算術教程(英文版) [A Course in Arithmetic]

算術教程(英文版) [A Course in Arithmetic] pdf epub mobi txt 電子書 下載 2025

[法] 賽瑞 著
想要找書就要到 靜思書屋
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!
齣版社: 世界圖書齣版公司
ISBN:9787510005350
版次:1
商品編碼:10184600
包裝:平裝
外文名稱:A Course in Arithmetic
開本:24開
齣版時間:2009-08-01
用紙:膠版紙
頁數:115
正文語種:英語

具體描述

內容簡介

The first one is purely algebraic. Its objective is the classification ofquadratic forms over the field of rational numbers (Hasse-Minkowskitheorem). It is achieved in Chapter IV. The first three chapters contain somepreliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols.Chapter V applies the preceding results to integral quadratic forms indiscriminant + 1. 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 arithmeticprogressions" due to Dirichlet; this theorem is used at a critical point in thefirst part (Chapter 111, no. 2.2). Chapter VII deals with modular forms,and in particular, with theta functions. Some of the quadratic forms ofChapter V reappear here.

內頁插圖

目錄

Preface
Part I-Algebraic Methods
ChapterI Finite fields
1-Generalities
2-Equations over a finite field
3-Quadratic reciprocity law
Appendix-Another proof of the quadratic reciprocity law
Chapter II p-adic fields
1-The ring Zp and the field
2-p-adic equations
3-The multiplicative group of
Chapter II nHilbert symbol
1-Local properties
2-Global properties
Chapter IV Quadratic forms over Qp and over Q
1-Quadratic forms
2-Quadratic forms over Q
3-Quadratic forms over Q
Appendix Sums of three squares
Chapter V Integral quadratic forms with discriminant
1-Preliminaries
2-Statement of results
3-Proofs
Part II-Analytic Methods
Chapter VI-The theorem on arithmetic progressions
1-Characters of finite abelian groups
2-Dirichlet series
3-Zeta function and L functions
4-Density and Dirichlet theorem
Chapter Vll-Modular forms
1-The modular group
2-Modular functions
3-The space of modular forms
4-Expansions at infinity
5-Hecke operators
6-Theta functions
Bibliography
Index of Definitions
Index of Notations

前言/序言

  This book is divided into two parts.
  The first one is purely algebraic. Its objective is the classification ofquadratic forms over the field of rational numbers (Hasse-Minkowskitheorem). It is achieved in Chapter IV. The first three chapters contain somepreliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols.Chapter V applies the preceding results to integral quadratic forms indiscriminant + 1. 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 arithmeticprogressions" due to Dirichlet; this theorem is used at a critical point in thefirst part (Chapter 111, no. 2.2). Chapter VII deals with modular forms,and in particular, with theta functions. Some of the quadratic forms ofChapter V reappear here.
  The two parts correspond to lectures given in 1962 and 1964 to secondyear students at the Ecole Normale Superieure. A redaction of these lecturesin the form of duplicated notes, was made by J.-J. Saosuc (Chapters l-IV)and J.-P. Ramis and G. Ruget (Chapters VI-VIi). They were very useful tome; I extend here my gratitude to their authors.

用戶評價

評分

評分

  讀者有一定的基本同調代數和代數拓撲知識就可以理解本書。每章末都附有練習,這些可以幫助學生更好的理解書中的知識體係。附錄給齣瞭部分習題的解答。第二版中在內容上做瞭較大的改動,增加瞭80多例子和大量更深層次的內容,如,Cech上同調、Oliver變換、插值理論、廣義流形、局部齊性空間、同調縴維和p進變換群。目次:層和準層;層上同調;與其他上同調定理的比較;譜序列的應用;Borel-Moore同調;上層和ech同調。

評分

不夠詳細,不夠完善,不夠變化。

評分

這一命題僅僅是這一般規律的一個特殊例子。因此當我們希望錶示整數之間的某個關係——不論涉及的一些特定的整數值如何——是正確的,我們可以用字母a,b,c,…作為錶示整數的符號。於是,我們所熟知的五個算術規律可敘述為:

評分

好難啊看不懂

評分

  讀者有一定的基本同調代數和代數拓撲知識就可以理解本書。每章末都附有練習,這些可以幫助學生更好的理解書中的知識體係。附錄給齣瞭部分習題的解答。第二版中在內容上做瞭較大的改動,增加瞭80多例子和大量更深層次的內容,如,Cech上同調、Oliver變換、插值理論、廣義流形、局部齊性空間、同調縴維和p進變換群。目次:層和準層;層上同調;與其他上同調定理的比較;譜序列的應用;Borel-Moore同調;上層和ech同調。

評分

國外係統地整理前人數學知識的書,要算是希臘的歐幾裏得的《幾何原本》最早。《幾何原本》全書共十五捲,後兩捲是後人增補的。全書大部分是屬於幾何知識,在第七、八、九捲中專門討論瞭數的性質和運算,屬於算術的內容。

評分

書很薄但內容多少都講到瞭,很不錯

評分

果斷推薦,好書,定一個

相關圖書

本站所有内容均为互联网搜索引擎提供的公开搜索信息,本站不存储任何数据与内容,任何内容与数据均与本站无关,如有需要请联系相关搜索引擎包括但不限于百度google,bing,sogou

© 2025 book.tinynews.org All Rights Reserved. 静思书屋 版权所有