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Abstract Algebra
Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and a large number of problems of varying levels of difficulty at the end of each chapter.
- GenresMathematicsReference
656 pages, Paperback
First published January 1, 1996
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April 23, 2012
I picked up this book to fill in a hole in my math education in preparation for the GRE math subject test, and because it was far and away the cheapest abstract algebra book I could find. I'm not particularly thrilled with it yet; it's better than an elementary approach I borrowed but I may just keep looking.
First, the text is a bit dated. It a corrected version of the 1966 printing. Some of the notation is not what is currently standard, which is a little inconvenient: "J" for the integers instead of "Z" (and without the mathbb font), etc. More irksome is the typography: the breaks between examples, lemmas, theorems, etc. are indistinguishable from equation line breaks, and so it's difficult to return to the statement of a theorem to verify something, or to notice at a glance where one one idea ends and another begins. The text is not overly cluttered with diagrams and simplistic explanations, which I like, but in areas such as Diophantine equations I feel it might benefit from a less dense approach. Theorems introduce 8 or 9 quantities by variable name only; even a bold typeface or subscripts or something might help certain subsets of variables stand apart from others in these cases.
The upside is that the text is pretty rigorous, and builds number systems and operations axiomatically all from the natural numbers. For someone who is already familiar with the properties of integers, the reals, etc., this is an interesting approach. The construction of the integers in particular was a new one for me.
First, the text is a bit dated. It a corrected version of the 1966 printing. Some of the notation is not what is currently standard, which is a little inconvenient: "J" for the integers instead of "Z" (and without the mathbb font), etc. More irksome is the typography: the breaks between examples, lemmas, theorems, etc. are indistinguishable from equation line breaks, and so it's difficult to return to the statement of a theorem to verify something, or to notice at a glance where one one idea ends and another begins. The text is not overly cluttered with diagrams and simplistic explanations, which I like, but in areas such as Diophantine equations I feel it might benefit from a less dense approach. Theorems introduce 8 or 9 quantities by variable name only; even a bold typeface or subscripts or something might help certain subsets of variables stand apart from others in these cases.
The upside is that the text is pretty rigorous, and builds number systems and operations axiomatically all from the natural numbers. For someone who is already familiar with the properties of integers, the reals, etc., this is an interesting approach. The construction of the integers in particular was a new one for me.
Displaying 1 of 1 review