Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a difficult problem with many applications outside of mathematics. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure often coming from geometry. This book focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such equations are common in applications. There are three main themes: upper bounds on the number of real solutions, lower bounds on the number of real solutions, and geometric problems that can have all solutions be real. The book begins with an overview, giving background on real solutions to univariate polynomials and the geometry of sparse polynomial systems. The first half of the book concludes with fewnomial upper bounds and with lower bounds to sparse polynomial systems. The second half of the book begins by sampling some geometric problems for which all solutions can be real, before devoting the last five chapters to the Shapiro Conjecture, in which the relevant polynomial systems have only real solutions.
An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.
Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a difficult problem with many applications outside of mathematics. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure often coming from geometry. This book focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such equations are common in applications. There are three main themes: upper bounds on the number of real solutions, lower bounds on the number of real solutions, and geometric problems that can have all solutions be real. The book begins with an overview, giving background on real solutions to univariate polynomials and the geometry of sparse polynomial systems. The first half of the book concludes with fewnomial upper bounds and with lower bounds to sparse polynomial systems. The second half of the book begins by sampling some geometric problems for which all solutions can be real, before devoting the last five chapters to the Shapiro Conjecture, in which the relevant polynomial systems have only real solutions.
In this behind-the-scenes look at one of the world's top Wall Street investment firms, Partnoy recounts his experience during the annual drunken skeet-shooting competition where he and his colleagues sharpen the killer instincts they're encouraged to use against competitors, clients, and each other.
The 5-Minute Clinical Consult provides rapid-access information on the diagnosis, treatment, medications, follow-up, and associated conditions of more than 700 medical conditions. Organized alphabetically by diagnosis, this best-selling clinical reference continues to present brief, bulleted points on disease topics in a consistent templated format.
The Treviso Arithmetic, or Arte dell'Abbaco, is an anonymous textbook in commercial arithmetic written in vernacular Venetian and published in Treviso, Italy in 1478. The Treviso Arithmetic is the earliest known printed mathematics book in the West, and one of the first printed European textbooks dealing with a science. The Treviso Arithmetic is a practical book intended for self study and for use in Venetian trade. It is written in vernacular Venetian and communicated knowledge to a large population. It helped to end the monopoly on mathematical knowledge and gave important information to the middle class. It was not written for a large audience, but was intended to teach mathematics of everyday currency. The Treviso became one of the first mathematics books written for the expansion of human knowledge. It provided an opportunity for the common person, rather than only a privileged few, to learn the art of computation. The Treviso Arithmetic provided an early example of the Hindu-Arabic numeral system computational algorithms."--Wikipedia.
A Businessweek Bestseller "You fail to read F.I.A.S.C.O. at your peril." —Los Angeles Times F.I.A.S.C.O. is the best-selling account of Frank Partnoy's education in the jungle of high finance from 1993 to 1995. It follows the young Morgan Stanley salesman as he learns to navigate a marketplace where billions of dollars are made and lost in the creation and trading of derivatives, a type of security that almost nobody fully understands. Seen in relief against the financial meltdown of 2008, F.I.A.S.C.O. appears ever more prescient, and in a new epilogue written for this edition, Partnoy connects his story to the central role derivatives played in that crisis.
The 5-Minute Clinical Conult 2014 Standard Edition provides rapid-access in a quick-reference format. It delivers diagnosis, treatment, medications, follow-up, and associated factors for a broad range of diseases and conditions. Organized alphabetically by diagnosis, this best-selling clinical reference continues to present brief, bulleted information on disease topics in a consistent and reader-friendly three-column format.
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