Preface fo r Instructor s
This book i s intended t o provide a n introduction t o finite frames , pre -
sented a t a leve l suitabl e fo r student s i n th e late r stage s o f thei r un -
dergraduate studies . Thi s boo k evolve d fro m th e result s o f Deguan g
Han an d Dav e Larso n i n [42] , whic h forme d th e kerne l fo r materia l
about frame s presente d i n a n NSF-sponsore d RE U (Researc h Expe -
rience fo r Undergraduates ) a t Texa s A& M Universit y entitle d Matrix
Analysis and Wavelets. Th e RE U wa s le d b y Dav e Larso n whil e Eri c
Weber an d Ker i Kornelso n acte d a s mentor s an d co-instructors .
The REU student s foun d frame s particularl y enticin g because th e
questions ca n be approached usin g techniques fro m linea r algebr a an d
geometry. The y wer e excite d b y th e fac t tha t ther e ar e interestin g
open question s regardin g frame s i n finite dimensions , an d eve n mor e
enthusiastic onc e the y realize d tha t frame s hav e widesprea d applica -
tions to a variety of mathematical, scientific , an d industria l problems .
We wished to develop a resource which would help undergraduate stu -
dents gai n acces s t o thi s burgeonin g are a o f mathematics .
The stud y o f finite frame s provide s a n excellent , highl y motivat -
ing framewor k (pardo n th e pun ) i n whic h t o introduc e th e essential s
of matri x analysi s an d th e rudiment s o f finite-dimensional operato r
theory. Student s lear n th e mathematica l theor y whil e simultaneousl y
seeing how operator theor y i s used t o develo p a body o f results abou t
frames. Man y o f th e 5 0 o r s o student s wh o hav e participate d i n
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