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

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☆☆☆☆☆

[法] 賽瑞 著

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

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.

評分☆☆☆☆☆

很薄的書，包在塑料膜裏就成S形瞭。不好。

評分☆☆☆☆☆

拉丁文的“算術”這個詞是由希臘文的“數和數(音屬，shû三音)數的技術”變化而來的。“算”字在中國的古意也是“數”的意思，錶示計算用的竹籌。中國古代的復雜數字計算都要用算籌。所以“算術”包含當時的全部數學知識與計算技能，流傳下來的最古老的《九章算術》以及失傳的許商《算術》和杜忠《算術》，就是討論各種實際的數學問題的求解方法。

評分☆☆☆☆☆

很好，就是喜歡原版的東西。

評分☆☆☆☆☆

　　讀者對象：數學專業的高年級本科生、研究生和相關專業的學者本書主要講述具有一般係數體係拓撲空間的上同調理論。層論包括對代數拓撲很重要的領域。書中有好多創新點，引進不少新概念，全書內容貫穿一緻。證實瞭廣義同調空間中層理論上同調滿足同調基本特性的事實。將相對上同調引入層理論中。

評分☆☆☆☆☆

有些難度的一本書，值得數學係數論代數專業的學生讀一下。

評分☆☆☆☆☆

算術的基礎在於：整數的加法和乘法服從某些規律。為瞭要敘述這些具有 普遍性的規律，我們不能用像1，2，3這種錶示特定數的符號。兩個整數，不管它們的次序如何，它們的和相同。而

評分☆☆☆☆☆

好

評分☆☆☆☆☆

自然數或正整數的數學理論就是眾所周知的算術.至於幾何、 代數等許多數學分支學科的名稱，都是後來很晚的時候纔有的。

評分☆☆☆☆☆

很不錯，很喜歡，物流給力