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Preface fo r Instructor s
our RE U sit e over the pas t si x years hav e found thi s pure/applie d ap -
proach to matrix analysis exciting, especially when the applied featur e
led t o publishabl e ne w results .
The prerequisite s w e woul d recommen d fo r thi s boo k ar e a one -
semester cours e i n colleg e leve l linea r algebra , an d a one-semeste r
proof-oriented cours e i n analysis . Th e analysi s cours e i s primaril y
a maturit y requirement , i n th e sens e tha t a studen t shoul d b e wel l
acquainted wit h readin g an d creatin g mathematica l proofs .
We hav e writte n thi s boo k wit h thre e sort s o f usage s i n mind .
(1) Thi s boo k ca n serv e a s th e primar y tex t fo r a n undergrad -
uate special-topic s cours e o n frames . A n earl y draf t wa s
used ver y successfull y a t Grinnel l Colleg e i n suc h a course .
Students wh o alread y hav e a secon d cours e i n linea r alge -
bra migh t ski m ove r Chapter s 1 and 2 fairly quickly , whil e
students havin g les s linear algebr a experienc e migh t nee d t o
spend mor e tim e i n thes e chapters . I n eithe r case , suc h a
course migh t star t i n Chapte r 3 , flipping bac k t o th e previ -
ous chapters as needed for review or to learn a necessary ne w
topic. I n thi s case , one coul d reasonabl y complet e Chapter s
3, 4 , 5 , 6, an d selecte d section s fro m Chapter s 7 , 8, an d 9 in
a one-semeste r course .
(2) W e realize tha t no t ever y mathematic s curriculu m contain s
a specia l topic s cours e fo r undergraduat e students . Thi s
book woul d als o serve very wel l for a secon d cours e i n linea r
algebra, usin g frame s a s a n applicatio n t o demonstrat e th e
new theory. Th e instructo r coul d spen d tim e carefull y goin g
through th e topic s i n the firs t tw o chapter s befor e introduc -
ing frames . Thi s cours e migh t reasonabl y cove r Chapter s
1, 2 , 3 (section s 3. 1 throug h 3.5) , 4 , 5 , an d 6 wit h a fe w
selected section s a s tim e permit s fro m th e othe r chapters .
(3) Becaus e thi s boo k wa s s o heavil y motivate d b y ou r RE U
experiences, w e naturall y intende d i t t o b e a resourc e fo r
summer researc h student s a s they lear n abou t fram e theor y
and matri x analysis . Th e metho d use d i n th e Texa s A& M
REU wa s to sen d th e tex t t o students befor e th e star t o f th e
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