A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems.Originally published in 1957.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Product Description: Designed for intermediate graduate studies, this text will broaden students' core knowledge of differential geometry providing foundational material to relevant topics in classical differential geometry. The method of moving frames, a natural means for discovering and proving important results, provides the basis of treatment for topics discussed...read more

Product Description: Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools...read more

Product Description: In questo libro sono presentati i presupposti teorici dei seguenti argomenti matematici: piano cartesiano segmenti, distanze e rette nel piano cartesiano parabole, circonferenze, ellissi, iperboli nel piano cartesiano fasci propri e impropri nel piano cartesiano Inoltre sono citate le principali applicazioni di tali argomenti e sono svolti alcuni esercizi...read more

Product Description: This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when  combinatorics was the focus...read more

Product Description: This textbook treats two important and related matters in convex geometry: the quantification of symmetry of a convex set―measures of symmetry―and the degree to which convex sets that nearly minimize such measures of symmetry are themselves nearly symmetric―the phenomenon of stability...read more

Product Description: From the Preface. The theory of the Ikosahedron has during the last few years obtained a place of such importance for nearly all departments of modern analysis, that it seemed expedient to publish a systematic exposition of the same...read more

Product Description: From the PREFACE. This book relates, not to the general theory of curves, but to the definite problem of ascertaining the form of a curve given by its equation in Cartesian coordinates, in such cases as are likely to arise in the actual applications of Analytical Geometry...read more

Product Description: From the AUTHOR'S PREFACE. This little book is an attempt to present simply and concisely the elementary principles of the "Extensive Analysis" as fully developed in the comprehensive treatises of Hermann Grassmann, restricting the treatment however to the geometry of two and three dimensional space...read more

Product Description: Euclid’s masterpiece textbook, The Elements, was written twenty-three hundred years ago. It is primarily about geometry and contains dozens of figures. Five of these are constructed using a line that “is cut in extreme and mean ratio...read more

Product Description: Arithmetic, Geometry, and Algebra are uniquely intertwined with architectural design in a worship space as found in Christ Church of Philadelphia. Many of this historic church members fathered the Nation’s history of independence...read more

Product Description: This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well...read more

Product Description: ​Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplay between these subjects...read more

Product Description: THE word theory in the title is to be understood in a very non-technical sense. Indeed, apart from the idea of the invariant elements of an elliptic involution on a straight line, no theory is found at all. The purpose of the book is rather to furnish a certain graphical representation of imaginaries under a number of conventions more or less well known...read more

Product Description: What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics...read more