A textbook for a one- or two-semester course, that develops ring theory first, in order to draw upon the students' familiarity with integers and with polynomials, which are used as the motivating examples for studying rings. Coverage includes: numbers, polynomials, and factoring; rings, domains, and fields; unique factorization; permutations and group homomorphisms; constructibility problems and field extensions; and vector spaces and field extensions. Includes answers to selected exercises. Annotation copyright Book News, Inc. Portland, Or.

A First Course in Abstract Algebra: Rings, Groups, and Fields

Science & Math

Anderson, Marlow

Feil, Todd

Mathematics

PWS Pub. Co.

This book picks up the history of mathematics from where Sherlock Holmes in Babylon left it. The 40 articles of Who Gave You the Epsilon? continue the story of the development of mathematics into the nineteenth and twentieth centuries. The articles have all been published in the Mathematical Association of America journals and are in many cases written by distinguished mathematicians such as G. H. Hardy and B. van der Waerden. The articles are arranged thematically to show the development of analysis, geometry, algebra and number theory through this period of time. Each chapter is preceded by a foreword, giving the historical background and setting and the scene, and is followed by an afterword, reporting on advances in our historical knowledge and understanding since the articles first appeared. This book is ideal for anyone wanting to explore the history of mathematics.

Who Gave you the Epsilon?: And Other Tales of Mathematical History (Spectrum)

Katz, Victor

Wilson, Robin

American Mathematical Society

Like its popular predecessors, A First Course in Abstract Algebra: Rings, Groups, and Fields, Third Edition develops ring theory first by drawing on students’ familiarity with integers and polynomials. This unique approach motivates students in the study of abstract algebra and helps them understand the power of abstraction. The authors introduce groups later on using examples of symmetries of figures in the plane and space as well as permutations. New to the Third Edition <ul>
<li>Makes it easier to teach unique factorization as an optional topic </li> <li>Reorganizes the core material on rings, integral domains, and fields</li> <li>Includes a more detailed treatment of permutations</li> <li>Introduces more topics in group theory, including new chapters on Sylow theorems</li> <li>Provides many new exercises on Galois theory</li>
</ul> The text includes straightforward exercises within each chapter for students to quickly verify facts, warm-up exercises following the chapter that test fundamental comprehension, and regular exercises concluding the chapter that consist of computational and supply-the-proof problems. Historical remarks discuss the history of algebra to underscore certain pedagogical points. Each section also provides a synopsis that presents important definitions and theorems, allowing students to verify the major topics from the section.

A First Course in Abstract Algebra: Rings, Groups, and Fields, Third Edition

Chapman and Hall/CRC

Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there is more natural-and ultimately more effective. Authors Anderson and Feil developed A First Course in Abstract Algebra: Rings, Groups and Fields based upon that conviction. The text begins with ring theory, building upon students' familiarity with integers and polynomials. Later, when students have become more experienced, it introduces groups. The last section of the book develops Galois Theory with the goal of showing the impossibility of solving the quintic with radicals. Each section of the book ends with a "Section in a Nutshell" synopsis of important definitions and theorems. Each chapter includes "Quick Exercises" that reinforce the topic addressed and are designed to be worked as the text is read. Problem sets at the end of each chapter begin with "Warm-Up Exercises" that test fundamental comprehension, followed by regular exercises, both computational and "supply the proof" problems. A Hints and Answers section is provided at the end of the book. As stated in the title, this book is designed for a first course--either one or two semesters in abstract algebra. It requires only a typical calculus sequence as a prerequisite and does not assume any familiarity with linear algebra or complex numbers.

A First Course in Abstract Algebra: Rings, Groups and Fields, Second Edition

The Physics of Scuba Diving

Sports & Outdoors

Water Sports

Nottingham University Press

While exploring the wonders of scuba diving, this educational account teaches the scientific and mathematical principles associated with the sport. Explaining how water pressure affects divers and describing exponential growth and decay in this context, it will appeal not only to academics, but also to scuba instructors and divers. With countless computations and step-by-step justification of the mathematics of dive tables, this record is both informative and entertaining.

Physics

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