Highly regarded by instructors in past editions for its sequencing of topics as well as its concrete approach, slightly slower beginning pace, and... extensive set of exercises, the latest edition of Abstract Algebra extends the thrust of the widely used earlier editions as it introduces modern abstract concepts only after a careful study of important examples. Beachy and Blair’s clear narrative presentation responds to the needs of inexperienced students who stumble over proof writing, who understand definitions and theorems but cannot do the problems, and who want more examples that tie into their previous experience. The authors introduce chapters by indicating why the material is important and, at the same time, relating the new material to things from the student’s background and linking the subject matter of the chapter to the broader picture. Instructors will find the latest edition pitched at a suitable level of difficulty and will appreciate its gradual increase in the level of sophistication as the student progresses through the book. Rather than inserting superficial applications at the expense of important mathematical concepts, the Beachy and Blair solid, well-organized treatment motivates the subject with concrete problems from areas that students have previously encountered, namely, the integers and polynomials over the real numbers.

Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant... results.

Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a 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 reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.* The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.

This is a new text for the Abstract Algebra course. The author has written this text with a unique, yet historical, approach: solvability by... radicals. This approach depends on a fields-first organization. However, professors wishing to commence their course with group theory will find that the Table of Contents is highly flexible, and contains a generous amount of group coverage.

The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its... hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.

The authors have used forty years of classroom experience to design a text that serves as a superb introduction to abstract algebra. All students,... even those with no previous knowledge of abstract or linear algebra, will benefit from the Fifth Edition's organization and selection of topics. Outstanding features include: (1) builds abstraction on a solid foundation of concrete examples; (2) develops concepts gradually but allows for more rapid progress as students' mathematical maturity increases; (3) offers unparalleled problem sets; and (4) foreshadows important topics and then clearly presents and applies them to facilitate retention, not mere exposure. The historical and biographical notes on major contributors to the development of algebra show that mathematics continues to be created by real people. The preface shows how to use the text's flexibility to achieve any of several goals.

This book explores the essential theories and techniques of modern algebra, including its problem-solving skills, basic proof techniques, many... applications, and the interplay between algebra and geometry. It takes a concrete, example-oriented approach to the subject matter.

The American Mathematical Monthly recommended this advanced undergraduate-level text for teacher education. It starts with groups, rings, fields, and... polynomials and advances to Galois theory, radicals and roots of unity, and solution by radicals. Numerous examples, illustrations, commentaries, and exercises enhance the text, along with 13 appendices. 1971 edition.

ABSTRACT ALGEBRA: AN INTRODUCTION is intended for a first undergraduate course in modern abstract algebra. Its flexible design makes... it suitable for courses of various lengths and different levels of mathematical sophistication, ranging from a traditional abstract algebra course to one with a more applied flavor.  The book is organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups, so students can see where many abstract concepts come from, why they are important, and how they relate to one another.  New Features:  A groups-first option that enables those who want to cover groups before rings to do so easily.  Proofs for beginners in the early chapters, which are broken into steps, each of which is explained and proved in detail.  In the core course (chapters 1-8), there are 35% more examples and 13% more exercises.

Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract... algebraic systems. Features many examples and a large number of problems of varying levels of difficulty at the end of each chapter.

This undergraduate text takes a novel approach to the standard introductory material on groups, rings, and fields. At the heart of the text is a... semi-historical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. Avoiding excessive abstraction whenever possible, the text focuses on the central problem of studying the solutions of polynomial equations. Highlights include a proof of the Fundamental Theorem of Algebra, essentially due to Euler, and a proof of the constructability of the regular 17-gon, in the manner of Gauss. Another novel feature is the introduction of groups through a meditation on the meaning of congruence in the work of Euclid. Everywhere in the text, the goal is to make clear the links connecting abstract algebra to Euclidean geometry, high school algebra, and trigonometry, in the hope that students pursuing a career as secondary mathematics educators will carry away a deeper and richer understanding of the high school mathematics curriculum. Another goal is to encourage students, insofar as possible in a textbook format, to build the course for themselves, with exercises integrally embedded in the text of each chapter.

This text is intended for a one- or two-semester undergraduate course in abstract algebra and covers the traditional theoretical aspects of groups,... rings, and fields. Many applications are included, including coding theory and cryptography. The nature of the exercises ranges over several categories; computational, conceptual, and theoretical problems are included.

This is an incisive look at the politics behind the negotiations and outcome of South Africa's transition to democracy. It is based on previously... unexamined archival material and will be of great interest to anyone interested in South African politics, constitutional law, democracy and human rights. During the early 1990s, South Africans kept a close eye on the media coverage of South Africa's negotiated transition to democracy. Likened to a soap opera by some, the negotiations featured violent interlopers, dramatic walkouts, alliances and, somehow, a fortunate conclusion in the form of the Interim Constitution and Bill of Rights. The importance of the negotiating process and the Interim Constitution itself should not be underestimated, however, in relation to their longer-term influence over the form of democracy currently enjoyed in South Africa. In this brave publication, Spitz and Chaskalson examine the politics behind the Kempton Park negotiations and the Interim Constitution, and the influence that these have had on the subsequent consolidation of a South African democracy.