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48504801
Algebra: Chapter 0 (Graduate Studies in Mathematics, 104)
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Item #:
48504801
TWD 3976
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Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, with an early introduction of categories as a unifying theme, an emphasis on homological algebra, and approximately 1,000 exercises.
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What Stands Out
Comprehensive Content
Covers essential algebra concepts thoroughly, providing a strong foundation for graduate studies in mathematics, making it ideal for advanced learners seeking depth and breadth in the subject.
Rigorous Approach
Adopts a formal, rigorous methodology that enhances critical thinking and problem-solving skills, appealing to students who aspire to excel in higher mathematics and theoretical applications.
Supplemental Resources
Includes exercises and solutions that facilitate active learning, empowering students to practice and master algebra concepts while preparing them for future mathematical challenges.
Product Details
- Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
| Publisher | American Mathematical Society |
| Publication date | August 29, 2009 |
| Language | English |
| Print length | 713 pages |
| ISBN-10 | 147046571X |
| ISBN-13 | 978-1470465711 |
| Dimensions | 7 x 1.5 x 10 inches (17.8 x 3.8 x 25.4 cm) |
| Part of series | Graduate Studies in Mathematics |
| Package Weight | 3.2000 Pound |
Who Should Buy?
-
Graduate Students
Ideal for graduate students pursuing advanced mathematics needing solid foundational algebra concepts to understand higher-level topics.
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Mathematics Instructors
Useful for instructors looking for comprehensive materials and exercises to support teaching abstract algebra and related subjects.
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Self-learners
Great for self-learners who want to deepen their understanding of algebra with rigorous content and exercises.
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Beginner Students
Not suitable for beginners who lack basic algebra understanding, as it assumes prior knowledge of advanced concepts.
Product Description
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Customer Questions & Answers
-
Question:
What topics are covered in Algebra: Chapter 0?
Answer: Algebra: Chapter 0 delves into a variety of essential topics in algebra, including group theory, ring theory, and field theory. The text is designed to lay the foundation for further studies in mathematics, providing readers with the necessary tools and concepts to explore advanced mathematical theories. This book is ideal for graduate students who wish to strengthen their understanding of abstract algebra concepts and theorems, making it a vital resource for academic and research purposes. -
Question:
Is Algebra: Chapter 0 suitable for beginners in mathematics?
Answer: Algebra: Chapter 0 is primarily tailored for graduate students and may not be suitable for beginners. It assumes a certain level of mathematical maturity, focusing on abstract concepts that require prior knowledge of basic algebra. Those just starting their mathematical journey might want to consider introductory texts before tackling this challenging material. However, for committed learners eager to dive into higher mathematics, this book offers a comprehensive and rigorous exploration of advanced algebraic concepts. -
Question:
Who are the authors of Algebra: Chapter 0?
Answer: Algebra: Chapter 0 is authored by esteemed mathematicians and scholars, David A. J. G. and Igor Shafarevich. Their expertise in the field of mathematics brings a wealth of knowledge to the text, making complex ideas accessible. Their collaboration results in a well-structured course that guides readers from fundamental algebraic principles toward more challenging mathematical theories, making it an authoritative guide for serious mathematics students. -
Question:
What level of math knowledge is recommended before reading this book?
Answer: Before diving into Algebra: Chapter 0, it is recommended that readers have a solid grasp of undergraduate-level mathematics. Familiarity with concepts like basic set theory, linear algebra, and introductory abstract algebra can significantly enhance comprehension. This background ensures that readers can engage with the text's advanced discussions more effectively, making it a valuable resource for those looking to deepen their mathematical understanding. -
Question:
Can this book be used for self-study?
Answer: Yes, Algebra: Chapter 0 can indeed be used for self-study, especially by dedicated mathematics students. The chapters are structured to facilitate self-paced learning, with exercises and examples strategically placed to reinforce key concepts. It’s an excellent resource for individuals looking to deepen their understanding of abstract algebra independently, encouraging critical thinking and problem-solving skills. -
Question:
What is the focus of the exercises in Algebra: Chapter 0?
Answer: The exercises in Algebra: Chapter 0 are meticulously designed to reinforce the theoretical concepts presented in the text. They encourage readers to apply what they've learned through challenging problems that range from straightforward applications to more complex proofs and theories. This focus on practical application helps solidify knowledge and ensures a deeper understanding of abstract algebra, paving the way for advanced research or academic pursuits. -
Question:
How does Algebra: Chapter 0 compare to other graduate-level algebra books?
Answer: Algebra: Chapter 0 stands out among graduate-level algebra texts due to its unique approach to presenting advanced topics in a structured manner. Unlike other textbooks that may overly complicate the subject, this book provides clarity and coherence, making challenging concepts more approachable. It serves as both a comprehensive guide and a reference, making it a go-to resource for students and educators aiming to navigate the complexities of algebra. -
Question:
Are there supplementary resources to accompany Algebra: Chapter 0?
Answer: While Algebra: Chapter 0 is a robust standalone resource, readers might find supplementary materials beneficial. Many universities offer additional lectures, problem sets, or study groups that can help. Online platforms may also host forums and videos that enhance the understanding of advanced algebraic concepts found within the text, providing a well-rounded approach to mastering the material. -
Question:
Where can I find reviews for Algebra: Chapter 0?
Answer: Reviews for Algebra: Chapter 0 can often be found on academic book review sites, educational forums, and online retailer platforms. These reviews provide insights into the book's strengths and challenges, helping prospective readers gauge whether it's the right fit for their studies. Engaging with community feedback can guide learners in utilizing the book effectively, supporting their academic success in advanced algebra. -
Question:
Where can I buy Algebra: Chapter 0 in Taiwan?
Answer: You can purchase Algebra: Chapter 0 through Ubuy in Taiwan. Ubuy offers a comprehensive platform for acquiring academic resources, ensuring that you can find this textbook conveniently. Their user-friendly interface allows for easy navigation and access to various educational materials, making it an ideal choice for students and educators alike.
Algebraic Geometry Editorial Review
Algebra: Chapter 0 Graduate Studies in Mathematics, 104 is a well-written algebra book that focuses heavily on category theory as a framework for learning the subject. It provides a conceptual understanding of the topic which is useful in the long run, with some suggesting it is better to learn algebra this way than attempting to force your knowledge into categories later in your studies. However, some people find the explanations confusing, and the ordering of some materials can be counterintuitive. Additionally, some of the definitions are Considered weird. It is recommended to keep another textbook as a reference, and some of the problems are Considered too easy. Nevertheless, the book's proofs are excellent, and the explanations are often jovial, making it fun to read. There is also a strong focus on category theory throughout the topics, with connections to concepts such as field theory, making the book a fantastic introduction for beginners.
Customer Reviews & Ratings
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Pros
- Excellent proofs
- Conversational tone and writing style
- Strong focus on category theory
- Fun to read
- Great for beginners
Cons
- Some explanations can be confusing
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Features & Benefits
- Self-contained introduction to main topics of algebra
- Early introduction of categories as a unifying theme
- Emphasis on homological algebra
- Approximately 1,000 exercises
- Adaptable to specific choice of topics
- Includes substantial hints and navigation aids
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