Beachy and Blairs 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 students 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.
|Published (Last):||11 January 2009|
|PDF File Size:||19.66 Mb|
|ePub File Size:||2.14 Mb|
|Price:||Free* [*Free Regsitration Required]|
John A. Beachy , William D. Blair My goal is to provide some help in reviewing Chapters 7 and 8 of our book Abstract Algebra. I have included summaries of most of these sections, together with some general comments. The review problems are intended to have relatively short answers, and to be more typical of exam questions than of standard textbook exercises.
By assuming that this is a review. I have been able make some minor changes in the order of presentation. The first section covers various examples of groups.
In presenting these examples, I have introduced some concepts that are not studied until later in the text. I think it is helpful to have the examples collected in one spot, so that you can refer to them as you review. A complete list of the definitions and theorems in the text can be found on the web site wu. Abstract Algebra begins at the undergraduate level, but Chapters are written at a level that we consider appropriate for a student who has spent the better part of a year learning abstract algebra.
Although it is more sharply focused than the standard graduate level textbooks, and does not go into as much generality. I hope that its features make it a good place to learn about groups and Galois theory, or to review the basic definitions and theorems. Finally, I would like to gratefully acknowledge the support of Northern Illinois University while writing this review. As part of the recognition as a "Presidential Teaching Professor.
I was given leave in Spring to work on projects related to teaching.
A number theory thread runs throughout several optional sections, and there is an overview of techniques for computing Galois groups. The book offers an extensive set of exercises that help to build skills in writing proofs. Chapter introductions, together with notes at the ends of certain chapters, provide motivation and historical context, while relating the subject matter to the broader mathematical picture. Although the book starts in a very concrete fashion, we increase the level of sophistication as the book progresses, and, by the end of Chapter 6, all of the topics taught in our two semester sequence have been covered. It is our conviction that the level of sophistication should increase, slowly at first, as the students become familiar with the subject. We think our ordering of the topics speaks directly to this assertion. In our classes we usually intend to cover Chapters 1, 2 and 3 in the first semester, and most of Chapters 4, 5 and 6 in the second semester.
About the author
by J.A.Beachy and W.D.Blair