Title
Elements Of Abstract Algebra (Dover Books On Mathematics),New
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This Concise, Readable, Collegelevel Text Treats Basic Abstract Algebra In Remarkable Depth And Detail. An Antidote To The Usual Surveys Of Structure, The Book Presents Group Theory, Galois Theory, And Classical Ideal Theory In A Framework Emphasizing Proof Of Important Theorems.Chapter I (Set Theory) Covers The Basics Of Sets. Chapter Ii (Group Theory) Is A Rigorous Introduction To Groups. It Contains All The Results Needed For Galois Theory As Well As The Sylow Theorems, The Jordanholder Theorem, And A Complete Treatment Of The Simplicity Of Alternating Groups. Chapter Iii (Field Theory) Reviews Linear Algebra And Introduces Fields As A Prelude To Galois Theory. In Addition There Is A Full Discussion Of The Constructibility Of Regular Polygons. Chapter Iv (Galois Theory) Gives A Thorough Treatment Of This Classical Topic, Including A Detailed Presentation Of The Solvability Of Equations In Radicals That Actually Includes Solutions Of Equations Of Degree 3 And 4 A Feature Omitted From All Texts Of The Last 40 Years. Chapter V (Ring Theory) Contains Basic Information About Rings And Unique Factorization To Set The Stage For Classical Ideal Theory. Chapter Vi (Classical Ideal Theory) Ends With An Elementary Proof Of The Fundamental Theorem Of Algebraic Number Theory For The Special Case Of Galois Extensions Of The Rational Field, A Result Which Brings Together All The Major Themes Of The Book.The Writing Is Clear And Careful Throughout, And Includes Many Historical Notes. Mathematical Proof Is Emphasized. The Text Comprises 198 Articles Ranging In Length From A Paragraph To A Page Or Two, Pitched At A Level That Encourages Careful Reading. Most Articles Are Accompanied By Exercises, Varying In Level From The Simple To The Difficult.
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- Q: How many pages is 'Elements of Abstract Algebra'? A: The book contains two hundred twenty-four pages. It covers essential topics in abstract algebra, making it a comprehensive resource.
- Q: What is the binding type of this book? A: The binding type is paperback. This makes it lightweight and flexible for easy handling.
- Q: Who is the author of 'Elements of Abstract Algebra'? A: The author is Allan Clark. He presents complex mathematical concepts in a clear and accessible manner.
- Q: What topics are covered in this book? A: The book covers group theory, Galois theory, and classical ideal theory. It emphasizes mathematical proofs and includes historical notes.
- Q: What is the reading level of this book? A: This book is suitable for college-level students. It is designed for those with a foundational understanding of mathematics.
- Q: How can I apply the concepts in 'Elements of Abstract Algebra'? A: You can apply the concepts through exercises provided in the chapters. These exercises range from simple to challenging.
- Q: Is this book suitable for beginners in abstract algebra? A: Yes, it is suitable for beginners who have a basic understanding of set theory and linear algebra. The book starts with fundamental concepts.
- Q: How does this book help with understanding Galois theory? A: It provides a thorough treatment of Galois theory, including solvability of equations in radicals. This comprehensive approach is rare in other texts.
- Q: Are there exercises included in the book? A: Yes, the book includes exercises with varying levels of difficulty. These exercises enhance understanding and encourage careful reading.
- Q: What should I do to keep this book in good condition? A: Store it in a cool, dry place away from direct sunlight. Handle it carefully to avoid bending or tearing the pages.
- Q: Can I return the book if I'm not satisfied? A: Yes, you can return the book within a specified period if it's in original condition. Check the return policy for details.
- Q: What if the book arrives damaged? A: You should contact customer service immediately to report the issue. They will guide you on how to return or replace the damaged book.
- Q: Is there a warranty for this book? A: Typically, books do not come with a warranty. However, you can check the seller's return policy for further assistance.
- Q: How does this book compare to other algebra texts? A: This book offers a more in-depth exploration of abstract algebra compared to typical survey texts, with a focus on proof and historical context.
- Q: Is 'Elements of Abstract Algebra' appropriate for self-study? A: Yes, it is appropriate for self-study due to its clear writing and structured content. The exercises also facilitate independent learning.