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This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become...
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One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers...
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Español
Description
Este libro cuenta con cinco capítulos que contienen los temas del programa de la electiva Geometría Euclidiana. Ha sido elaborado para que los estudiantes de tecnología e ingeniería puedan seguirlo, razón por la cual se han tenido en cuenta los contenidos de dicha asignatura Con este trabajo se muestra a los estudiantes que no tienen una formación en matemática pura que es posible formalizar las matemáticas mediante la presentación de definiciones,...
Author
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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
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
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English
Description
Jacques Gasqui is Professor of Mathematics at Institut Fourier, Université de Grenoble I. Hubert Goldschmidt is Visiting Professor of Mathematics at Columbia University and Professeur des Universités in France.
This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. Its primary focus...
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English
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In recent decades twistor theory has become an important focus for students of mathematical physics. Central to twistor theory is the geometrical transform known as the Penrose transform, named for its groundbreaking developer. Geared toward students of physics and mathematics, this advanced text explores the Penrose transform and presupposes no background in twistor theory and a minimal familiarity with representation theory. An introductory chapter...
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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,...
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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...
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English
Description
Theorems stating the existence of an object-such as the solution to a problem or equation-are known as existence theorems. This text examines fundamental and general existence theorems, along with the Picard iterants, and applies them to properties of solutions and linear differential equations. The authors assume a basic knowledge of real function theory, and for certain specialized results, of elementary functions of a complex variable. They do...
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English
Description
This well-written and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. The hands-on approach features many exercises to be completed by readers. Prerequisites are only a basic familiarity with linear algebra and a willingness to explore the subject in a hands-on manner. The opening chapter offers activities that explore the world of knots and links - including games with...
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English
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Hailed by The New York Times Book Review as "nothing less than a major contribution to the scientific culture of this world," this major survey features the work of 18 outstanding mathematicians. Primary subjects include analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, and theories of probability and functions. Other topics include linear and non-Euclidean...
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English
Description
Designed for advanced undergraduate or beginning graduate study, this text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; and development of the method of integral formulas for global differential geometry.
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Description
Induction in Geometry discusses the application of the method of mathematical induction to the solution of geometric problems, some of which are quite intricate. The book contains 37 examples with detailed solutions and 40 for which only brief hints are provided. Most of the material requires only a background in high school algebra and plane geometry; chapter six assumes some knowledge of solid geometry, and the text occasionally employs formulas...
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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...
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English
Description
Useful for independent study and as a reference work, this introduction to differential geometry features many examples and exercises. It defines geometric structure by specifying the parallel transport in an appropriate fiber bundle, focusing on the simplest cases of linear parallel transport in a vector bundle. The treatment opens with an introductory chapter on fiber bundles that proceeds to examinations of connection theory for vector bundles...
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Description
Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, geometry on a surface, envelopes, conformal mapping, minimal surfaces, more. Well-illustrated, with abundant problems and solutions. Bibliography.
Author
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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.
99) Lie Algebras
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English
Description
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses. Chapter I introduces basic concepts that are necessary for an understanding...
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English
Description
This classic monograph by a mathematician affiliated with Trinity College, Cambridge, offers a brief account of the invariant theory connected with a single quadratic differential form. Suitable for advanced undergraduates and graduate students of mathematics, it avoids unnecessary analysis and offers an accessible view of the field for readers unfamiliar with the subject. A historical overview is followed by considerations of the methods of Christoffel...
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