X Preface illustrations here . Thi s chapte r i s a grea t introductio n t o som e o f the man y importan t relationship s amon g th e calculu s o f variations , complex analysis , an d differentia l geometry . Differential equation s fo r modelin g traffi c flo w ar e derive d an d analyzed i n th e chapte r b y Barbar a Keyfitz . Th e continuu m mode l derived her e i s natural, consistent , an d lead s bot h t o man y observe d familiar discontinuous phenomen a suc h a s shoc k wave s an d t o man y important ope n mathematica l problems . I t i s a grea t exampl e o f the fruitfu l interpla y betwee n pur e an d applie d mathematics . Prope r careful modelin g no t onl y give s bette r scientifi c application s bu t re - veals beautifu l ofte n hidde n mathematica l structures . On Saturda y afternoo n o f the Ric e conference , student s als o ha d the opportunit y t o activel y participat e i n Stev e Cox' s experiment s with vibratin g string s (se e th e illustration s i n Chapte r 3 ) o r wit h Frank Morgan' s soa p film s an d soa p bubble s o r t o hea r fro m Robi n Forman abou t man y recen t ope n problem s i n mathematics . Th e for - mat o f the Calculu s o f Variations Conferenc e worke d well , and thre e other similarl y structure d undergraduat e conference s hav e since bee n held a t Rice : Low Dimensional Geometry and Topology, Geometric Aspects of Combinatorics, an d Mathematical Problems in Biology. The editor appreciates the great patience and help of Ed Dunne of the America n Mathematica l Societ y i n assemblin g thi s boo k an d th e suggestion of Carl Pomerance for the title "Si x Themes on Variation".
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