Abstract Algebra I

The present volume is the first of three that will be published under the general title Lectures in Abstract Algebra. These vol­ umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale "University. The general plan of the work IS as follows: The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraIc concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond the foundations and elementary properties of the algebraic sys­ tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under­ standing of a few topics is to be preferred to a superficial under­ standing of many. The second and third volumes of this work will be more special­ ized in nature and will attempt to give comprehensive accounts of the topics which they treat. Volume II will bear the title Linear Algebra and will deal with the theorv of vectQ!_JlP. -a. ces. . . . . Volume III, The Theory of Fields and Galois Theory, will be con­ cerned with the algebraic structure offieras and with valuations of fields. All three volumes have been planned as texts for courses.

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject.

Guide to Abstract Algebra is a clear and readable text which covers the basic topics of an introductory course in abstract algebra. New concepts are introduced gradually with many worked examples to illustrate them. A wide variety of exercises is included for readers to undertake themselves and fairly detailed solutions are given for these. There are also sets of problems for which answers are not given.

This volume offers English translations of three early works by Ernst Schröder (1841-1902), a mathematician and logician whose philosophical ruminations and pathbreaking contributions to algebraic logic attracted the admiration and ire of figures such as Dedekind, Frege, Husserl, and C. S. Peirce. Today he still engages the sympathetic interest of logicians and philosophers.

Modern Algebra for Group Theory, Linear Algebra, Discrete Mathematics, Cryptography, Complex Analysis, Topology Students

A beautiful course on the Theory of Groups:)

This book is an attempt to communicate to undergraduate math­ ematics majors my enjoyment of abstract algebra. It grew out of a course offered at California State University, Northridge, in our teacher preparation program, titled Foundations of Algebra, that was intended to provide an advanced perspective on high-school mathe­ matics. When I first prepared to teach this course, I needed to select a set of topics to cover.