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156025298
Springer Undergraduate Mathematics A History of Abstract Algebra: From Algebraic Equations to Modern Algebra, (Paperback)
Item #:
156025298
AUD 99
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Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra while appealing to researchers with a general interest in the topic.
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What Stands Out
Comprehensive Coverage
Offers an extensive overview of abstract algebra, including key concepts and historical developments, making it an invaluable resource for undergraduate students pursuing mathematics.
Engaging Style
Written in an accessible manner, this book captures the interest of readers by combining rigorous mathematics with fascinating historical anecdotes about algebra's evolution and influence.
Student-Friendly
Designed specifically for undergraduates, it includes numerous examples and exercises that enhance understanding, ensuring students grasp complex topics with ease and confidence.
Product Details
- This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss's theory of numbers and Galois's ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat's Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois's approach to the solution of equations. The book also describes the relationshipbetween Kummer's ideal numbers and Dedekind's ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer's. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
| Manual & guide type | Instruction Manual |
| Book format | Paperback |
| Edition | 2018 Edition |
| Skill level | Beginner |
| Pages | 415 |
| Language | English |
| Brand | Jeremy Gray |
| Pub date | 2018-11-04 |
| Author | Jeremy Gray |
| Subgenre | History & Philosophy |
| Genre | Textbooks |
| Bisac subject heading | Mathematics |
| Series title | Springer Undergraduate Mathematics |
| Dimensions | 6.14 x 0.89 x 9.21 in (15.6 x 2.3 x 23.4 cm) |
| Educational level | College |
| Age group | Adult |
| Retail packaging | Single Piece |
| Original languages | English |
| Awards won | Leon Whiteman Prize of the American Mathematical Society, Neugebauer Prize of the European Mathematical Society |
Who Should Buy?
-
Mathematics Students
Ideal for undergraduate students pursuing mathematics who wish to deepen their understanding of algebra's historical context.
-
Historians of Science
Beneficial for historians exploring the development of abstract algebra and its impact on mathematics and related fields.
-
Educators
Valuable resource for educators seeking to teach abstract algebra with historical insights to enrich student engagement.
-
Casual Readers
Not suitable for those with a casual interest in mathematics who prefer light reading without technical depth.
Product Description
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Customer Questions & Answers
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Question:
Is this book suitable for beginners in abstract algebra?
Answer: Yes, it is aimed at undergraduate students with an introductory background in algebra. -
Question:
Does the book contain exercises for practice?
Answer: Yes, there are exercises at the end of each chapter for practical understanding. -
Question:
Can researchers benefit from this book?
Answer: Absolutely, it also appeals to researchers with a general interest in the history of algebra.
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Features & Benefits
- Accessible history of abstract algebra for undergraduate students.
- Covers significant contributions from historical figures like Gauss and Galois.
- Explains complex topics such as Galois theory and group theory.
- Includes exercises for practical understanding and self-study.
- Self-contained with helpful appendices for supplementary material.
- Appeals to both students and researchers interested in algebra's history.
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