Modern Algebra (Dover Books on Mathematics) by Seth Warner (PDF)

Description

This standard text, written for junior and senior undergraduates, is unusual in that its presentation is accessible enough for the beginner, yet its thoroughness and mathematical rigor provide the more advanced student with an exceptionally comprehensive treatment of every aspect of modern algebra. It especially lends itself to use by beginning graduate students unprepared in modern algebra.The presentation opens with a study of algebraic structures in general; the first part then carries the development from natural numbers through rings and fields, vector spaces, and polynomials. The second part (originally published as a separate volume) is made up of five chapters on the real and complex number fields, algebraic extensions of fields, linear operations, inner product spaces, and the axiom of choice.For the benefit of the beginner who can best absorb the principles of algebra by solving problems, the author has provided over 1300 carefully selected exercises. “There is a vast amount of material in these books and a great deal is either new or presented in a new form.” — Mathematical Reviews. Preface. List of Symbols. Exercises. Index. 28 black-and-white line illustrations.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent textbook. It is a classic from which my highschool precalculus instructor used examples while teaching us about injections, surjections, and bijections. Plus, it was used at the first stop on my college voyage, Vanderbilt, for a junior level course in Abstract Algebra. As a recreational mathematician, I skimmed the first 150 pages one evening while resting on a gurney without any other forms of entertainment. It is highly readable, simple, and easily understood when one has the proper prerequisite knowledge.

⭐I used this book as a supplement while an undergrad. I misplaced my original copy, so I ordered another copy to brush up on a few topics. This book contains more than two-semesters work of material. The sections are clearly written and each section contains practice problems.

⭐This is a unique book on modern algebra. Anyone who wants to learn mathematics starting from the foundations then this is one of the best books. The author treats recursion very well defining things like powers of element in a group, sums of elements in a ring very very carefully. The problem collection is great and very well graded. Most of them are doable. Highly recommended!

⭐I bought this book for self study. I would not recommend it for that purpose. My main problem was that there aren’t any solutions to any of the problems. I am (and I think most people are) someone who learns math by doing math. I also need to know if I am making widely outrageous mistakes. I don’t require every problem to have a solution, but I can’t learn when I have no idea if I’m doing it right.

⭐The topic is very broad, but not so deep. It will be beneficial to read it for fun if you want to focus on algebra in graduate studies, but not sure what you might encounter.

⭐It is an okay book. It is very long and has a lo of material in it. Sometimes way more than need. A very good book for refance

⭐This is a reprint of the 1965 edition. This book was originally a two volume set. It’s now a large 818-page, unwieldy paperback in the narrow format of Dover reprints. (Don’t get me wrong I love Dover reprints, this one is just too thick for the format). The second half from page 512 on is all that is worth while anyway. This book is very pendantic in the worse “New Math” sense (circa 1960). Meaning it emphasizes arbitrary abstract axioms, lacks historic perspective, concrete examples and real world applications; and, much is left to the reader as exercises. This is a shame since Modern Algebra is rich in history and application. The pedantic pretensions don’t stop there. The book uses the number theorem approach to proofs without mentioning their common names (Since history is completely absent, this isn’t a surprise). This is NOT a standard reference today, if it ever was in the past. Memorizing the theorem numbers will do you no good in your coffee shop conversations. The book only gets interesting in it’s latter half, it’s too bad you have to lug the first 500 pages along for the ride. Adding insult to pedantry, the really interesting parts are left as exercises! That’s ok if you’re paying big bucks for a professor and a TA to help you along, but as a self-study book, it’s down right annoying. If you’re looking for an introduction, I’d recommend Herstein’s Topics in Algebra or Birkoff & MacLane’s Survey over this one. If you’re looking for more advanced treatment, I’d recommend Van der Waerden’s Modern Algebra or Jacobson’s Lectures in Abstract Algebra. These come in multi-volume sets that making reading easier. I’m sure there are better current books on the subject, but I’m not familiar enough to make a recommendation. I can only dissuade you from purchasing this one as your only reference or an intro.

⭐As other reviewers have pointed out, this massive volume by Seth Warner misses the mark — no matter what the target. It’s a poor choice for an initial exposure to modern algebra because it gives absolutely no motivation or historical context for any topics. (It’s as if the entire body of modern algebra just popped out of someone’s head one day.) In addition, the development of some crucial topics is left entirely as an exercise for the reader (with no guidance at all). As someone else pointed out, it’s absolutely the worst of the wrong-headed “modern math” pedagogy that turned so many young people off to mathematics back in the mid-1960s. Better alternatives are Herstein or Fraleigh, or for someone on a budget, the Dover reprint of Pinter or Deskins (maybe supplemented with Clark and/or Maxfield).For someone who’s already gone through undergrad modern algebra and is taking a graduate course, this book fails because of its shallowness. Lots of breadth, very little depth. Theorem numbers that don’t relate to anything used by the rest of the mathematical community. Just stick with Dummit & Foote or (shudder) Lang.Any readership you can name would benefit more from a text other than this one. Stay away…

⭐… besonders gut gefallen haben mir die Kapitel II “New Structures from old” und Kapitel V “Vector Spaces”. Ansonsten ist das Buch zwar solide, aber eher konventionell aufgebaut. Ich vermisse die Darstellung von Zusammenhängen mit anderen Gebieten der Mathematik (z.B. Analysis) und der theoretischen Physik.

⭐

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