Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.

A Preliminary Study: Body Dysmorphic Disorder in Division I Women’s Collegiate Soccer Players

The prevalence of Body Dysmorphic Disorder (BDD) among collegiate athletes has not been clearly determined. The purpose of this study was to determine if there are symptoms of body dysmorphic disorder found in Division I women’s soccer players. The researcher hypothesized that there would be some symptoms found within the participants of sport and that there was a need to research this area further. The study consisted of four participants who participated in semi-structured interviews. The subjects were asked a series of questions from the Yale-Brown Obsessive Compulsive Scale Modified for Body Dysmorphic Disorder (BDD-YBOCS) to determine if they indicated any symptoms of BDD. The prevalence of symptoms of BDD found among these four participants was very low. There was only one athlete who scored high on the questions that could be questionable of whether the indicators or symptoms of BDD were present. In conclusion there was not enough evidence to support the research hypothesis. The sample used was not a clear representation of all Division I women’s soccer players. Further research is needed to determine if BDD symptoms are found among Division I women’s soccer players.

Class Notes for Math 905: Commutative Algebra, Instructor Sylvia Wiegand

Topics include: Rings, ideals, algebraic sets and affine varieties, modules, localizations, tensor products, intersection multiplicities, primary decomposition, the Nullstellensatz