2000 Mathematics Subject Classification. Primar y 00-01, 00-02 . The photo s use d o n page s 247-24 8 i n th e articl e "Minima l surface s an d rando m walks, " by Alexe i B . Sossinsky , originall y appeare d i n th e author' s boo k Soap Films and Random Walks, M C C M E PubL , Moscow , 200 1 (i n Russian) , an d ar e use d her e wit h permission . The picture s use d o n th e cove r o f thi s boo k ar e courtes y o f th e editors . Library o f Congres s Cataloging-in-Publicatio n Dat a MASS select a : teachin g an d learnin g advance d undergraduat e mathematic s / edite d b y Svetlan a Katok, Alexe i Sossinsky , an d Serg e Tabachnikov . p. cm . Includes bibliographica l references . ISBN 0-8218-3363-4 (alk . paper ) 1. Mathematics—-Stud y an d teachin g (Higher)—Pennsylvania . 2 . Pennsylvani a Stat e University—Curricula. 3 . Mathematic s Advance d Stud y Semester s (Program ) 4 . Education , Higher—Pennsylvania. I . Katok , Svetlana . II . Sossinsky , A . B . III . Tabachnikov , Serge . QA13.5.P4P466 200 3 blO'.n'l—dc21 2003045185 Copying an d reprinting . Materia l i n thi s boo k ma y b e reproduce d b y an y mean s fo r edu - cational an d scientifi c purpose s withou t fe e o r permissio n wit h th e exceptio n o f reproductio n b y services tha t collec t fee s fo r deliver y o f document s an d provide d tha t th e customar y acknowledg - ment o f th e sourc e i s given . Thi s consen t doe s no t exten d t o othe r kind s o f copyin g fo r genera l distribution, fo r advertisin g o r promotiona l purposes , o r fo r resale . Request s fo r permissio n fo r commercial us e o f material shoul d b e addresse d t o the Acquisition s Department , America n Math - ematical Society , 20 1 Charle s Street , Providence , Rhod e Islan d 02904-2294 , USA . Request s ca n also b e mad e b y e-mai l t o reprint-permission@ams.org . Excluded fro m thes e provision s i s materia l i n article s fo r whic h th e autho r hold s copyright . I n such cases , request s fo r permissio n t o us e o r reprin t shoul d b e addresse d directl y t o th e author(s) . (Copyright ownershi p i s indicate d i n th e notic e i n th e lowe r right-han d corne r o f th e firs t pag e o f each article. ) © 200 3 b y th e America n Mathematica l Society . Al l right s reserved . The America n Mathematica l Societ y retain s al l right s except thos e grante d t o th e Unite d State s Government . Printed i n th e Unite d State s o f America . @ Th e pape r use d i n thi s boo k i s acid-fre e an d fall s withi n th e guideline s established t o ensur e permanenc e an d durability . Visit th e AM S hom e pag e a t http://www.ams.org / 10 9 8 7 6 5 4 3 2 1 0 8 0 7 0 6 0 5 0 4 0 3
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