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☆☆☆☆☆

很棒

評分☆☆☆☆☆

算術是數學的一個分支，其內容包括自然數和在各種運算下産生的性質，運算法則以及在實際中的應用。可是，在數學發展的曆史中算術的含義要廣泛得多。

評分☆☆☆☆☆

前兩個是加法和乘法的交換律，它說明人們可以交換加法或乘法中元素的次序。第三個是加法的結閤律，它錶明三個數相加時，或者我們把第一個加上第二個與第三個的和；或者我們把第三個加上第一個與第二個的和，其結果都相同。第四個是乘法的結閤律。最後一個是分配律，它錶明用一個整數去乘一個和時，我們可以用這整數去乘這和的每一項，然後把這些乘積加起來。

評分☆☆☆☆☆

給娃娃囤書中 好好學習 天天嚮上

評分☆☆☆☆☆

好難啊看不懂

評分☆☆☆☆☆

評分☆☆☆☆☆

短小精悍，名傢經典。

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☆☆☆☆☆

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。