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48504801
Algebra: Chapter 0 (Graduate Studies in Mathematics, 104)
88% of respondents would recommend this to a friend
Item #:
48504801
SAR 432
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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.
-
Mathematics Instructors
Useful for instructors looking for comprehensive materials and exercises to support teaching abstract algebra and related subjects.
-
Self-learners
Great for self-learners who want to deepen their understanding of algebra with rigorous content and exercises.
-
Beginner Students
Not suitable for beginners who lack basic algebra understanding, as it assumes prior knowledge of advanced concepts.
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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.
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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
Product Price History
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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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