Adam B. Levy

Professor of Mathematics and Chair of Mathematics Department

Teaching this semester

MATH 1800. Multivariate Calculus

Adam Levy
Multivariate calculus in two and three dimensions. Vectors and curves in two and three dimensions; partial and directional derivatives; the gradient; the chain rule in higher dimensions; double and triple integration; polar, cylindrical, and spherical coordinates; line integration; conservative vector fields; and Green’s theorem. An average of four to five hours of class meetings and computer laboratory sessions per week.

MATH 3209. Partial Differential Equations

Adam Levy
A study of some of the partial differential equations that model a variety of systems in the natural and social sciences. Classical methods for solving partial differential equations are covered, as well as modern, numerical techniques for approximating solutions. Applications to the analysis of a broad set of topics, including air quality, traffic flow, and imaging. Computer software is used as an important tool.

Professor Levy's research interests include applied mathematics, optimization, variational analysis, and control theory. He enjoys
teaching on these subjects and differential equations, dynamical systems, numerical analysis, and linear algebra.

Education

  • Ph.D., University of Washington; Seattle, WA
  • B.A., Williams College; Williamstown, MA

Selected Publications

The Basics of Practical Optimization

The Basics of Practical Optimization

Society for Industrial and Applied Mathematics (June 10, 2009)

This textbook provides undergraduate students with an introduction to optimization and its uses for relevant and realistic problems. The only prerequisite for readers is a basic understanding of multivariable calculus because additional materials, such as explanations of matrix tools, are provided in a series of Asides both throughout the text at relevant points and in a handy appendix.

Stationarity and Convergencein Reduce-or-RetreatMinimization

Stationarity and Convergence in Reduce-or-Retreat Minimization

Springer Briefs in Optimization. Springer, New York, 2012

This monograph presents and analyzes a unifying framework for a wide variety of numerical minimization methods. Our “reduce-or-retreat” framework is a conceptual method outline that covers essentially any method whose iterations choose between the two options of reducing the objective in some way at a trial point, or (if reduction is not possible) retreating to a closer set of trial points. Included in this category are many derivative-based methods (which depend on the objective gradient to generate trial points), as well as many derivative-free and direct methods that generate trial points either from some model of the objective or from some designated pattern in the variable space.

Research Publications

MathSciNet reviews for most of the above »