Algebra: Abstract and Concrete 1st Edition by Frederick M. Goodman (PDF)

Description

Addresses the needs of those who often have weak analytic ability, little idea of strategies of problem solving, and less of the patience and confidence needed to work proofs. It introduces readers to the active practice of mathematics — luring them away from the view of mathematics as a system of rules and procedures and helping them learn to think things through for themselves and to explain accurately what they have understood. Uses linear algebra and complex numbers throughout. Highlights all theorems (propositions, lemmas, corollaries) and definitions in boxes. Features an abundance of high-quality exercises.

User’s Reviews

Editorial Reviews: From the Back Cover Addresses the needs of those who often have weak analytic ability, little idea of strategies of problem solving, and less of the patience and confidence needed to work proofs. It introduces readers to the active practice of mathematics — luring them away from the view of mathematics as a system of rules and procedures and helping them learn to think things through for themselves and to explain accurately what they have understood. Uses linear algebra and complex numbers throughout. Highlights all theorems (propositions, lemmas, corollaries) and definitions in boxes. Features an abundance of high-quality exercises.

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

⭐We used it in my first course. I missed the book after it was stolen because it is easy and decently entertaining to read. I remember being bothered by the ‘proof left as excercise’ bits there are maybe too many for a first course…otherwise fairly content with it… This is a gentle start to real algebra. Afterwards, like post first semester, I would use something like lang herstein or van der waerden (if they still print it).

⭐There exists the free version of this book as well. However, I dislike this book because the font, in both paper and electronic version, negatively affects comprehension

⭐Used this as the text for my first algebra course as an undergrad. Very readable, enjoyable, and full of well written exercises. I would guess that probably 80-90% of the exercises can be done without assistance, for anybody carefully reading through this book and with a little prior experience to proofs. Good book for self study, however perhaps not comprehensive enough if you plan to use a significant amount of abstract algebra in your work.

⭐The reason it gets a bad review is that it not very good with concrete example and some of the abstract idea as well. It gives very few examples in both the concrete and abstract ideas. Then in the later chapter it covers only the abstract view points with full of holes left for you to fill in the picture on your own. A book tool to learn from due to its limited examples and the proofs being so concise that they are no good and would not be accepted by any math class or academic paper. The title is very misleading and should be called A very brief view of Abstract Algebra ideas.

⭐Personally, I do not like this book at all. The idea is you teach yourself, which may appeal to some people, but not to me. Why should I teach myself when I’m paying tuition? The book gives you a few very obvious facts, then expects you to build everything up yourself. This ends up a) being a lot of work or b) making the exercises very difficult because you’ve missed all the middle ground. Not my style.

⭐Personally, as an undergraduate, I do not like this book at all… It leaves a lot of important proofs to the reader which is not helpful when first learning Abstract. Plus definitions and concepts are not clearly states, a lot is “assumed.” All in all, I would go for another book, or at least two supplements…

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