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Basic Algebra I
A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.
Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as Lie and Jordan algebras, lattices, and Boolean algebras. Exercises appear throughout the text, along with insightful, carefully explained proofs. Volume II comprises all subjects customary to a first-year graduate course in algebra, and it revisits many topics from Volume I with greater depth and sophistication.
Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as Lie and Jordan algebras, lattices, and Boolean algebras. Exercises appear throughout the text, along with insightful, carefully explained proofs. Volume II comprises all subjects customary to a first-year graduate course in algebra, and it revisits many topics from Volume I with greater depth and sophistication.
528 pages, Paperback
Published June 22, 2009
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Displaying 1 - 2 of 2 reviews
September 4, 2014
I haven't finished this book yet, but I've spent enough time with it that I feel I can say something about it.
I knew nothing about this book or its author when I picked it up, and selected it because it was the only one available at the time. I spent a while just flipping through it, picking out random pieces that looked interesting and reading them with no particular goal in mind. That's not the ideal way to use this book, and I think this might account for some of the negative reviews this book has received on other sites.
Set aside a block of time, get a few sheets of paper, and work through a section from start to finish. The proofs he provides are not always as clear as you might wish, but it's worth the time to understand them; in fact, if you choose to skip over them, you'll find yourself going back to review when you work the exercises -- and then you'll realize why the proof was constructed that way. You can certainly take the author's word for it that a certain property is true, but if you don't understand why, you'll end up working far harder than you have to later on.
The exercises at the end of each section are beautifully chosen to test your understanding and ability to use the material. In most sections I've covered so far, the first few examples are "softballs", to make sure you were paying attention. The following examples build on those, and the last example brings all the concepts of the section together. What does this mean for the reader? Well, if you're studying this book on your own as I am, it can be frustrating, because there's no good way to "just skip it and come back later" since the problems generally depend directly on previous exercises. I do feel like almost everything you need to solve the problems is contained in the book, but you might not recognize it right away.
Read with sufficient attention, this book is full of "a-ha!" moments. But there are places where different/better organization might have made things easier on readers. The section on cosets contains a problem which gets directly at the concept of a stabilizer, but stabilizers aren't officially introduced until several sections later. I see why Jacobson made the decision he did, because he covers stabilizers more thoroughly later on -- but it sometimes feels like you're doing extra work to "create" machinery that he could simply have told you about.
The subject matter he covers is impressive, and I suspect this is far more material than most people cover in a year of undergrad algebra. I've made several half-hearted attempts at the subject with other books, but this one has held my interest and has been very helpful. If you're willing to spend the time it deserves, this book won't disappoint you.
I knew nothing about this book or its author when I picked it up, and selected it because it was the only one available at the time. I spent a while just flipping through it, picking out random pieces that looked interesting and reading them with no particular goal in mind. That's not the ideal way to use this book, and I think this might account for some of the negative reviews this book has received on other sites.
Set aside a block of time, get a few sheets of paper, and work through a section from start to finish. The proofs he provides are not always as clear as you might wish, but it's worth the time to understand them; in fact, if you choose to skip over them, you'll find yourself going back to review when you work the exercises -- and then you'll realize why the proof was constructed that way. You can certainly take the author's word for it that a certain property is true, but if you don't understand why, you'll end up working far harder than you have to later on.
The exercises at the end of each section are beautifully chosen to test your understanding and ability to use the material. In most sections I've covered so far, the first few examples are "softballs", to make sure you were paying attention. The following examples build on those, and the last example brings all the concepts of the section together. What does this mean for the reader? Well, if you're studying this book on your own as I am, it can be frustrating, because there's no good way to "just skip it and come back later" since the problems generally depend directly on previous exercises. I do feel like almost everything you need to solve the problems is contained in the book, but you might not recognize it right away.
Read with sufficient attention, this book is full of "a-ha!" moments. But there are places where different/better organization might have made things easier on readers. The section on cosets contains a problem which gets directly at the concept of a stabilizer, but stabilizers aren't officially introduced until several sections later. I see why Jacobson made the decision he did, because he covers stabilizers more thoroughly later on -- but it sometimes feels like you're doing extra work to "create" machinery that he could simply have told you about.
The subject matter he covers is impressive, and I suspect this is far more material than most people cover in a year of undergrad algebra. I've made several half-hearted attempts at the subject with other books, but this one has held my interest and has been very helpful. If you're willing to spend the time it deserves, this book won't disappoint you.
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August 19, 2019not great
Displaying 1 - 2 of 2 reviews