Elementary Abstract Algebra: Examples and Applications

Opinión de Mark Koester, Associate Professor, Metropolitan State University of Denver on 3/26/21, updated 5/26/21

Exhaustividad clasificación: 4 ver menos

Extensive index is included. The book includes more topics than a semester course could study.

Precisión de contenido clasificación: 4

There appears to be accuracy in the book.

Relevancia / Longevidad clasificación: 5

These topics in Abstract Algebra are appropriate for secondary preservice mathematics teachers. Many of our state's mathematics standards connect to the topics in the book.

Claridad clasificación: 5

I enjoy the conversational style of the authors. It is so important that textbooks are accessible for all.

Consistencia clasificación: 4

The same terminology is used throughout.

Modularidad clasificación: 4

There are twenty chapters. Of course, some ideas build on others, but often, it is noted in what chapter these other ideas can be found.

Organización / Estructura / Flujo clasificación: 4

There is a logical order to the text.

Interfaz clasificación: 4

I like having the ability to click on hints or propositions n the book rather than being inundated with text on a page.

Errores gramaticales clasificación: 4

I didn't notice grammatical errors.

Relevancia cultural clasificación: 4

I believe that this book is inclusive of others because it is so readable. There is not the inherent bias that one must be able to read cryptic symbols or to read the author's words obviously, clearly, or this is easy. This was so damaging to having a positive identity as a mathematics major.

Opinión de Diana Morris, Assistant Professor, University of Virginia on 12/13/20

Exhaustividad clasificación: 5 ver menos

At almost 1000 pages, this book certainly covers the basics comprehensively. You might not find the Sylow Theorems or Jordan Canonical Form, but it accomplishes what it sets out to do, covering the basic background of numbers and set theory, the main examples of groups and rings, and then developing these concepts more formally.

Precisión de contenido clasificación: 4

Given the trade-off between perfect mathematical clarity (think Rudin) and being intelligible to undergraduates, I think the book strikes a good balance.

Relevancia / Longevidad clasificación: 5

Abstract algebra books typically struggle to convince undergraduates of their relevance. The sustained application in the book is Cryptography, but they did a beautiful job of relating basic concepts like modular arithmetic to practical applications that we do every day (e.g. if December 1st is on a Tuesday, what day of the week is Christmas?)

Claridad clasificación: 5

Their basic wording of mathematical concepts was impressive, e.g. the explanation of multiplicative and additive identities is completely fool-proof, as were the every day examples of mathematical concepts, e.g. the notion of "grandfather" being a composition of "parent" and "father". There is a real effort to guide students through proofs, e.g. how to justify each step and what qualifies as justification. I also appreciated the generous hints on the exercises spread throughout the book and the Study Guides at the end of each chapter identifying competencies.

Consistencia clasificación: 4

The material has numerous different sources. None of the transitions were jarring, but sometimes it felt more like a compendium than one flowing volume.

Modularidad clasificación: 4

Given the length of the text, an instructor would certainly want to pull out different chapters and make particular note of which leads to which. There is actually a chart at the beginning of the text explaining how sections are related and which rely on previous sections.

Organización / Estructura / Flujo clasificación: 4

I could not decide if the organization of the book was confusing or brilliant. For example, major examples of groups / rings are first defined in great depth without formally defining them as such, then in later chapters, one starts from the beginning with the definitions of groups and rings and discovers that they are already familiar.

I did feel that there was an overwhelming amount of material, more a reference book of basic abstract algebra topics than a simple narrative, but there were highly coherent sub-narratives throughout.

Interfaz clasificación: 5

The only thing that made it difficult to navigate was the sheer length of the document.

Errores gramaticales clasificación: 4

The book had its share of misspellings, but not to the point of compromising or distracting from the meaning.

Relevancia cultural clasificación: 5

The book did an excellent job of relating abstract mathematical concepts to practical examples familiar to any person.

I would certainly recommend this book as a reference to any student wanting simple explanations and practical examples for the concepts of basic abstract algebra. For most single semester introductory courses, it would make a fine basic textbook, with some selective pruning and perhaps a few additions where the instructor sees fit.