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Condition
This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability and complexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming.
Homesickness
The collapse of China’s Qing dynasty coincided roughly with discoveries that helped revolutionize views of infectious disease. Together, these parallel developments generated a set of paradigm shifts in the understanding of society, the individual, as well as the cultural matrix that mediates between them. In Homesickness, Carlos Rojas examines an array of Chinese literary and cinematic tropes of illness, arguing that these works approach sickness not solely as a symptom of dysfunction but more importantly as a key to its potential solution. Rojas focuses on a condition he calls “homesickness”—referring to a discomfort caused not by a longing for home but by an excessive proximity to...
Combined Membership List
Lists for 19 include the Mathematical Association of America, and 1955- also the Society for Industrial and Applied Mathematics.
Fractal Geometry, Complex Dimensions and Zeta Functions
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.
The Notebooks of Joseph Joubert
The elusive French luminary Joseph Joubert is a great explorer of the mind's open spaces. Edited and translated by Paul Auster, this selection from Joubert's notebooks introduces a master of the enigmatic who seeks "to call everything by its true name" while asking us to "remember everything is double." "Joubert speaks in whispers," Auster writes. "One must draw very close to hear what he is saying."
Topics in Algebraic Geometry and Geometric Modeling
Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture. The NSF sponsored the four-day ''Vilnius Workshop on Algebraic Geometry and Geometric Modeling'', which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, ''On the determination of the degree of an equations obtained by elimination'', which foreshadows the modern application of mixed volumes in algebraic geometry. The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.
Tropical Algebraic Geometry
These notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.
