Libros de Matemáticas, página 22 de 470

Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.

This volume contains all the exercises and their solutions for Lang''s second edition of UNDERGRADUATE ANALYSIS. The wide variety of exercises, which range from computational to more conceptual and which are of varying difficulty, cover the following subjects and more: real numbers, limits, continuous functions, differentiation and elementary integration, normed vector spaces, compactness, series, integration in one variable, improper integrals, convolutions, Fourier series and the Fourier integral, functions in n-space, derivatives in vector spaces, inverse and implicit mapping theorem, ordinary differential equations, multiple integrals and differential forms. This volume also serves as an independent source of problems with detailed answers beneficial for anyone interested in learning analysis. Intermediary steps and original drawings provided by the author assists students in their mastery of problem solving techniques and increases their overall comprehension of the subject matter.

This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. A certain number of concepts are essential for all three of these areas, and are so basic and elementary, that it is worthwhile to collect them together so that more advanced expositions can be given without having to start from the very beginning. The concepts are concerned with the general basic theory of differential manifolds. As a result, this book can be viewed as a prerequisite to Fundamentals of Differential Geometry. Since this book is intended as a text to follow advanced calculus, manifolds are assumed finite dimensional. In the new edition of this book, the author has made numerous corrections to the text and he has added a chapter on applications of Stokes'' Theorem.

 ,This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer&ndash,Cartan form, and the Lie derivative are covered.Readers will find useful applications to special and general relativity, Yang&ndash,Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry._,

Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. The heart of this book is the language of generalized operads. This is as natural and transparent a language for higher category theory as the language of sheaves is for algebraic geometry, or vector spaces for linear algebra. It is introduced carefully, then used to give simple descriptions of a variety of higher categorical structures. In particular, one possible definition of n-category is discussed in detail, and some common aspects of other possible definitions are established. This is the first book on the subject and lays its foundations. It will appeal to both graduate students and established researchers who wish to become acquainted with this modern branch of mathematics.

Martin J OsborneAn exposition of modern game theory suitable for advanced undergraduates. The book emphasizes the ideas behind the theory rather than their mathematical expression, but defines all concepts precisely. It covers strategic, extensive and coalitional games and includes the topics of repeated games, bargaining theory and evolutionary equilibrium.

Este libro de Larson cumple 35 años de ser un clásico. Por lo que a lo largo de los años el objetivo de los autores ha sido siempre escribir con precisión y de manera legible conceptos fundamentales de calculo, claramente definidos y demostrados. Ofrece caracteristicas y materiales que desarrollen las habilidades de todos los tipos de estudiantes y en cuanto a los profesores, proporciona un instrumento de enseñanza amplio que emplea tecnicas pedagogicas probadas, y se da libertad para que usen en forma mas eficiente el tiempo en el salon de clase.

"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." Ed Witten, Recipient of the Fields Medal"I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. Its a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." Abigail Thompson, Distinguished Professor of Mathematics at University of California, DavisKnot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers.

Arfken (Miami U., Oxford, Ohio) and Weber (U. of Virginia) offer a textbook with more than enough material for a two-semester undergraduate or graduate course. They include proofs as well as examples of almost all the mathematical relations, though in some cases mathematicians would scoff at the level of rigor. Some of the theorems they incorporate are usually not cited under the most general assumptions, but are tailored to the more restricted applications required by physics. Earlier editions appeared between 1966 and 1995; the fifth is revised to account for changes not so much in the field as in the content of standard courses.