Schaum's Outline of Group Theory

This is another of the Schaum's outline books that helped me launch my career. I was taking a master's level course in abstract algebra and was loaded down with homework problems. After struggling to get one assignment done, I went to the local bookstore and purchased this book. My performance immediately improved. I found a few of the homework problems in this book, but the main advantage was that there were similar problems that I could work through and understand. From this, it was a relatively simple matter to execute a similar proof to solve the problem I was given. My final grade was an A and it wasn't even close.

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 wanted to focus on groups because, as stated in the Introduction of this book, 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. Initially I did not want to use a Schaum outline to study groups. I wanted a hard-cover textbook. But I found this book irresistible in both its scope and its detailed discussion of group concepts. In summary, I would say that if you are truly serious about abstract algebra, you cannot afford to be without this fascinating, thorough, and inexpensive text.

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 and groupoids, 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.