Discourses on algebra代数论说
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作者： Igor R. Shafarevich著
出 版 社： 湖南文艺出版社
出版时间： 2002-11-1字数：版次： 1页数： 276印刷时间： 2002/11/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783540422532包装： 平装内容简介
The classic geometry of Euclid has attracted many for its beauty, elegance, and logical cohesion. In this book, the leading Russian algebraist I.R. Shafarevich argues with examples that algebra is no less beautiful, elegant, and logically cohesive than geometry.
It contains an exposition of some rudiments of algebra, number theory, set theory and probability presupposing very limited knowledge of mathematics. I.R. Shafarevich is known to be one of the leading mathematicians of the 20th century, as well as one of the best mathematical writers.
目录
Preface
1.Integers (Topic: Numbers)
1.Is Not Rational
2.The Irrationality of Other Square Roots
3.Decomposition into Prime Factors
2.Simplest Properties of Polynomials (Topic: Polynomials)
4.Roots and the Divisibility of Polynomials
5.Multiple Roots and the Derivative
6.Binomial Formula
Supplement: Polynomials and Bernoulli Numbers
3.Finite Sets (Topic: Sets)
7.Sets and Subsets
8.Combinatorics
9.Set Algebra
10.The Language of Probability
Supplement: The Chebyshev Inequality
4.Prime Numbers (Topic: Numbers)
11.The Number of Prime Numbers is Infinite
12.Euler's Proof That the Number of Prime Numbers is Infinite
13.Distribution of Prime Numbers
Supplement: The Chebyshev Inequality for π(n)
5.Real Numbers and Polynomials (Topic: Numbers and Polynomials)
14.Axioms of the Real Numbers
15.Limits and Infinite Sums
16.Representation of Real Numbers as Decimal Fractions
17.Real Roots of Polynomials
Supplement: Sturm's Theorem
6.Infinite Sats(Topic: Sats)
18.Equipotence
19.Continuum
20.Thin Sets
Supplement: Normal Numbers
7.Power Series(Topic:Polynomials)
21.Polynomials as Generating Functions
22.Power Series
23.Partitio Numerorum
Supplement 1:THe Euler Pentagon Theorem
Supplement 1:Generating Function for
Bernoulli Numbers
Dates of Lives of Mathematicians Mentioned in the Text
Index