The School Journal

The School Journal PDF Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 464

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The School Journal

The School Journal PDF Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 464

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Book Description


Introduction to Cardinal Arithmetic

Introduction to Cardinal Arithmetic PDF Author: Michael Holz
Publisher: Springer Science & Business Media
ISBN: 3034603274
Category : Mathematics
Languages : en
Pages : 309

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Book Description
This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the fundamental investigations in pcf-theory which has been developed by S. Shelah to answer the questions left open in the seventies. All theorems presented in Chapter 3 and Chapters 5 to 9 are due to Shelah, unless otherwise stated. We are greatly indebted to all those set theorists whose work we have tried to expound. Concerning the literature we owe very much to S. Shelah's book [Sh5] and to the article by M. R. Burke and M. Magidor [BM] which also initiated our students' interest for Shelah's pcf-theory.

The Publishers Weekly

The Publishers Weekly PDF Author:
Publisher:
ISBN:
Category : American literature
Languages : en
Pages : 1550

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A Classical Introduction to Modern Number Theory

A Classical Introduction to Modern Number Theory PDF Author: K. Ireland
Publisher: Springer Science & Business Media
ISBN: 1475717792
Category : Mathematics
Languages : en
Pages : 355

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Book Description
This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.

The Business Educator

The Business Educator PDF Author:
Publisher:
ISBN:
Category : Business education
Languages : en
Pages : 654

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A Course of Modern Analysis

A Course of Modern Analysis PDF Author: E. T. Whittaker
Publisher: Cambridge University Press
ISBN: 9780521588072
Category : Mathematics
Languages : en
Pages : 620

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Book Description
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.

Algebra

Algebra PDF Author: Michael Artin
Publisher: Pearson
ISBN: 9781292027661
Category : Algebra
Languages : en
Pages : 486

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Book Description
Algebra, Second Edition, by Michael Artin, is ideal for the honors undergraduate or introductory graduate course. The second edition of this classic text incorporates twenty years of feedback and the author's own teaching experience. The text discusses concrete topics of algebra in greater detail than most texts, preparing students for the more abstract concepts; linear algebra is tightly integrated throughout.

Publishers' Weekly

Publishers' Weekly PDF Author:
Publisher:
ISBN:
Category : American literature
Languages : en
Pages : 1762

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El-Hi Textbooks in Print, 1982

El-Hi Textbooks in Print, 1982 PDF Author: R. R. Bowker LLC
Publisher: R. R. Bowker
ISBN: 9780835214360
Category : Education
Languages : en
Pages : 848

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A Course in Arithmetic

A Course in Arithmetic PDF Author: J-P. Serre
Publisher: Springer Science & Business Media
ISBN: 1468498843
Category : Mathematics
Languages : en
Pages : 126

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Book Description
This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors.