Böcker av Ivar Ekeland

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.

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.