Libros de Matemáticas, página 33 de 470

El presente libro recoge una amplia colección de problemas relacionados con tres disciplinar muy importantes de las matemáticas: la teoría de variable compleja, las ecuaciones diferenciales ordinarias y la estadisticas.La experiencia docente nos ha enseñado que, en muchas ocasiones, los alumnos tiene problemas para conectar los conceptos aprendidos dentro de unidades tematicas aparentemente independientes entre si. Los problemas aqui recogidos engloban varios aspectos de la materia estudiada y hay que verlos dentro del contexto de la asignatura completa. El amplio espectro de temas tratados y los diferentes grados de dificultad de los ejercicios hacen de esta recopilacion una herramienta muy util para afianzar los conceptos teoricos expuestos en otros libros de esta misma coleccion. En ultimo termino, la utilidad de un problema resuelto depende de como el alumno se enfrenta a el. Lo importante no es conocer la solucion del mismo, sino realizar el esfuerzo de intentar varios caminos para alcanzar la solucion y comprender cual es el correcto y por que.

El presente libro corresponde a la materia enseñada en la asignatura con título "Ampliación de Variable Compleja" correspondiente al 2º ciclo del Grado de Matemáticas Fundamentales de la UNED. Pretende ser un segundo curso en la teoria de funciones de variable compleja y, por tanto, una continuacion del libro del mismo autor con titulo Teoria de Variable Compleja en esta misma coleccion.

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense.By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.

This book is a clear exposition, with exercises, of the basic ideas of algebraic topology: homology (singular, simplicial, and cellular), homotopy groups, and cohomology rings. It is suitable for a two-semester course at the beginning graduate level, requiring as a prerequisite a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced, making this book of great value to the student.

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.