Preface fo r Instructor s

XI

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

you.

Deguang Ha n

Keri Kornelso n

David Larso n

Eric Webe r