Foreword The ide a fo r writin g thi s boo k aros e a s a resul t o f conversation had wit h Shanno n Ree d whe n sh e wa s a studen t i n Mat h 4980 , t problem solvin g class , a t th e Universit y o f Missour i durin g th e F semester o f 2004 . Thi s wa s a capston e cours e fo r uppe r divisio n s dents designe d t o brin g togethe r technique s an d idea s fro m th e sta dard undergraduat e curriculum . Anothe r purpos e fo r th e cours e w to teac h student s proble m solvin g technique s an d t o prepar e the for th e nationa l Putna m examinatio n i n December . I wa s excite d discover ove r the year s that thes e goals , far fro m bein g incompatib work han d i n han d t o enhanc e th e students ' hand s o n knowledg e mathematics an d t o provid e the m wit h a glimps e int o th e worl d research an d discovery . The ide a o f a capstone clas s i s absolutely wonderfu l an d i t kee growing o n m e eac h year . To o man y undergraduat e student s for an impressio n o f mathematic s a s bein g compartmentalize d int o sp cific subject area s like analysis, algebra, numbe r theory , topolog y a others. Th e ide a o f unit y o f mathematic s an d interaction s betwe fundamental area s ar e seldo m mentione d an d almos t neve r taug The purpos e o f thi s boo k i s t o attemp t t o brea k throug h thi s b rier. I t i s a hopeles s tas k t o illustrat e eve n a smal l slive r o f exciti and surprisin g connection s tha t mathematic s i s s o ful l of . Th e a thor confine s himsel f t o the connection s tha t ar e near an d dea r t o

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