Author : Lawrence M Graves
Publisher : Courier Corporation
Page : 361 pages
File Size : 29,88 MB
Release : 2012-01-27
Category : Mathematics
ISBN : 0486158136
This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.
Author : Bowen Kerins
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 11,66 MB
Release : 2015-10-15
Category : Education
ISBN : 147042195X
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Famous Functions in Number Theory is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. Famous Functions in Number Theory introduces readers to the use of formal algebra in number theory. Through numerical experiments, participants learn how to use polynomial algebra as a bookkeeping mechanism that allows them to count divisors, build multiplicative functions, and compile multiplicative functions in a certain way that produces new ones. One capstone of the investigations is a beautiful result attributed to Fermat that determines the number of ways a positive integer can be written as a sum of two perfect squares. Famous Functions in Number Theory is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Author : Henri Cartan
Publisher : Courier Corporation
Page : 242 pages
File Size : 25,54 MB
Release : 2013-04-22
Category : Mathematics
ISBN : 0486318672
Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
Author : Konrad Knopp
Publisher :
Page : 142 pages
File Size : 35,21 MB
Release : 1948
Category : Functions
ISBN :
Author : Vasiliy Sergeyevich Vladimirov
Publisher : Courier Corporation
Page : 370 pages
File Size : 38,22 MB
Release : 2007-01-01
Category : Mathematics
ISBN : 0486458121
This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.
Author : Reinhold Remmert
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 20,62 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461209390
A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure.
Author : Konrad Knopp
Publisher : Courier Corporation
Page : 340 pages
File Size : 33,35 MB
Release : 2013-07-24
Category : Mathematics
ISBN : 0486318702
Handy one-volume edition. Part I considers general foundations of theory of functions; Part II stresses special and characteristic functions. Proofs given in detail. Introduction. Bibliographies.
Author : Gennadiĭ Mikhaĭlovich Goluzin
Publisher : American Mathematical Soc.
Page : 690 pages
File Size : 14,80 MB
Release : 1969
Category : Functions of complex variables
ISBN : 9780821886557
Author : A. I. Markushevich
Publisher : American Mathematical Soc.
Page : 1178 pages
File Size : 31,96 MB
Release : 2013
Category : Analytic functions
ISBN : 082183780X
Author : Matthew Katz
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 46,33 MB
Release : 2018-10-03
Category : Mathematics
ISBN : 1470442906
This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey's theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, “There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.”
