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## Wednesday, November 18, 2009

### Rotman

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...
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.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)