathematics
    • Numerical Weather Prediction
    • Turbulence
  6. Example Problems
    • Foams
    • Searching a Graph
    • Robotics
    • The N-Body Problem and the Fast Multipole Method
  7. Application Areas
    • Aircraft Noise
    • Chip Design
    • Medical Imaging
    • High-Performance Computing
    • Electronic Structure Calculations
    • Mathematical Economics
  8. Final Perspectives
    • Mathematical Writing
    • Reproducible Research in the Mathematical Sciences
    • Teaching Applied Mathematics

The overall impression in looking over this book is to be overwhelmed at the scope and professionalism involved. Higham and his editorial team are certainly to be congratulated on what is clearly a landmark contribution to the field.

The present authors contributed the article Experimental Applied Mathematics, which appeared in the Final Perspectives section. In this article we describe several applications of the experimental mathematics paradigm to applied mathematics. This article, plus a sample of other articles from the volume, is freely available online at the Princeton University Press site.

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