（已有8条评价）基本信息
- 原书名：An Introduction to the Theory of Numbers
- 原出版社： Oxford University Press
- 作者： (美)G.H.Hardy E.M Wright
- 丛书名： 图灵原版数学.统计学系列
- 出版社：人民邮电出版社
- ISBN：9787115156112
- 上架时间：2009-11-20
- 出版日期：2007 年3月
- 开本：16开
- 页码：435
- 版次：5-1
- 所属分类：数学 > 代数，数论及组合理论 > 数论及应用
教材 > 研究生/本科/专科教材 > 理学 > 数学
编辑推荐
本书是数论领域的一部传世名著，也是现代数学大师哈代的代表作之一。自出版以来一直备受学界推崇，被很多知名大学，如牛津大学、麻省理工学院 、加州大学伯克利分校等指定为教材或参考书，也是美国斯坦福大学每个数学与计算机科学专业学生必读的一本书。
内容简介
书籍
数学书籍
本书是一本经典的数论名著的第5版，书的内容成于作者在牛津大学、剑桥大学等大学讲课的讲义，从各个不同角度对数论进行了阐述，包括素数、无理数、同余、Fermat定理、同余式、连分数、不定式、二次域、算术函数、分划等等。第二作者为此书每章增加了必要的注解，便于读者理解并进一步学习。
本书读者对象为大学数学专业学生以及对数论感兴趣的专业人士。
本书是数论领域的一部传世名著，也是现代数学大师哈代的代表作之一。书中作者从多个角度对数论进行了深入阐述，内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分划等。新版由第二作者在每章末尾增写了评注，更便于读者阅读。虽然是为数学专业的人士所写，但是大学一年级学生也能读懂。
本书自出版以来一直备受学界推崇，被很多知名大学，如牛津大学、麻省理工学院 、加州大学伯克利分校等指定为教材或参考书，也是美国斯坦福大学每个数学与计算机科学专业学生必读的一本书。
数学书籍
本书是一本经典的数论名著的第5版，书的内容成于作者在牛津大学、剑桥大学等大学讲课的讲义，从各个不同角度对数论进行了阐述，包括素数、无理数、同余、Fermat定理、同余式、连分数、不定式、二次域、算术函数、分划等等。第二作者为此书每章增加了必要的注解，便于读者理解并进一步学习。
本书读者对象为大学数学专业学生以及对数论感兴趣的专业人士。
本书是数论领域的一部传世名著，也是现代数学大师哈代的代表作之一。书中作者从多个角度对数论进行了深入阐述，内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分划等。新版由第二作者在每章末尾增写了评注，更便于读者阅读。虽然是为数学专业的人士所写，但是大学一年级学生也能读懂。
本书自出版以来一直备受学界推崇，被很多知名大学，如牛津大学、麻省理工学院 、加州大学伯克利分校等指定为教材或参考书，也是美国斯坦福大学每个数学与计算机科学专业学生必读的一本书。
作译者
G．H．Hardy(1877－1947 ) 20世纪上半叶享有世界声誉的数学大师，是英国数学界和英国分析学派的领袖，对数论和分析学的发展有巨大的贡献和重大的影响。除了自己的研究工作之外，他还培养和指导了众多数学大家，包括印度数学奇才拉马努金和我国数学家华罗庚。
E．M．Wright (1906－2005 ) 英国著名数学家，毕业于牛津大学，是G．H．Hardy的学生。
生前担任英国名校阿伯丁大学校长多年。爱丁堡皇家学会会士、伦敦数学会会士。曾任Journal of Graph Theory 和Zentralblatt für Mathematik的名誉主编。
E．M．Wright (1906－2005 ) 英国著名数学家，毕业于牛津大学，是G．H．Hardy的学生。
生前担任英国名校阿伯丁大学校长多年。爱丁堡皇家学会会士、伦敦数学会会士。曾任Journal of Graph Theory 和Zentralblatt für Mathematik的名誉主编。
目录
I. THE SERIES OF PRIMES (1)
1.1. Divisibility of integers
1.2. Prime numbers
1.3. Statement of the fundamer/tal theorem of arithmetic
1.4. The sequence of primes
1.5. Some questions concerning primes
1.6. Some notations
1.7. The logarithmic function
1.8. Statement of the prime number theorem
II. THE SERIES OF PRIMES (2)
2.1. First proof of Euclid's second theorem
2.2. Further deductions from Euclid's argument
2.3. Primes in certain arithmetical progressions
2.4. Second proof of Euclid's theorem
2.5. Fermat's and Mersenne's numbers
2.6. Third proof of Euclid's theorem
2.7. Further remarks on formulae for primes
2.8. Unsolved problems concerning primes
2.9. Moduli of integers
2.10. Proof of the fundamental theorem of arithmetic
1.1. Divisibility of integers
1.2. Prime numbers
1.3. Statement of the fundamer/tal theorem of arithmetic
1.4. The sequence of primes
1.5. Some questions concerning primes
1.6. Some notations
1.7. The logarithmic function
1.8. Statement of the prime number theorem
II. THE SERIES OF PRIMES (2)
2.1. First proof of Euclid's second theorem
2.2. Further deductions from Euclid's argument
2.3. Primes in certain arithmetical progressions
2.4. Second proof of Euclid's theorem
2.5. Fermat's and Mersenne's numbers
2.6. Third proof of Euclid's theorem
2.7. Further remarks on formulae for primes
2.8. Unsolved problems concerning primes
2.9. Moduli of integers
2.10. Proof of the fundamental theorem of arithmetic
前言
PREFACE TO THE FIFTH EDITION
THE main changes in this edition are in the Notes at the end of eachchapter. I have sought to provide up-to-date references for the readerwho wishes to pursue a particular topic further and to present, bothin the Notes and in the text, a reasonab]y accurate account of the present state of knowledge. For this I have been dependent on the relevant sections of those invaluable publications, the Zentralblatt and the Mathematical Reviews. But I was also greatly helped by several correspondents who suggested amendments or answered queries. I am especially grateful to Professors J. W. S. Cassels and H. Halber-stam, each of whom supplied me at my request with a long and most valuable list of suggestions and references.
There is a new, more transparent proof of Theorem 445 and an account of my changed opinion about Theodorus' method in irrationals. To facilitate the use of this edition for reference purposes, I have, so far as possible, kept the page numbers unchanged. For this reason, I have added a short appendix on recent progress in some aspects of the theory of prime numbers, rather than insert the material in the appropriate places in the text.
E. M. W.
ABERDEEN
October 1978
PREFACE TO THE FIRST EDITION
THIS book has developed gradually from lectures delivered in a number of universities during the last ten years, and, like many books which have grown out of lectures, it has no very definite plan.
It is not in any sense (as an expert can see by reading the table of contents) a systematic treatise on the theory of numbers. It does not even contain a fully reasoned account of any one side of that many-sided theory, but is an introduction, or a series of introductions, to almost all of these sides in turn. We say something about each of a number of subjects which are not usually combined in a single volume, and about some which are not always regarded as forming part of the theory of numbers at all. Thus Chs. XII-XV belong to the 'algebraic' theory of numbers, Chs. XIX-XXI to the 'additive', and Ch. XXII to the 'analytic' theories; while Chs. III, XI, XXIII, and XXIV deal with matters usually classified under the headings of 'geometry of numbers' or 'Diophantine approximation'. There is plenty of variety in our programme, but very little depth; it is impossible, in 400 pages, to treat any of these many topics at all profoundly.
There are large gaps in the book which will be noticed at once by any expert. The most conspicuous is the omission of any account of the theory of quadratic forms. This theory has been developed more systematically than any other part of the theory of numbers, and there are good discussions of it in easily accessible books. We had to omit something, and this seemed to us the part of the theory where we had the least to add to existing accounts.
We have often allowed our personal interests to decide our programme, and have selected subjects less because of their importance (though most of them are important enough) than because we found them congenial and because other writers have left us something to say. Our first aim has been to write an interesting book, and one unlike other \ books. We may have succeeded at the price of too much eccentricity, or we may have failed; but we can hardly have failed completely, the subject-matter being so attractive that only extravagant incompetence could make it dull.
The book is written for mathematicians, but it does not demand any great mathematical knowledge or technique. In the first eighteen chapters we assume nothing that is not commonly taught in schools, and any intelligent university student should find them comparatively easy reading. The last six are more difficult, and in them we presuppose a little more, but nothing beyond the content of the simpler university courses.
The title is the same as that of a very well-known book by Professor L. E. Dickson (with which ours has little in common). We proposed at one time to change it to An introduction to arithmetic, a more novel and in some ways a more appropriate title; but it was pointed out that this might lead to misunderstandings about the content of the book.
A number of friends have helped us in the preparation of the book. Dr. H. Heilbronn has read all of it both in manuscript and in print, and his criticisms and suggestions have led to many very substantial improvements, the most important of which are acknowledged in the text. Dr. H. S. A. Potter and Dr. S. Wylie have read the proofs and helped us to remove many errors and obscurities. They have also checked most of the references to the literature in the notes at the ends of the chapters. Dr. H. Davenport and Dr. R. Rado have also read parts of the book, and in particular the last chapter, which, after their suggestions and Dr. Heilbronn's, bears very little resemblance to the original draft.
We have borrowed freely from the other books which are catalogued on pp. 417-19, and especially from those of Landau and Perron. To Landau in particular we, in common with all serious students of the theory of numbers, owe a debt which we could hardly overstate.
G. H. H.
OXFORDE.M.W.
August 1938
THE main changes in this edition are in the Notes at the end of eachchapter. I have sought to provide up-to-date references for the readerwho wishes to pursue a particular topic further and to present, bothin the Notes and in the text, a reasonab]y accurate account of the present state of knowledge. For this I have been dependent on the relevant sections of those invaluable publications, the Zentralblatt and the Mathematical Reviews. But I was also greatly helped by several correspondents who suggested amendments or answered queries. I am especially grateful to Professors J. W. S. Cassels and H. Halber-stam, each of whom supplied me at my request with a long and most valuable list of suggestions and references.
There is a new, more transparent proof of Theorem 445 and an account of my changed opinion about Theodorus' method in irrationals. To facilitate the use of this edition for reference purposes, I have, so far as possible, kept the page numbers unchanged. For this reason, I have added a short appendix on recent progress in some aspects of the theory of prime numbers, rather than insert the material in the appropriate places in the text.
E. M. W.
ABERDEEN
October 1978
PREFACE TO THE FIRST EDITION
THIS book has developed gradually from lectures delivered in a number of universities during the last ten years, and, like many books which have grown out of lectures, it has no very definite plan.
It is not in any sense (as an expert can see by reading the table of contents) a systematic treatise on the theory of numbers. It does not even contain a fully reasoned account of any one side of that many-sided theory, but is an introduction, or a series of introductions, to almost all of these sides in turn. We say something about each of a number of subjects which are not usually combined in a single volume, and about some which are not always regarded as forming part of the theory of numbers at all. Thus Chs. XII-XV belong to the 'algebraic' theory of numbers, Chs. XIX-XXI to the 'additive', and Ch. XXII to the 'analytic' theories; while Chs. III, XI, XXIII, and XXIV deal with matters usually classified under the headings of 'geometry of numbers' or 'Diophantine approximation'. There is plenty of variety in our programme, but very little depth; it is impossible, in 400 pages, to treat any of these many topics at all profoundly.
There are large gaps in the book which will be noticed at once by any expert. The most conspicuous is the omission of any account of the theory of quadratic forms. This theory has been developed more systematically than any other part of the theory of numbers, and there are good discussions of it in easily accessible books. We had to omit something, and this seemed to us the part of the theory where we had the least to add to existing accounts.
We have often allowed our personal interests to decide our programme, and have selected subjects less because of their importance (though most of them are important enough) than because we found them congenial and because other writers have left us something to say. Our first aim has been to write an interesting book, and one unlike other \ books. We may have succeeded at the price of too much eccentricity, or we may have failed; but we can hardly have failed completely, the subject-matter being so attractive that only extravagant incompetence could make it dull.
The book is written for mathematicians, but it does not demand any great mathematical knowledge or technique. In the first eighteen chapters we assume nothing that is not commonly taught in schools, and any intelligent university student should find them comparatively easy reading. The last six are more difficult, and in them we presuppose a little more, but nothing beyond the content of the simpler university courses.
The title is the same as that of a very well-known book by Professor L. E. Dickson (with which ours has little in common). We proposed at one time to change it to An introduction to arithmetic, a more novel and in some ways a more appropriate title; but it was pointed out that this might lead to misunderstandings about the content of the book.
A number of friends have helped us in the preparation of the book. Dr. H. Heilbronn has read all of it both in manuscript and in print, and his criticisms and suggestions have led to many very substantial improvements, the most important of which are acknowledged in the text. Dr. H. S. A. Potter and Dr. S. Wylie have read the proofs and helped us to remove many errors and obscurities. They have also checked most of the references to the literature in the notes at the ends of the chapters. Dr. H. Davenport and Dr. R. Rado have also read parts of the book, and in particular the last chapter, which, after their suggestions and Dr. Heilbronn's, bears very little resemblance to the original draft.
We have borrowed freely from the other books which are catalogued on pp. 417-19, and especially from those of Landau and Perron. To Landau in particular we, in common with all serious students of the theory of numbers, owe a debt which we could hardly overstate.
G. H. H.
OXFORDE.M.W.
August 1938
