初等数论及其应用

所属分类:数学  
出版时间:2010-9   出版时间:机械工业出版社   作者:罗森   页数:752  
Tag标签:数学,数论  

前言

My goal in writing this text has been to write an accessible and inviting introduction to number theory. Foremost, I wanted to create an effective tool for teaching and learning.I hoped to capture the richness and beauty of the subject and its unexpected usefulness.Number theory is both classical and modem, and, at the same time, both pure and applied. In this text, I have strived to capture these contrasting aspects of number theory. I have worked hard to integrate these aspects into one cohesive text. This book is ideal for an undergraduate number theory course at any level. No formal prerequisites beyond college algebra are needed for most of the material, other than some level of mathematical maturity. This book is also designed to be a source book for elementary number theory; it can serve as a useful supplement for computer science courses and as a primer for those interested in new developments in number theory and cryptography. Because it is comprehensive, it is designed to serve both as a textbook and as a lifetime reference for elementary number theory and its wide-ranging applications. This edition celebrates the silver anniversary of this book. Over the past 25 years,close to 100,000 students worldwide have studied number theory from previous editions.Each successive edition of this book has benefited from feedback and suggestions from many instructors, students, and reviewers. This new edition follows the same basic approach as all previous editions, but with many improvements and enhancements. I invite instructors unfamiliar with this book, or who have not looked at a recent edition, to carefully examine the sixth edition. I have confidence that you will appreciate the rich exercise sets, the fascinating biographical and historical notes, the up-to-date coverage, careful and rigorous proofs, the many helpful examples, the rich applications, the support for computational engines such as Maple and Mathematica, and the many resources available on the Web.

内容概要

本书特色:    经典理论与现代应用相结合。通过丰富的实例和练习,将数论的应用引入了更高的境界,同时更新并扩充了对密码学这一热点论题的讨论。    内容与时俱进。不仅融合了最新的研究成果和新的理论,而且还补充介绍了相关的人物传记和历史背景知识。    习题安排别出心裁。书中提供两类由易到难、富有挑战的习题:一类是计算题,另一类是上机编程练习。这使得读者能够将数学理论与编程技巧实践联系起来。此外,本书在上一版的基础上对习题进行了大量更新和修订。

作者简介

Kenneth H.Rosen,1972年获密歇根大学数学学士学位,1976年获麻省理工学院数学博士学位,1982年加入贝尔实验室,现为AT & T实验室特别成员,国际知名的计算机数学专家。Rosen博士对数论领域与数学建模领域颇有研究,并写过很多经典论文及专著。他的经典著作《离散数学及其应

书籍目录

PrefaceList
of
SymbolsWhat
Is
Number
Theory?1
The
Integers
1.1
Numbers
and
Sequences
1.2
Sums
and
Products
1.3
Mathematical
Induction
1.4
The
Fibonacci
Numbers
1.5
Divisibility2
Integer
Representations
and
Operations
2.1
Representations
of
Integers
2.2
Computer
Operations
with
Integers
2.3
Complexity
of
Integer
Operations3
Primes
and
Greatest
Common
Divisors
3.1
Prime
Numbers
3.2
The
Distribution
of
Primes
3.3
Greatest
Common
Divisors
and
their
Properties
3.4
The
Euclidean
Algorithm
3.5
The
Fundamental
Theorem
of
Arithmetic
3.6
Factorization
Methods
and
the
Fermat
Numbers
3.7
Linear
Diophantine
Equations4
Congruences
4.1
Introduction
to
Congruences
4.2
Linear
Congruences
4.3
The
Chinese
Remainder
Theorem
4.4
Solving
Polynomial
Congruences
4.5
Systems
of
Linear
Congruences
4.6
Factoring
Using
the
Pollard
Rho
Method5
Applications
of
Congruences
5.1
Divisibility
Tests
5.2
The
Perpetual
Calendar
5.3
Round-Robin
Tournaments
5.4
Hashing
Functions
5.5
Check
Dieits6
Some
Special
Congruences
6.1
Wilson's
Theorem
and
Fermat's
Little
Theorem
6.2
Pseudoprimes
6.3
Euler's
Theorem7
Multiplicative
Functions
7.1
The
Euler
Phi-Function
7.2
The
Sum
and
Number
of
Divisors
7.3
Perfect
Numbers
and
Mersenne
Primes
7.4
M6bius
Inversion
7.5
Partitions8
Cryptology
8.1
Character
Ciphers
8.2
Block
and
Stream
Ciphers
8.3
Exponentiation
Ciphers
8.4
Public
Key
Cryptography
8.5
Knapsack
Ciphers
8.6
Cryptographic
Protocols
and
Applications9
Primitive
Roots
9.1
The
Order
of
an
Integer
and
Primitive
Roots
9.2
Primitive
Roots
for
Primes
9.3
The
Existence
of
Primitive
Roots
9.4
Discrete
Logarithms
and
Index
Arithmetic
9.5
Primality
Tests
Using
Orders
of
Integers
and
Primitive
Roots
9.6
Universal
Exponents10
Applications
of
Primitive
Roots
and
the
Order
of
an
Integer
10.1
Pseudorandom
Numbers
10.2
The
E1Gamal
Cryptosystem
10.3
An
Application
to
the
Splicing
of
Telephone
Cables11
Quadratic
Residues
11.1
Quadratic
Residues
and
Nonresidues
11.2
The
Law
of
Quadratic
Reciprocity
11.3
The
Jacobi
Symbol
11.4
Euler
Pseudoprimes
11.5
Zero-Knowledge
Proofs12
Decimal
Fractions
and
Continued
Fractions
12.1
Decimal
Fractions
12.2
Finite
Continued
Fractions
12.3
Infinite
Continued
Fractions
12.4
Periodic
Continued
Fractions
12.5
Factoring
Using
Continued
Fractions13
Some
Nonlinear
Diophantine
Equations
13.1
Pythagorean
Triples
13.2
Fermat's
Last
Theorem
13.3
Sums
of
Squares
13.4
Pell's
Equation
13.5
Congruent
Numbers14
The
Gaussian
Integers
14.1
Gaussian
Integers
and
Gaussian
Primes
14.2
Greatest
Common
Divisors
and
Unique
Factorization
14.3
Gaussian
Integers
and
Sums
of
SquaresAppendix
A
Axioms
for
the
Set
of
IntegersAppendix
B
Binomial
CoefficientsAppendix
C
Using
Maple
and
Mathematica
for
Number
Theory
C.1
Using
Maple
for
Number
Theory
C.2
Using
Mathematica
for
Number
TheoryAppendix
D
Number
Theory
Web
LinksAppendix
E
Tables
Answers
to
Odd-Numbered
Exercises
Bibliography
Index
of
Biographies
Index
Photo
Credits

章节摘录

插图:Experimentation
and
exploration
play
a
key
role
in
the
study
of
number
theory.
Theresults
in
this
book
were
found
by
mathematicians
who
often
examined
large
amounts
ofnumerical
evidence,
looking
for
patterns
and
making
conjectures.
They
worked
diligentlyto
prove
their
conjectures;
some
of
these
were
proved
and
became
theorems,
others
wererejected
when
counterexamples
were
found,
and
still
others
remain
unresolved.
As
youstudy
number
theory,
I
recommend
that
you
examine
many
examples,
look
for
patterns,and
formulate
your
own
conjectures.
You
can
examine
small
examples
by
hand,
much
asthe
founders
of
number
theory
did,
but
unlike
these
pioneers,
you
can
also
take
advantageof
today's
vast
computing
power
and
computational
engines.
Working
through
examples,either
by
hand
or
with
the
aid
of
computers,
will
help
you
to
learn
the
subject——and
youmay
even
find
some
new
results
of
your
own!

图书封面

图书标签Tags

数学,数论


    初等数论及其应用下载



用户评论 (总计29条)

 
 

  •     数论其实在密码学或者另外一些工程上都能看到一些身影(比如众所周知的中国余数定理在好多地方都能见到)。书的内容也很全面。是数学爱好者必收的书,然后喜欢研究程序算法的大概也能从中吸取很多营养~
  •     Rosen的书,木话说,好书!我从第4版买到第6版
  •     内容详实,逻辑清晰,比国内的教材更充实易懂,适合数学爱好者
  •     今天刚收到这本书,无论是从纸张还是内容都让人感觉很舒服
  •     很多著作的水平因译者水平而异,还是看原版来得明了,收藏了。
  •     我的最爱 收藏了
  •     收到书和以前一样快,但是还没读
  •     感觉这本书比北大潘老师写的要温暖些,推理上更亲切些。当然潘老师的书早已作为初等数论的精典教材为大家所熟知。两本书结合来看,效果更好。
  •     书的内容不错,就是书的纸张不好。
  •     发货很快,很有感觉
  •     这是很比较经典的一部,好
  •     容易看懂,给远方的同学买的
  •     本来爱好数学和密码学,同类的数论书没有这样详细的
  •     封面有点花。,值得收藏
  •     里面写了一位伟人的经历,适合小学奥赛用吧
  •     建议计院的同学买来看看,虽然书很好
  •     王元老师肯定只确认了这本书数学方面没问题,应该可以
  •     收到书和以前一样快,挑不出毛病
  •     居然还有减震空气包~~~~~~~~~~,还没看
  •     否则看不懂!,内容很翔实
  •     值得一读,什么时候才有货呢?????之前看的是电子书
  •     初学者去看具有相当大的挑战!,入门的好书
  •     王元的《谈谈素数》叙述深入浅出,此书是很伟大的
  •     一看就是盗版,一直想看的一本书
  •     好好好!,这么好的书还会绝版
  •     话不多说,孩子奥数竞赛正需要
  •     不错的,让吾辈继承其事业吧!
  •     需要膜拜,毕竟是大家之作
  •     书很好,当然还是数论的内容
 

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