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English
Description
Charles Fefferman is the Herbert E. Jones, Jr., '43 University Professor of Mathematics at Princeton University. C. Robin Graham is professor of mathematics at the University of Washington.
This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric,...
Author
Language
English
Description
The theoretical assumptions of the following mathematical topics are presented in this book:Cartesian planesegments, distances, and lines in the Cartesian planeparabolas, circumferences, ellipses, hyperbolas in the Cartesian planeproper and improper bundles in the Cartesian planeIn addition, the main applications of these topics are mentioned and some exercises are carried out.
Author
Language
Español
Description
En este libro se realizan ejercicios sobre los siguientes temas matemáticos:
Plano cartesiano y traslaciones.
línea en el plano cartesiano
cónicas en el plano cartesiano (parábola, circunferencia, elipse, hipérbola)
También se presentan sugerencias teóricas iniciales para hacer comprensible la realización de los ejercicios.
Author
Language
Français
Description
Dans ce livre, des exercices sont réalisés sur les sujets mathématiques suivants:
généralisation de la géométrie analytique dans le plan
géométrie analytique dans l'espace
longueur et régularité d'une courbe
caractérisation paramétrique au niveau géométrique
Des conseils théoriques initiaux sont également présentés pour faire comprendre l'exécution des exercices
Author
Language
Español
Description
En este libro se realizan ejercicios sobre los siguientes temas matemáticos: generalización de la geometría analítica en el planogeometría analítica en el espaciolongitud y regularidad de una curvacaracterización paramétrica a nivel geométricoTambién se presentan indicaciones teóricas iniciales para que se entienda la realización de los ejercicios.
Author
Language
Français
Description
Dans ce livre, des exercices sont réalisés sur les sujets mathématiques suivants:
Plan cartésien et translations
droite dans le plan cartésien
coniques dans le plan cartésien (parabole, circonférence, ellipse, hyperbole)
Des conseils théoriques initiaux sont également présentés pour rendre compréhensible l'exécution des exercices
Author
Language
Español
Description
En este libro se presentan los supuestos teóricos de los siguientes temas matemáticos:
Plano cartesiano
segmentos, distancias y rectas en el plano cartesiano
parábolas, circunferencias, elipses, hipérbolas en el plano cartesiano
haces propios e impropios en el plano cartesiano
Además, se mencionan las principales aplicaciones de estos temas y se realizan algunos ejercicios.
Author
Language
English
Description
In this book, exercises are carried out regarding the following mathematical topics:Cartesian plane and translationsline in the Cartesian planeconics in the Cartesian plane (parabola, circumference, ellipse, hyperbola)Initial theoretical hints are also presented to make the performance of the exercises understandable
Author
Series
Language
English
Description
The first seven chapters of this concise text provide an exposition of the basic topics of solid analytic geometry and comprise the material for a one-semester course on the subject for undergraduate mathematics majors. The remaining two chapters offer additional material for longer courses or supplementary study. Chapters 1 and 2 contain a treatment of the equations of lines and planes. Subsequent chapters offer an exposition of classical elementary...
Author
Language
English
Description
This single-volume compilation of two books explores the construction of geometric proofs. In addition to offering useful criteria for determining correctness, it presents examples of faulty proofs that illustrate common errors. High-school geometry is the sole prerequisite. Proof in Geometry, the first in this two-part compilation, discusses the construction of geometric proofs and presents criteria useful for determining whether a proof is logically...
Author
Language
English
Description
Based on a historic approach taken by instructors at MIT, this text is geared toward junior and senior undergraduate courses in analytic and projective geometry. Starting with concepts concerning points on a line and lines through a point, it proceeds to the geometry of plane and space, leading up to conics and quadrics developed within the context of metrical, affine, and projective transformations. The algebraic treatment is occasionally exchanged...
Author
Language
English
Description
Illustrated with interesting examples from everyday life, this text shows how to create ellipses, parabolas, and hyperbolas and presents fascinating historical background on their ancient origins. The text starts with a discussion of techniques for generating the conic curves, showing how to create accurate depictions of large or small conic curves and describing their reflective properties, from light in telescopes to sound in microphones and amplifiers....
Author
Language
English
Description
Specifically designed as an integrated survey of the development of analytic geometry, this classic study takes a unique approach to the history of ideas. The author, a distinguished historian of mathematics, presents a detailed view of not only the concepts themselves, but also the ways in which they extended the work of each generation, from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and...
Author
Language
English
Description
Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics. Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied...
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Series
Language
English
Description
This well-thought-out text, filled with many special features, is designed for a two-semester course in calculus for technology students with a background in college algebra and trigonometry. The author has taken special care to make the book appealing to students by providing motivating examples, facilitating an intuitive understanding of the underlying concepts involved, and by providing much opportunity to gain proficiency in techniques and skills....
Author
Language
English
Description
Ehud Hrushovski is professor of mathematics at the Hebrew University of Jerusalem. He is the coauthor of Finite Structures with Few Types (Princeton) and Stable Domination and Independence in Algebraically Closed Valued Fields. François Loeser is professor of mathematics at Pierre-and-Marie-Curie University in Paris.
Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter...
Author
Language
English
Description
Jean-Michel Bismut is professor of mathematics at the Université Paris-Sud, Orsay.
This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the...
Author
Language
English
Description
Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry. Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from...
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