Whereas many partial solutions and sketches for the odd-numbered exercises appear in the book, the Student Solutions Manual, written by the author, has comprehensive solutions for all odd-numbered exercises and large number of even-numbered exercises. This Manual also offers many alternative solutions to those appearing in the text. These will provide the student with a better understanding of the material.
This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra, Tenth Edition and is designed to supplement that text.
Table of Contents
Integers and Equivalence Relations
0. Preliminaries
Groups
1. Introduction to Groups
2. Groups
3. Finite Groups; Subgroups
4. Cyclic Groups
5. Permutation Groups
6. Isomorphisms
7. Cosets and Lagrange’s Theorem
8. External Direct Products
9. Normal Subgroups and Factor Groups
10. Group Homomorphisms
11. Fundamental Theorem of Finite Abelian Groups
Rings
12. Introduction to Rings
13. Integral Domains
14. Ideals and Factor Rings
15. Ring Homomorphisms
16. Polynomial Rings
17. Factorization of Polynomials
18. Divisibility in Integral Domains Fields
Fields
19. Extension Fields
20. Algebraic Extensions
21. Finite Fields
22. Geometric Constructions
Special Topics
23. Sylow Theorems
24. Finite Simple Groups
25. Generators and Relations
26. Symmetry Groups
27. Symmetry and Counting
28. Cayley Digraphs of Groups
29. Introduction to Algebraic Coding Theory
30. An Introduction to Galois Theory
31. Cyclotomic Extensions
Abstract Algebra, 3rd Edition by David S. Dummit, Richard M. Foote
This revision of Dummit and Foote’s widely acclaimed introduction to abstract algebra helps students experience the power and beauty that develops from the rich interplay between different areas of mathematics.
The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the student’s understanding. With this approach, students gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.
The text is designed for a full-year introduction to abstract algebra at the advanced undergraduate or graduate level, but contains substantially more material than would normally be covered in one year. Portions of the book may also be used for various one-semester topics courses in advanced algebra, each of which would provide a solid background for a follow-up course delving more deeply into one of many possible areas: algebraic number theory, algebraic topology, algebraic geometry, representation theory, Lie groups, etc.
Abstract Algebra: An Integrated Approach (Pure and Applied Undergraduate Texts, 55)
This abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups, rings, vector spaces, and fields, emphasising examples, definitions, homomorphisms, and proofs. The goal is to explain how all of the constructions fit into an axiomatic framework and to emphasise the importance of studying those maps that preserve the underlying algebraic structure. This fast-paced introduction is followed by chapters in which each of the four main topics is revisited and deeper results are proven. The second half of the book contains material of a more advanced nature. It includes a thorough development of Galois theory, a chapter on modules, and short surveys of additional algebraic topics designed to whet the reader’s appetite for further study. This book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course.
Basic Modern Algebra with Applications 2014th Edition, by Mahima Ranjan Adhikari (Author), Avishek Adhikari (Author) || Full PDF Download
The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text.
In addition, it studies semigroup, group action, Hopf’s group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.
Contemporary Abstract Algebra-10th Ed-Chapman and Hall_CRC (2021) by Joseph A. Gallian
Contemporary Abstract Algebra, Tenth Edition
For more than three decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.
The author presents the concepts and methodologies of contemporary abstract algebra as used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop but rarely do. Applications are included to illustrate the utility of the abstract concepts.
Examples and exercises are the heart of the book. Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The exercises often foreshadow definitions, concepts, and theorems to come.
Changes for the tenth edition include new exercises, new examples, new quotes, and a freshening of the discussion portions. The hallmark features of previous editions of the book are enhanced in this edition. These include:
- A good mixture of approximately 1900 computational and theoretical exercises, including computer exercises, that synthesize concepts from multiple chapters
- Approximately 300 worked-out examples from routine computations to the challenging
- Many applications from scientific and computing fields and everyday life
- Historical notes and biographies that spotlight people and events
- Motivational and humorous quotations
- Numerous connections to number theory and geometry
While many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructor’s Solutions Manual written by the author has comprehensive solutions for all exercises and some alternative solutions to develop a critical thought and deeper understanding. It is available from CRC Press only. The Student Solution Manual has comprehensive solutions for all odd-numbered exercises and many even-numbered exercises.
Contemporary Abstract Algebra-Cengage Learning_Brooks Cole_Cengage (2017) by Joseph A Gallian
CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. Gallian’s text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists.
Schaum’s Outline of Abstract Algebra by Frank Ayres; Lloyd R Jaisingh || Full PDF
This long-awaited revision provides a concise introduction to topics in abstract algebra, taking full account of the major advances and developments that have occurred over the last half-century in the theoretical and conceptual aspects of the discipline, particularly in the areas of groups and fields.
Key features include:
A new section on binary linear codes New chapter on Automorphisms and Galois Theory 450 fully solved problems and 420 supplementary problems for individual practice More than 175 illustrative examples
Schaum’s Outline of Intermediate Algebra, Third Edition by Ray Steege, Kerry Bailey || Full PDF
Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately, there’s Schaum’s.
More than 40 million students have trusted Schaum’s to help them succeed in the classroom and on exams. Schaum’s is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, sovled problems, and practice exercises to test your skills.
This Schaum’s Outline gives you:
• 800 supplemental problems to reinforce knowledge
• Concise exaplanations of all intermediate algebra concepts
• Information on polynomials, rational expressions, exponents, roots, radicals, sequences, series and the bionomical theorem
• New end of chapter quiz for every chapter
• New cumulative test
• New “Alternate Method” for factoring
• New appendix on the “Frentheway Method” including the proof and examples
• Support for all major textbooks for courses in Intermediate Algebra
Schaum’s reinforces the main concepts required in your course and offers hundreds of practice questions to help you suceed. Use Schaum’s to shorten your study time-and get your best test scores!
Schaum’s Outlines – Problem solved.