Why does nature prefer some shapes and not others? The variety of sizes, shapes, and irregularities in nature is endless. Skillfully integrating striking full-color illustrations, the authors describe the efforts by scientists and mathematicians since the Renaissance to identify and describe the principles underlying the shape of natural forms. But can one set of laws account for both the symmetry and irregularity as well as the infinite variety of nature's designs? A complete answer to this question is likely never to be discovered. Yet, it is fascinating to see how the search for some simple universal laws down through the ages has increased our understanding of nature. The Parsimonious Universe looks at examples from the world around us at a non-mathematical, non-technical level to show that nature achieves efficiency by being stingy with the energy it expends.

Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of "edge-crawling" along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a "global theory of minimal surfaces" as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmüller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau ́s problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented.

History of Mathematics is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on History of Mathematics discusses: Mathematics in Egypt and Mesopotamia; History of Trigonometryto 1550; Mathematics in Japan; The Mathematization of The Physical Sciences-Differential Equations of Nature; A Short History of Dynamical Systems Theory:1885-2007; Measure Theories and Ergodicity Problems; The Number Concept and Number Systems; Operations Research and Mathematical Programming: From War to Academia - A Joint Venture; Elementary Mathematics From An Advanced Standpoint; The History and Concept of Mathematical Proof; Geometry in The 20th Century; Bourbaki: An Epiphenomenon in The History of Mathematics This volume is aimed at the following five major target audiences: University and College Students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers, NGOs and GOs.

Inside PFTB ("Proofs from The Book") is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. Some of the proofs are classics, but many are new and brilliant proofs of classical results--"Notices of the AMS," August 1999.

This is a provocative account of the astounding new answers to the most basic philosophical question: Where did the universe come from and how will it end?

This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.

Challenging historic assumptions about human relationships with nature, Jan G. Laitos examines how environmental laws have addressed environmental problems in the past, and the reasons for the laws' inability to successfully prevent environmental contamination and alterations of critical environmental systems. This forward-thinking book offers a creative and organic alternative to traditional but ultimately unsuccessful environmental rules. It explains the need for a new generation of environmental laws grounded in the universal laws of nature which might succeed where past and current approaches have largely failed.

Maps were at the heart of cultural life in the Americas from before colonization to the formation of modern nation-states. The fourteen essays in Early American Cartographies examine indigenous and European peoples' creation and use of maps to better represent and understand the world they inhabited. Drawing from both current historical interpretations and new interdisciplinary perspectives, this collection provides diverse approaches to understanding the multilayered exchanges that went into creating cartographic knowledge in and about the Americas. In the introduction, editor Martin Bruckner provides a critical assessment of the concept of cartography and of the historiography of maps. The individual essays, then, range widely over space and place, from the imperial reach of Iberian and British cartography to indigenous conceptualizations, including "dirty," ephemeral maps and star charts, to demonstrate that pre-nineteenth-century American cartography was at once a multiform and multicultural affair. This volume not only highlights the collaborative genesis of cartographic knowledge about the early Americas; the essays also bring to light original archives and innovative methodologies for investigating spatial relations among peoples in the western hemisphere. Taken together, the authors reveal the roles of early American cartographies in shaping popular notions of national space, informing visual perception, animating literary imagination, and structuring the political history of Anglo- and Ibero-America. The contributors are: Martin Bruckner, University of Delaware Michael J. Drexler, Bucknell University Matthew H. Edney, University of Southern Maine Jess Edwards, Manchester Metropolitan University Junia Ferreira Furtado, Universidade Federal de Minas Gerais, Brazil William Gustav Gartner, University of Wisconsin–Madison Gavin Hollis, Hunter College of the City University of New York Scott Lehman, independent scholar Ken MacMillan, University of Calgary Barbara E. Mundy, Fordham University Andrew Newman, Stony Brook University Ricardo Padron, University of Virginia Judith Ridner, Mississippi State University

A New York Times Bestseller “Maps allow the armchair traveler to roam the world, the diplomat to argue his points, the ruler to administer his country, the warrior to plan his campaigns and the propagandist to boost his cause… rich and beautiful.” – Wall Street Journal Throughout history, maps have been fundamental in shaping our view of the world, and our place in it. But far from being purely scientific objects, maps of the world are unavoidably ideological and subjective, intimately bound up with the systems of power and authority of particular times and places. Mapmakers do not simply represent the world, they construct it out of the ideas of their age. In this scintillating book, Jerry Brotton examines the significance of 12 maps - from the almost mystical representations of ancient history to the satellite-derived imagery of today. He vividly recreates the environments and circumstances in which each of the maps was made, showing how each conveys a highly individual view of the world. Brotton shows how each of his maps both influenced and reflected contemporary events and how, by considering it in all its nuances and omissions, we can better understand the world that produced it. Although the way we map our surroundings is more precise than ever before, Brotton argues that maps today are no more definitive or objective than they have ever been. Readers of this beautifully illustrated and masterfully argued book will never look at a map in quite the same way again. “A fascinating and panoramic new history of the cartographer’s art.” – The Guardian “The intellectual background to these images is conveyed with beguiling erudition…. There is nothing more subversive than a map.” – The Spectator “A mesmerizing and beautifully illustrated book.” —The Telegraph