Problems In Abstract Algebra
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Problems in Abstract Algebra
Author | : A. R. Wadsworth |
Publsiher | : American Mathematical Soc. |
Total Pages | : 277 |
Release | : 2017-05-10 |
Genre | : Algebra, Abstract |
ISBN | : 9781470435837 |
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This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
Problems in Abstract Algebra
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Author | : Adrian R. Wadsworth |
Publsiher | : Unknown |
Total Pages | : 277 |
Release | : 2017 |
Genre | : Algebra, Abstract |
ISBN | : 147044044X |
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5.9. Cyclotomic polynomials and cyclotomic extensions -- 5.10. Radical extensions, norms, and traces -- 5.11. Solvability by radicals -- Suggestions for Further Reading -- Bibliography -- Index of Notation -- Subject and Terminology Index -- Back Cover
A Book of Abstract Algebra
Author | : Charles C Pinter |
Publsiher | : Courier Corporation |
Total Pages | : 402 |
Release | : 2010-01-14 |
Genre | : Mathematics |
ISBN | : 9780486474175 |
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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Abstract Algebra Manual
Author | : Ayman Badawi |
Publsiher | : Nova Publishers |
Total Pages | : 128 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 159033924X |
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This is the most current textbook in teaching the basic concepts of abstract algebra. The author finds that there are many students who just memorise a theorem without having the ability to apply it to a given problem. Therefore, this is a hands-on manual, where many typical algebraic problems are provided for students to be able to apply the theorems and to actually practice the methods they have learned. Each chapter begins with a statement of a major result in Group and Ring Theory, followed by problems and solutions. Contents: Tools and Major Results of Groups; Problems in Group Theory; Tools and Major Results of Ring Theory; Problems in Ring Theory; Index.
Challenging Problems in Algebra
Author | : Alfred S. Posamentier,Charles T. Salkind |
Publsiher | : Courier Corporation |
Total Pages | : 288 |
Release | : 2012-05-04 |
Genre | : Mathematics |
ISBN | : 9780486131542 |
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Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.
Introduction to Abstract Algebra
Author | : W. Keith Nicholson |
Publsiher | : John Wiley & Sons |
Total Pages | : 560 |
Release | : 2012-03-20 |
Genre | : Mathematics |
ISBN | : 9781118135358 |
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Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.
Abstract Algebra with Applications
Author | : Audrey Terras |
Publsiher | : Cambridge University Press |
Total Pages | : 331 |
Release | : 2018-12-20 |
Genre | : Mathematics |
ISBN | : 9781107164079 |
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This text offers a friendly and concise introduction to abstract algebra, emphasizing its uses in the modern world.
Abstract Algebra
Author | : Thomas Judson |
Publsiher | : Orthogonal Publishing L3c |
Total Pages | : 0 |
Release | : 2023-08-11 |
Genre | : Electronic Book |
ISBN | : 1944325190 |
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Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.