Title
Groups and Symmetry (Undergraduate Texts in Mathematics),New
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Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or a new idea. Throughout the book, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the seventeen wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the NielsenSchreier theorem, using group actions on trees. There are more than three hundred exercises and approximately sixty illustrations to help develop the student's intuition.
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- Q: How many pages does this book have? A: This book has one hundred ninety-eight pages. It's a comprehensive text focused on elementary group theory.
- Q: What is the binding type of this book? A: The binding type of this book is hardcover. This makes it durable for frequent use by students.
- Q: What are the dimensions of the book? A: The dimensions are six point five inches in length, zero point seventy-five inches in width, and nine point seventy-six inches in height.
- Q: Who is the author of this book? A: The author of this book is Mark A. Armstrong. He provides an informal approach to complex mathematical topics.
- Q: What is the genre of this book? A: The genre is educational mathematics. It is specifically designed for undergraduate students studying group theory.
- Q: Is this book suitable for beginners in mathematics? A: Yes, this book is suitable for beginners. It offers a gentle introduction to group theory with accessible explanations.
- Q: How is the material organized in the book? A: The material is organized into short sections. Each section covers a significant result or new idea in group theory.
- Q: Are there exercises in this book? A: Yes, there are more than three hundred exercises. These exercises help reinforce understanding of the concepts presented.
- Q: Does this book include illustrations? A: Yes, the book includes approximately sixty illustrations. These help to visualize mathematical concepts, particularly geometrical ones.
- Q: What key concepts are covered in this book? A: This book covers key concepts like Lagrange's theorem and the Sylow theorems. It emphasizes both theoretical results and concrete examples.
- Q: Is this book appropriate for self-study? A: Yes, this book is appropriate for self-study. Its informal style and numerous exercises make it conducive for independent learning.
- Q: What kind of examples are used in this book? A: The book uses many geometrical examples. This approach helps students relate abstract concepts to visual representations.
- Q: Can this book be used in a classroom setting? A: Yes, this book can be used in a classroom setting. It is structured to facilitate both teaching and learning in mathematics.
- Q: What unique feature does this book offer? A: A unique feature is the proof of the Nielsen-Schreier theorem. It presents this proof using group actions on trees.
- Q: What is the target audience for this book? A: The target audience is undergraduate mathematics students. The book is tailored to those beginning their study of group theory.