These note s ar e base d o n lecture s give n i n Jun e o f 1998 a t Colorad o Stat e
University. Sinc e thos e lecture s som e materia l ha s bee n added . I n addition , th e
writing proces s ha s le d t o a reworkin g o f significan t amount s o f material . Finally ,
some (no t to o serious ) mathematica l error s fro m th e lecture s hav e bee n corrected .
Beyond this , le t m e refer th e reade r t o th e introductio n fo r a summary an d expla -
nation o f the contents .
These lectures were conceived and organized by Frank DeMeyer. I join the other
participants in thanking him for his efforts. I would also like to thank the Conferenc e
Board of the Mathematical Sciences , and the National Science Foundation, fo r thei r
support. I am grateful t o the America n Mathematica l Societ y fo r bein g supportiv e
in bringin g thes e note s t o publication . I als o would lik e to than k Margare t Comb s
for he r hel p with th e "TJ^Xnica r sid e of these notes .
There ar e a n enormou s numbe r o f people , i n thi s field, I shoul d thank . Man y
people hav e bee n helpfu l i n m y mathematica l life . I n fact , ther e ar e to o man y t o
list here . I need to, however, specificall y than k Natha n Jacobso n for m y beginning s
in th e subject . Fo r th e others , le t m e jus t sa y tha t on e o f th e pleasure s o f thi s
subject ha s bee n th e peopl e I have com e know becaus e o f division algebras .
David J . Sal t man
January 1999
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