Essentials of Modern Algebra [OP]

This book is intended for the undergraduate one or two semester course in modern algebra, also called abstract algebra. It follows that basic plan, using the axioms or rules to understand structures such as groups, rings, and fields, and giving the reader examples to help, but leaving many theorems and examples for them to try. The unique feature of the text is the list of projects at the end of each chapter that can be used in the classroom (with students solving them), alone, or in groups with the aid of an instructor. Because of their interactive nature, the projects are designed to understand concepts or to lead the student to new ideas they will encounter later. This title features a logic-based presentation, with the structures of groups, rings, and fields presented in similar ways through objects, sub-objects, mappings between objects, and quotients of objects. It follows a fairly straight path without many of the side areas, such as modules, in order to introduce Galois Theory and solvability of polynomials. It provides numerous examples, exercises and the inclusion of projects in each chapter. It is an instructor's resources available upon adoption. See more