Bøger af Ivar Ekeland

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.

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.

Optimists believe this is the best of all possible worlds, and pessimists fear that might really be the case. There was a time, during the 17th and 18th centuries, when scientists and mathematicians felt they could provide the answer. This book is their story.

This work extends the author's consideration of the catastrophe theory of the universe begun in "Mathematics and the Unexpected", by drawing on literary sources, particularly the Norse saga of Saint Olaf, and such current topics as chaos theory, information theory and particle physics.

In the case of completely integrable systems, periodic solutions are found by inspection.

This text assumes no knowledge of mathematical logic. Beginning with a nonstandard construction of the real number system, it leads students thorough the basic topics of elementary real analysis, topological spaces, and Hilbert space. Includes nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. 1977 edition.

In this brief treatise, 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, but particulars are practically impossible.

At Mr. and Mrs. Hilbert's Hotel Infinity, the resident cat is puzzled. The hotel is fully booked - the rooms are full of Numbers, both Odds and Evens - yet guests continue to arrive. When Zero shows up, there's a massive room switching, and he stays, even though Mr. Hilbert insists he's not really a Number. Then the Letters appear and everyone still has a room, even though no Numbers have left. No matter how many guests arrive or depart, the hotel accommodates them all, and is always full. But when the Fractions arrive, demanding rooms, real chaos threatens. Can an ingenious solution be found to house them all?Based on mathematician David Hilbert's famous paradox of the Grand Hotel, The Cat in Numberland offers a refreshingly clear explanation of infinity for readers of all ages. John O'Brien's imaginative line drawings further elucidate the complex concept, as well as simple functions like addition, subtraction, division, and multiplication.

No one working in duality should be without a copy of this book. It contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension).