- Paperback: 288 pages
- Publisher: Schaum's Outlines (1 January 1968)
- Language: English
- ISBN-10: 0070041245
- ISBN-13: 978-0070041240
- Product Dimensions: 20.8 x 1.4 x 27.7 cm
- Average Customer Review: 2 customer reviews
- Amazon Bestsellers Rank: #84,358 in Books (See Top 100 in Books)
Schaum's Outline of Group Theory (Schaum's Outline Series) Paperback – 1 Jan 1968
Customers who viewed this item also viewed
Customers who bought this item also bought
About the Author
McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
To get the free app, enter mobile phone number.
Top customer reviews
There was a problem filtering reviews right now. Please try again later.
Most helpful customer reviews on Amazon.com
Group theory was thrown in at the tail end almost as an afterthought. How I would loved to have had this book along side me as a back-up resource during those trying days? Even though the class purposefully was brutally rigorous, owing mostly to proceeding through all three books at a breakneck pace, at the time, it was impossible to know that our instructor was also willingly gliding pass several fundamental intermediate steps. The importance of which have all now been exposed to me by seeing them added back in for the first, in this book.
For instance, introducing “groupoids” and “semigroups” on the road to the larger concept of a “group” itself, in retrospect, strikes me as indispensable information.
The same can be said for breaking mappings down into their more elemental constituent parts — of “epimorphisms,” and “semigroups;” and then reassembling them into a smoother more graduated conceptual net.
The best proof that this approach worked is in the way these intermediate concepts were both put to good use in introducing and proving Caley’s theorem.
Browsing ahead, this strategy of “filling-in” all the substantive blanks in the theory with intermediate concepts, and then using them in lots of graduated examples, strikes me as a winning strategy — and certainly is the proper way to build confidence, and facility, while maximizing understanding.
I am only half way through the book, but feel sure that this slower more certain pace, one that adds back in all the intermediate missing steps, cannot be but helpful in taking on later chapters. Four stars, so far.
I had thought, after the book was lost, of trying another text. But most of the introductory textbooks on abstract algebra cover a lot of other things besides group theory. And as a result, they do not go very deeply into any one algebraic structure, but just scratch the surface. I want to focus on groups because this will bring me into the advanced areas of more quickly as a result of the narrowness of focus.
The notation in this book is initially peculiar. I was not used to seeing the notation xf for a function instead of f(x). The lack of parentheses was confusing, so when making my notes I simply added them, creating the notation (x)f. In fact this backward notation does seem to work better for abstract algebra, and after a while it becomes natural, and the standard notation f(x) becomes odd. So expect to see such things as this for automorphisms: (a*b)f = (a)f*(b)f.
Another problem with the book that I've encountered is a number of typos. They are few but still enough to cause some real confusion. The first four chapters are, in my opinion, outstanding. As the author states, chapters 5-8 cover a variety of intermediate-level topics and can be studied in any order whatsoever. Going into chapter 5, I encountered an increasing difficulty understanding this text just prior to presenting proofs of the Sylow theorems. In particular, I did not feel that conjugacy classes were very well presented. On the plus side, however, there is a thorough coverage of cyclic and finite groups, and a strong emphasis throughout the text on proving the various theorems and lemmas.
However, I wasn't able to truly understand them. The book by Baumslag and Chandler is a good introduction. The writing is clear, the examples showed me how to use the theorems. According to the authors, the required level is high-school math. That may be true, but I guess having a little backgroud in group, rings, field, etc... helped me.
I am going back to Milne now, but this book is good if you are learning group theory on your own, and just for fun.