People in all walks of life—and perhaps mathematicians especially—delight in working on problems for the sheer pleasure of meeting a challenge. The problem section of SIAM Review offers classroom instructors and their students as well as other interested problemists, a set of problems—solved or unsolved—illustrating various applications of mathematics. In many cases the unsolved problems were eventually solved. Problems in Applied Mathematics is a compilation of 380 of the most interesting problems found in SIAM Review dating back to the journal's inception in 1959.

The problems are classified into 22 broad categories including Series, Special Functions, Integrals, Polynomials, Probability, Combinatorics, Matrices and Determinants, Optimization, Inequalities, Ordinary Differential Equations, Boundary Value Problems, Asymptotics and Approximations, Mechanics, Graph Theory, and Geometry. The broad range of material will appeal to a large audience including, but not limited to, students, teachers, professional mathematicians, and engineers from elementary through advanced levels.

Keywords: series, special functions, integrals, polynomials, probability, combinatorics, matrices and determinants, optimization, inequalities, ordinary differential equations, boundary value problems, asymptotics and approximations, mechanics, graph theory, geometry.