Schaum's Outline of Group Theory

I had been studying group theory on my own independently using this book for the last seven months when I misplaced it while at work - along with the notebook which I had painstakingly and carefully created from my hundreds of hours of study in this book. To say the least, I've been absolutely devastated at losing my notes; but the Schaum Outline I can easily replace.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.

This Schaum's outline is not superior to some texts on group theory, but it fills in gaps left by other books by offering solutions to concrete problems, such as classification of some finite simple groups of low order whose proofs are tedious. I learned a great deal from the solved problems, but found the development of non-problem-related material to be routine. I recognize that some of this is necessary for completeness for the uninitiated, so I skipped most of the beginning of the book, and started somewhere in the middle without the least bit of regret. Recommended for anybody taking a course in group theory.

I first started to look at J.S. Milne's class notes:[...]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.

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This book is well organized and broad for a problem-solver, and has several useful features for beginners such as classification of groups up to order 15 and complete multiplication tables for A4 and S4 (no one would take the time to actually write and print these out, but they did in this book).I also find the problems very well-selected and are frequently used later on, so you feel you didn't just go randomly solving problems.The authors give many examples of groups andgroupoids, ranging from isometries to Moebius transformations, and a bit of free groups and group presentations are also covered.The Sylow Theorems are proved in the usual way, as well as the Cauchy Theorem for abelian groups, even though it is not explicitly called by that name.

This book is suitable for my study in group theory! From the book, I appreciate that there are readable examples!

Recebi hoje. Capa e páginas/impressão são excelentes.

Like most Schaum books, this is an excellent collection of solved and unsolved problems, that are very useful for both students and teachers alike. In particular, this book contains a chapter on permutational representations, which looks very useful to me.

Very very useful.

Great reference for all maths and physics students.

Très bon livre pour entrer dans les arcanes de Lagrange, Galois, etc. Ce livre permet une lente introduction sur les groupes, mais permet surtout de comprendre la quintessence de cette partie passionnante des mathématiques.