Preface fo r Instructor s
summer program, s o that the y could start readin g and work -
ing ou t th e exercise s i n th e firs t thre e chapters . Onc e th e
program starte d up , th e mentor s gav e lecture s ove r th e ke y
ideas an d topic s in the material . Student s use d the tex t a s a
reference a s the y bega n workin g o n researc h problems . W e
also foun d tha t th e mor e advance d student s i n th e progra m
began volunteerin g t o presen t lectures .
The chapte r entitle d Student Presentations i s intende d t o giv e a
tutorial o n a selectio n o f topics , i n suc h a wa y tha t goo d student s
can lear n an d compos e individua l o r smal l grou p presentation s o n
the topics . Fo r instance , on e o f thes e i s a detaile d expositio n o n
the proo f o f th e Pola r Decompositio n Theore m i n finite dimensions .
In thi s way , student s ca n ge t involve d i n th e clas s b y actuall y givin g
lectures on important topics . Th e presenters gai n valuable experienc e
communicating a technical proo f t o their peers , while giving the othe r
students a chang e o f styl e an d pac e fro m th e instructor' s lectures .
The las t chapter , Anecdotes, tell s som e storie s abou t differen t
types o f student s a s the y lear n abou t frames . Wit h these , w e inten d
to offer snapshot s of the various settings - classrooms , REU programs ,
independent studie s - i n whic h w e find student s excite d b y thi s sub -
ject. Th e author s welcom e you r feedbac k an d suggestions . We' d als o
enjoy hearin g you r "anecdotes" , sinc e we were able to share our s wit h
Deguang Ha n
Keri Kornelso n
David Larso n
Eric Webe r
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