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Vita.

Charles Arthur Messick was born in Wilsofi, Kansas, in 1896,
but at the age of tyo nmoved with his parents to Abiline, Kansas,
where his education began. At the age of nine he moved mith his
parents to Topeka, Kansas, and there he graduated fromw the grade
schools, and from Topéka High Schoel with honors, in 1215. He
attended Washburn College at Topeka, and Kansas State Teacher's
College at Emporia from which be received the B, S. degree in the
summer of 1818. He taught four years in Kansas high schocls, after
which he went to the University of Kansas and became Agsistant
Instructor ip the Department of Matnematics in 1923. In 1925 he
received the M. A. degree in Mathematics, from the University of
Kansas, having takeq courses with Frofessors C_ H, Ashton,

Ui- G. Mitchéll,.and S. Lefschetz. Fe then Lecawe a full time

Assistant in the Cepartamert cf Matheratics at the Cniversity of ¢
Towa, remaininé‘tfie}e until 1€27, ana studying under Professor

E. W, Chittenden in additicn to his regular teaching schedule, v
From 1927 tc the time of this writing he has been Assistant

Professor of Mathematics at the University of Fleorida, Every

summer beginning with the summer cf 1925 and continuing through

the summer of 193C he has studied at the University of Chicage

in the Departmenf of Matheratics, taking courses taught by

Frofessors H, E. Slaught, C. 4, Eliss, & F. lane, E, T. Bell,

Dynham Jackscn, and others. The writer wishes to express his

sincere appreciation of the valuable instructiop and assistance

ziver by all the atove Frofessers, and mest especially to E, T.

Bell add L. M. Graves, who have supervised the writing of this

dissertaticn. Sincere thanks are expressed to them for their

valuable comments and suggestions,