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
Murray S. Klamkin is Professor Emeritus of Mathematics at the University of Alberta. He served as problem Editor for SIAM Review from 1959 to 1993. Professor Klamkin received the 1988 Award for Distinguished Service from the MAA for “his contributions to the realm of problem solving, for his inspiring influence on young problem solvers, and for his many other contributions to mathematics.” He has chaired the Advisory Board of the applied Mathematical Division of the National Bureau of Standards and has authored three books, approximately 165 articles, and many problems and/solutions.
Chapter 1: Mechanics; Chapter 2: Electrical Resistance; Chapter 3: Probability; Chapter 4: Combinatorics; Chapter 5: Series; Chapter 6: Special Functions; Chapter 7: Ordinary Differential Equations; Chapter 8: Partial Differential Equations; Chapter 9: Definite Integrals; Chapter 10: Integral Equations; Chapter 11: Matrices and Determinants; Chapter 12: Numerical A; Chapter 13: Inequalities; Chapter 14: Optimization; Chapter 15: Graph Theory; Chapter 16: Geometry; Chapter 17: Polynomials; Chapter 18: Simultaneous Equations; Chapter 19: Identities; Chapter 20: Zeros; Chapter 21: Functional Equations; Chapter 22: Miscellaneous; Appendix.