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Wednesday, November 18, 2009


How time flies. Two and a half year ago I discovered Rotman's book on Group Theory. From what I understood of it I found it a fascinating book but I knew -and hated the fact- that I simply wasn't ready for it at the time. Wasn't I? I doubt if I have been studying hard enough. I am going to give the book another try.

As Rotman put it...
To the Reader
Exercises in a text generally have two functions: to reinforce the reader's grasp of the material and to provide puzzles whose solutions give a certain pleasure. Here, the exercises have a third function: to enable the reader to discover important facts, examples, and counterexamples. The serious reader should attempt all the exercises (many are not difficult), for subsequent proofs may depend on them; the casual reader should regard the exercises as part of the text proper.

I think that's the trick to understanding his book.

As a matter of fact I already started. As Rotman wrote ( many ) are not difficult. The following exercise is an easy one if you studied Stirling numbers, if you didn't I wouldn't call it simple.

Exercise 1.5 ( in Rotman ). If 1 < r < n, then there are (1/r) [n(n — 1)... (n — r + 1)] r-cycles in Sn.
Why doesn't he use Stirling numbers ? I am going to need to review Stirling numbers.

Now I remember, I encountered this before and decided I had to study some Discrete Math first. Well, I did. So that won't hold me up studying this book. I think all the prerequisites are 'in' now for attacking this book.

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