Problems IN Modern Mathematics

During the last fifty years, the development of better numerical methods and more powerful computers has been a major enterprise for the scien- tific community. Today, problems of extreme complexity can be solved. However, for real life applications, the availability of reliable scientific soft- ware seems to be emerging as a limiting factor.

During the last fifty years, the development of better numerical methods and more powerful computers has been a major enterprise for the scien- tific community. Today, problems of extreme complexity can be solved. However, for real life applications, the availability of reliable scientific soft- ware seems to be emerging as a limiting factor.

The main feature of this text is the discussion on how modern concepts in computer science can be applied in order to develop scientific software that is easier to extend, maintain and use than the more traditional counterparts.

"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes.