Algebra, 2/e (Paperback)
暫譯: 代數，第二版（平裝本）

Michael Artin

Algebra, 2/e (Paperback)

相關主題

商品描述

本書序言

●Exercises have been added throughout the book.
●Extensive rewriting incorporates 20 years' worth of user feedback and the author's own teaching experience.。Permutations are introduced early, and computation with them is clarified. Correspondence Theorem discussion (Chapter 2) has been revised. Linear Transformations coverage has been split into two (now Chapters 4 and 5). Jordan Form is presented earlier, with Fillipov's proof (now in Chapter 4).
。The proof of the orthogonality relations for characters has been improved (Chapter 10). The discussion of the representations of SU2 is improved (Chapter 10).
。The discussion of function fields has been improved (Chapter 15). The chapter on Factorization has been split into two (now Chapters 12 and 13), with quadratic number fields appearing in the latter chapter.
●New topics have been introduced throughout the text, including a short section on using continuity to deduce facts about linear operators (Chapter 5); proof that the alternating groups are simple (Chapter 7); a section on spheres (Chapter 9); a section on product rings (Chapter 11); a short discussion of computer methods to factor polynomials (Chapter 12); Cauchy's theorem bounding the roots of a polynomial (Chapter 12); a proof of the splitting theorem based on symmetric functions (Chapter 16).

本書特色

●High emphasis on concrete topics such as symmetry, linear groups, quadratic number fields, and lattices prepares students to learn more abstract concepts. This focus also allows some abstractions to be treated more concisely.
●The chapter organization emphasizes the connections between algebra and geometry at the start, with the beginning chapters containing the content most important for students in other fields. To counter the fact that arithmetic receives less initial emphasis, the later chapters have a strong arithmetic slant.
●Treatment beyond the basics sets this book apart. Students with a reasonably mature mathematical background will benefit from the relatively informal treatments the author gives to the more advanced topics.
●Content notes in the preface include teaching tips from the author's own classroom experience.
●Challenging exercises are indicated with an asterisk, allowing instructors to easily create the right assignments for their class.

商品描述(中文翻譯)

本書序言

●本書中新增了練習題。

●廣泛的重寫整合了20年的使用者反饋和作者自身的教學經驗。排列組合的概念被早期引入，並對其計算進行了澄清。對應定理的討論（第2章）已經修訂。線性變換的內容被拆分為兩章（現在是第4章和第5章）。Jordan 形式的介紹提前，並包含 Fillipov 的證明（現在在第4章）。

。角色的正交性關係的證明已改進（第10章）。對 SU2 表示的討論已改進（第10章）。

。對函數域的討論已改進（第15章）。因式分解的章節被拆分為兩章（現在是第12章和第13章），其中二次數域出現在後一章。

●文本中引入了新主題，包括使用連續性推導線性算子的事實的簡短部分（第5章）；交替群是簡單的證明（第7章）；球體的部分（第9章）；乘積環的部分（第11章）；因式分解多項式的計算機方法的簡短討論（第12章）；Cauchy 定理界定多項式根的範圍（第12章）；基於對稱函數的分裂定理的證明（第16章）。

本書特色

●高度強調具體主題，如對稱性、線性群、二次數域和格，為學生學習更抽象的概念做好準備。這種重點也使某些抽象概念能夠更簡潔地處理。

●章節組織強調代數與幾何之間的聯繫，前幾章包含對其他領域學生最重要的內容。為了彌補算術初期受到的較少重視，後面的章節則強調算術。

●超越基礎的處理使本書與眾不同。具有相對成熟數學背景的學生將從作者對更高級主題的相對非正式處理中受益。

●前言中的內容註解包括作者自身教室經驗的教學提示。

●具有挑戰性的練習題用星號標示，方便教師為其班級輕鬆創建合適的作業。

作者簡介

Michael Artin received his A.B. from Princeton University in 1955 and his M.A. and Ph.D. from Harvard University in 1956 and 1960, respectively. He continued at Harvard as Benjamin Peirce Lecturer, 1960 - 63. He joined the MIT mathematics faculty in 1963, and was appointed Norbert Wiener Professor from 1988 - 93. Outside MIT, Artin served as President of the American Mathematical Society from 1990-92. He has received honorary doctorate degrees from the University of Antwerp and University of Hamburg.

Professor Artin is an algebraic geometer, concentrating on non-commutative algebra. He has received many awards throughout his distinguished career, including the Undergraduate Teaching Prize and the Educational and Graduate Advising Award. He received the Leroy P. Steele Prize for Lifetime Achievement from the AMS. In 2005 he was honored with the Harvard Graduate School of Arts & Sciences Centennial Medal, for being "an architect of the modern approach to algebraic geometry." Professor Artin is a Member of the National Academy of Sciences, Fellow of the American Academy of Arts & Sciences, Fellow of the American Association for the Advancement of Science, and Fellow of the Society of Industrial and Applied Mathematics. He is a Foreign Member of the Royal Holland Society of Sciences, and Honorary Member of the Moscow Mathematical Society.

作者簡介(中文翻譯)

邁克爾·阿丁 (Michael Artin) 於1955年獲得普林斯頓大學的學士學位，並於1956年和1960年分別獲得哈佛大學的碩士和博士學位。他在哈佛大學擔任本傑明·皮爾斯講師 (Benjamin Peirce Lecturer) 直至1963年。1963年，他加入麻省理工學院 (MIT) 數學系，並於1988年至1993年擔任諾伯特·維納教授 (Norbert Wiener Professor)。在麻省理工學院之外，阿丁於1990年至1992年擔任美國數學學會 (American Mathematical Society) 會長。他曾獲得安特衛普大學和漢堡大學的榮譽博士學位。

阿丁教授是一位代數幾何學家，專注於非交換代數 (non-commutative algebra)。在他卓越的職業生涯中，他獲得了許多獎項，包括本科教學獎 (Undergraduate Teaching Prize) 和教育及研究生指導獎 (Educational and Graduate Advising Award)。他還獲得了美國數學學會 (AMS) 的萊羅伊·P·斯蒂爾終身成就獎 (Leroy P. Steele Prize for Lifetime Achievement)。2005年，他因為「成為現代代數幾何方法的架構師」而獲得哈佛大學文理學院百年紀念獎章 (Harvard Graduate School of Arts & Sciences Centennial Medal)。阿丁教授是美國國家科學院 (National Academy of Sciences) 成員、美國藝術與科學學院 (American Academy of Arts & Sciences) 會士、美國科學促進會 (American Association for the Advancement of Science) 會士，以及工業與應用數學學會 (Society of Industrial and Applied Mathematics) 會士。他是荷蘭皇家科學學會 (Royal Holland Society of Sciences) 的外籍成員，以及莫斯科數學學會 (Moscow Mathematical Society) 的榮譽成員。

目錄大綱

1. Matrices
2. Groups
3. Vector Spaces
4. Linear Operators
5. Applications of Linear Operators
6. Symmetry
7. More Group Theory
8. Bilinear Forms
9. Linear Groups
10. Group Representations
11. Rings
12. Factoring
13. Quadratic Number Fields
14. Linear Algebra in a Ring
15. Fields
16. Galois Theory
Appendix A. Background Material
A.1 About Proofs
A.2 The Integers
A.3 Zorn's Lemma
A.4 The Implicit Function Theorem
A.5 Exercises

目錄大綱(中文翻譯)

1. Matrices

2. Groups

3. Vector Spaces

4. Linear Operators

5. Applications of Linear Operators

6. Symmetry

7. More Group Theory

8. Bilinear Forms

9. Linear Groups

10. Group Representations

11. Rings

12. Factoring

13. Quadratic Number Fields

14. Linear Algebra in a Ring

15. Fields

16. Galois Theory

Appendix A. Background Material

A.1 About Proofs

A.2 The Integers

A.3 Zorn's Lemma

A.4 The Implicit Function Theorem

A.5 Exercises

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