Foreword: MAS S an d
RE U a t Pen n Stat e
This boo k i s par t o f a collectio n publishe d jointl y b y th e Amer -
ican Mathematica l Societ y an d th e MAS S (Mathematic s Advance d
Study Semesters ) progra m a s a par t o f th e Studen t Mathematica l
Library series . Th e book s i n th e collectio n ar e base d o n lectur e
notes fo r advance d undergraduat e topic s courses taught a t th e MAS S
and/or Pen n Stat e summe r RE U (Researc h Experience s fo r Under -
graduates). Eac h boo k present s a self-containe d expositio n o f a non -
standard mathematica l topic , ofte n relate d t o curren t researc h areas ,
accessible t o undergraduat e student s familia r wit h a n equivalen t o f
two year s o f standar d colleg e mathematic s an d suitabl e a s a tex t fo r
an uppe r divisio n undergraduat e course .
Started i n 1996, MAS S i s a semester-lon g progra m fo r advance d
undergraduate student s fro m acros s the USA . The program' s curricu -
lum amount s t o sixtee n credi t hours . I t include s thre e cor e course s
from th e genera l area s o f algebra/numbe r theory , geometry/topolog y
and analysis/dynamica l systems , custo m designe d ever y year ; a n in -
terdisciplinary seminar ; an d a specia l colloquium . I n addition , ev -
ery participan t complete s thre e researc h projects , on e fo r eac h cor e
course. Th e participant s ar e full y immerse d int o mathematics , an d
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