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Integers and theory of numbers 整数与数论

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Integers and theory of numbers 整数与数论

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定 价：￥316.40

作 者：Abraham A. Fraenkel　著 著

出 版 社：Oversea Publishing House

出版时间：2004-6-1

I S B N：9780486495880

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    内容简介
    A concise work on important topics in number theory, this classic text was devised by a prominent twentieth-century mathematician. Developed from a series of presentations to adult education courses, it explains the essentials of mathe-matics in a manner accessible to high school and college students as well as to other readers.
    The mathematical work of author Abraham A. Fraenkel spans many decades and numerous areas. A well-known expert on combinatorial games, he also made advances in number theory, combinatorics, and computer science. In this text, he offers clear-cut explanations of natural numbers as cardinals, with discussions of positional notation and the ordering of numbers according to magnitude; natural numbers as ordinals, including Peano's axioms and the relation of ordinals to car-dinals;the theory of numbers, encompassing prime numbers and their distribu-tion, partitions of the circle, Fermat's simple and last theorems, perfect numbers,amicable numbers, and algebraic and ideal numbers; and rational numbers, with considerations of positive fractions, negative integers, and the field of rationals.

    作者简介

    目录
    CHAPTER I.NATURAL NUMBERS AS CARDINALS
    1.The Positional Notation, 1
    2.The Concept of Cardinal Number, 4
    3.The Ordering of Numbers According to Magnitude,9
    CHAPTER II.NATURAL NUMBERS AS ORDINALS
    1.Peano's Axioms, 12
    2.The Independence of the Axioms for Ordinals, 14
    3.Mathematical Induction.Addition and Multiplica- tion, 17
    4.The Relation of Ordinals to Cardinals, 21
    CHAPTER III.THEORY OF NUMBERS
    1.Prime Numbers and Their Distribution, 26
    2.Partition of the Circle, 38
    3.Fermat's Simple and Last Theorems.The Concept of Congruence, 41
    4.Perfect Numbers and Amicable Numbers, 47
    5.Algebraic and Ideal Numbers, 52
    CHAPTER IV.RATIONAL NUMBERS
    1.Positive Fractions, 59
    2.Negative Integers, 68
    3.The Field of Rationals, 72
    APPENDIX
    INDEX OF TERMS
    INDEX OF PROPER NAMES

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