Elementary Number Theory & Its Applications, 7/e (Paperback)
暫譯: 初等數論及其應用，第七版（平裝本）

Kenneth H. Rosen

Elementary Number Theory & Its Applications, 7/e (Paperback)

商品描述

本書序言

Up-to-date,  engaging coverage of essential topics
●Expanded coverage of cryptography including Elliptic curve photography; coverage of knapsack ciphers has been removed. Also, the important notion of homomorphic encryption is introduced in this edition.
●Coverage of recent numerical discoveries, including four new Mersenne primes; the largest known twin primes; the evidence supporting many important conjectures, and more.
●Coverage of new theoretical discoveries,  such as the proof of weak Goldbach conjecture  and the result that there is an algorithm to multiply two  n-bit integers using  O (nlog2 n) bit operations.
A proven approach
●Enhanced exercise sets have been examined and improved  sets even  further, plus several hundred new exercises, from routine to challenging. New computational and exploratory exercises  are included.
●Connections with abstract algebra: The  book does not assume prior knowledge of abstract algebra, but  introduces some basic algebraic structures such as groups, rings, and fields.
●Available resources for the 7th Edition are posted on the Pearson media servers here.

本書特色

●Now available as a Pearson eText. This new interactive version of the book  provides many interactive applets that can be used by students for some common computations in number theory and to help understand concepts and explore conjectures.
●A collection of cryptographic applets is provided along with algorithms for computations in number theory,  These include applets for  encryption, decryption, cryptanalysis, and cryptographic protocols,  addressing  both classical ciphers and the RSA cryptosystem. Cryptographic applets can be used for individual, group, and classroom activities.

商品描述(中文翻譯)

本書序言

最新且引人入勝的基本主題涵蓋

● 擴展了密碼學的內容，包括橢圓曲線密碼學；已移除背包密碼的相關內容。此外，本版引入了同態加密（homomorphic encryption）的重要概念。

● 涵蓋最近的數值發現，包括四個新的梅森質數（Mersenne primes）；已知的最大雙質數（twin primes）；支持許多重要猜想的證據等。

● 涵蓋新的理論發現，例如弱哥德巴赫猜想（weak Goldbach conjecture）的證明，以及存在一種算法可以使用 O(n log₂ n) 位元操作來乘以兩個 n 位元整數的結果。

經過驗證的方法

● 增強的練習題集經過檢查和進一步改進，並新增數百道練習題，從常規到具挑戰性。還包括新的計算和探索性練習題。

● 與抽象代數的聯繫：本書不假設讀者具備抽象代數的先前知識，但介紹了一些基本的代數結構，如群（groups）、環（rings）和域（fields）。

● 第七版的可用資源已在 Pearson 媒體伺服器上發布，詳情請見這裡。

本書特色

● 現在可作為 Pearson eText 使用。這個新互動版本的書籍提供了許多互動小程式，學生可以用來進行數論中的一些常見計算，幫助理解概念並探索猜想。

● 提供了一系列密碼學小程式，連同數論計算的算法，這些包括加密、解密、密碼分析和密碼協議的小程式，涵蓋了古典密碼和 RSA 密碼系統。密碼學小程式可用於個人、小組和課堂活動。

作者簡介

Kenneth H. Rosen received his BS in mathematics from the University of Michigan - Ann Arbor (1972) and his PhD in mathematics from MIT (1976). Before joining Bell Laboratories in 1982, he held positions at the University of Colorado - Boulder, The Ohio State University - Columbus, and the University of Maine - Orono, where he was an associate professor of mathematics. While working at AT&T Laboratories, he taught at Monmouth University, teaching courses in discrete mathematics, coding theory, and data security.

作者簡介(中文翻譯)

Kenneth H. Rosen於1972年獲得密西根大學安娜堡分校的數學學士學位，並於1976年獲得麻省理工學院的數學博士學位。在1982年加入貝爾實驗室之前，他曾在科羅拉多大學博爾德分校、俄亥俄州立大學哥倫布分校和緬因大學奧羅諾分校擔任數學副教授。在AT&T實驗室工作期間，他在蒙茅斯大學教授離散數學、編碼理論和數據安全等課程。

目錄大綱

1.The Integers
2.Integer Representations and Operations
3.Greatest Common Divisors
4.Prime Numbers
5.Congruences
6.Applications of Congruences
7.Some Special Congruences
8.Arithmetic Functions
9.Cryptography
10.Primitive Roots
11.Applications of Primitive Roots and the Order of an Integer
12.Quadratic Residues
13.Decimal Fractions and Continued Fractions
14.Nonlinear Diophantine Equations and Elliptic Curves
15.The Gaussian Integers

目錄大綱(中文翻譯)

1.The Integers

2.Integer Representations and Operations

3.Greatest Common Divisors

4.Prime Numbers

5.Congruences

6.Applications of Congruences

7.Some Special Congruences

8.Arithmetic Functions

9.Cryptography

10.Primitive Roots

11.Applications of Primitive Roots and the Order of an Integer

12.Quadratic Residues

13.Decimal Fractions and Continued Fractions

14.Nonlinear Diophantine Equations and Elliptic Curves

15.The Gaussian Integers

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