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

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

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

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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.

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

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

評分☆☆☆☆☆

很薄的書，包在塑料膜裏就成S形瞭。不好。

評分☆☆☆☆☆

好

評分☆☆☆☆☆

很薄，但是有塑封，沒有損壞。書印刷質量正常。

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☆☆☆☆☆

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☆☆☆☆☆

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☆☆☆☆☆

開捲有益處,不忘送書人

評分☆☆☆☆☆

算術演變

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。

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