In this volume, Ekeland and Turnbull are mainly concerned with existence theory. They seek to determine whether, when given an optimization problem consisting of minimizing a functional over some feasible set, an optimal solution-a minimizer-may be found.

"Not the least unexpected thing about "Mathematics and the Unexpected" is that a real mathematician should write not just a literate work, but a literary one." Ian Stewart, "New Scientist"
"In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)." "Village Voice""

Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what "is" the best of all possible worlds? How do we define it? This question has preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer.
This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose...

This introductory text offers simple presentations of the fundamentals of nonlinear analysis, with direct proofs and clear applications. Its full treatment ranges from smooth to nonsmooth functions, from convex to nonconvex variational problems, and from economics to mechanics. 1984 edition.

This volume contains the proceedings of a NATO Advanced Research Workshop on Periodic Solutions of Hamiltonian Systems held in II Ciocco, Italy on October 13-17, 1986. It also contains some papers that were an outgrowth of the meeting. On behalf of the members of the Organizing Committee, who are also the editors of these proceedings, I thank all those whose contributions made this volume possible and the NATO Science Committee for their generous financial support. Special thanks are due to Mrs. Sally Ross who typed all of the papers in her usual outstanding fashion. Paul H. Rabinowitz...

This is the third volume in the Paris-Princeton Lectures in Financial Mathematics, which publishes, on an annual basis, cutting-edge research in self-contained, expository articles from outstanding specialists, both established and upcoming. Coverage includes articles by Rene Carmona, Ivar Ekeland/Erik Taflin, Arturo Kohatsu-Higa, Pierre-Louis Lions/Jean-Michel Lasry, and Huyen Pham.

During the academic year 1995/96, I was invited by the Scuola Normale Superiore to give a series of lectures. The purpose of these notes is to make the underlying economic problems and the mathematical theory of exterior differential systems accessible to a larger number of people. It is the purpose of these notes to go over these results at a more leisurely pace, keeping in mind that mathematicians are not familiar with economic theory and that very few people have read Elie Cartan.

In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial mechanics, they are found by perturbation theory: there is a small parameter in the problem, the mass of the perturbing body for instance, and for = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for -# 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2-form L =l dPi 1 dqi' The most...