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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. CONTEMPORARY ABSTRACT ALGEBRA, EIGHTH EDITION provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists.
The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
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Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics.
The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.
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. This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book.
The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra.
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New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity.
Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences.
Generalized eigenvectors are then used to provide insight into the structure of a linear operator. Welcome to the new face of mending! Don’t hide patches — make them into bold, beautiful embellishments. Repair holes with colorful thread and a creative darning stitch, or use fun embroidery to bring new life to a stained shirt. With detailed step-by-step photography, Kristin Roach teaches you a wide range of patching, darning, and repair stitches using both hand and machine sewing. Revive your wardrobe with these traditional mending techniques to make worn-out clothing not just wearable, but better than ever. 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. The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field.
(Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics. This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level.
The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups.
The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedderburn-Artin theorem for semisimple artinian rings, Noether-Lasker theorem, the Smith-Normal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules. Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises.
In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solution to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving. This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem. In addition, there are over 150 new problems and examples. This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165).
Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.
New York Times bestselling author Laura Griffin’s Desperate Girls is a tightly wound, fast-paced romantic thriller that follows a desperate woman on the run as she hides from a killer’s symbolic revenge spree. Defense attorney Brynn Holloran is right at home among cops, criminals, and tough-as-nails prosecutors. With her sharp wit and pointed words, she has a tendency to intimidate, and she likes it that way. She’s a force to be reckoned with in the courtroom, but in her personal life, she’s a mess. When a vicious murderer she once helped prosecute resurfaces and starts a killing spree to wipe out those who put him behind bars, one thing becomes clear: Brynn needs to run for her life. When the police come up empty-handed, Brynn turns to a private security firm for protection.
But when she defies advice and gets involved in the investigation, even the former Secret Service agent assigned to protect her may not be able to keep her safe. With every new clue she discovers, Brynn is pulled back into the vortex of a disturbing case from her past.
As the clock ticks down on a manhunt, Brynn’s desperate search for the truth unearths long-buried secrets and reignites a killer’s fury.
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