technical detail s an d tak e a panoramic vie w o f how th e idea s a t
fit int o the larger mathematica l landscape . Commentarie s fo r se
Big Picture Question s ar e als o included a t th e en d o f the book .
the tex t a s you r guid e an d you r ow n creativ e contribution s a
points of interest, I hope you find your journey to be a truly inter
...the primary question was not What we
but How do we know it.
Aristotl e
Although thi s boo k i s small , it s aim s ar e not . Th e boo k
invitation t o develop the idea s of diophantine analysi s an d t o di
the fundamental result s on your own. I believe that thi s subject
of th e mos t beautifu l an d ric h area s o f mathematics , an d I hop
will shar e my poin t o f vie w an d enjo y th e sight s an d challenge
lie ahead. Thi s boo k als o provides a setting wher e differen t area
ideas o f mathematic s com e together . Her e yo u wil l se e basi c n
from algebra , analysis , geometry , an d topolog y joi n togethe r a
collective whole . Mos t importantl y however , I hop e tha t throug
process o f activel y generatin g th e idea s behin d th e subject , yo
continue t o hon e th e habit s o f thought require d t o analyz e issu
reason i n a mor e effectiv e an d creativ e manner .
Uncovering th e mysteriou s structur e o f numbe r ha s bee n
the grea t intellectua l challenge s o f huma n history . I hop e yo
joy you r journe y throug h th e beautifu l mathematic s tha t lie s
and enjo y th e challeng e o f conquerin g thi s are a o f numbe r theo
yourself. You can do it!
With al l goo d wis
Edward Burge r
January 1, 2000
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