Foreword: MAS S an d

RE U a t Pen n Stat e

University

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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