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.

Infinite-Dimensional Optimization and Convexity (Chicago Lectures in Mathematics)

Science & Math

Ekeland, Ivar

Turnbull, Thomas

Mathematics

Univ of Chicago Pr

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.

Business & Money

University of Chicago Press

Discusses the concept of time from a mathematical perspective, looks at the controversial catastrophe theory, and covers the shortcomings of Newtonian mathematics

Mathematics And the Unexpected

"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

Mathematics and the Unexpected

Ivar Ekeland extends his consideration of the catastrophe theory of the universe begun in his widely acclaimed Mathematics and the Unexpected, by drawing on rich literary sources, particularly the Norse saga of Saint Olaf, and such current topics as chaos theory, information theory, and particle physics. "Ivar Ekeland gained a large and enthusiastic following with Mathematics and the Unexpected, a brilliant and charming exposition of fundamental new discoveries in the theory of dynamical systems. The Broken Dice continues the same theme, and in the same elegant, seemingly effortless style, but focuses more closely on the implications of those discoveries for the rest of human culture. What are chance and probability? How has our thinking about them been changed by the discovery of chaos? What are all of these concepts good for? . . . Ah, but, I mustn't give the game away, any more than I should if I were reviewing a detective novel. And this is just as gripping a tale. . . . Beg, borrow, or preferably buy a copy. . . . I guarantee you won't be disappointed."—Ian Stewart, Science

The Broken Dice: And Other Mathematical Tales of Chance

The Broken Dice, and Other Mathematical Tales of Chance

Evolution

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? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have 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 least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today. Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popular-science buffs and historians of science alike.

The Best of All Possible Worlds: Mathematics and Destiny

History & Philosophy

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? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have 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 least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today. Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popular-science buffs and historians of science alike.

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.

The Cat in Numberland

Children's Books

Growing Up & Facts of Life

Cricket Books

No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book 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). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Convex Analysis and Variational Problems (Classics in Applied Mathematics, Series Number 28)

Témam, Roger

Society for Industrial and Applied Mathematics

See the best price to sell, buy, or rent books by Ekeland, Ivar. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Ekeland, Ivar

See the best price to sell, buy, or rent books by Ekeland, Ivar. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Infinite-Dimensional Optimization and Convexity (Chicago Lectures in Mathematics)

Infinite-Dimensional Optimization and Convexity (Chicago Lectures in Mathematics)

Mathematics And the Unexpected

Mathematics and the Unexpected

The Broken Dice: And Other Mathematical Tales of Chance

The Broken Dice, and Other Mathematical Tales of Chance

The Best of All Possible Worlds: Mathematics and Destiny

The Best of All Possible Worlds: Mathematics and Destiny

The Cat in Numberland

Convex Analysis and Variational Problems (Classics in Applied Mathematics, Series Number 28)