Maxwell Arboretum Anniversary Celebration

What a pleasure it is to have this opportunity to welcome you to campus today as we celebrate the 35th anniversary of the Earl G. Maxwell Arboretum. Henry Van Dyke once wrote that "He that planteth a tree ... provideth a kindness for many generations, and faces that he hath not seen shall bless him."

Review of The Biology of Freshwater Wetlands: Biology of Habitats by Arnold G. van der Valko

Wetland ecology is a relatively new field that developed from an initial interest in a few direct benefits that wetlands provide to society. Consequently, much early scientific work was stimulated by economic returns from specific wetland services, such as production of peat and provision of habitat for economically valuable wildlife (e.g., waterfowl and furbearers). Over time, societal interest in wetlands broadened, and these unique habitats are now valued for many additional services, including some that bear non market value. Common examples include carbon sequestration, flood reduction, water purification, and aesthetics. The increased recognition of the importance of wetlands has generated a diversity of job opportunities in wetland ecology and management. Despite the increased knowledge base and enhanced job market, I am not aware of any institutions that offer specialty degrees in this new discipline. Indeed, relatively few institutions offer specific wetland ecology classes, with Arnold G. van der Valk and a few of his peers at other universities being notable exceptions.

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.

Class Notes for Math 918: Homological Conjectures, Instructor Tom Marley

This course was an overview of what are known as the “Homological Conjectures,” in particular, the Zero Divisor Conjecture, the Rigidity Conjecture, the Intersection Conjectures, Bass’ Conjecture, the Superheight Conjecture, the Direct Summand Conjecture, the Monomial Conjecture, the Syzygy Conjecture, and the big and small Cohen Macaulay Conjectures. Many of these are shown to imply others. This document contains notes for a course taught by Tom Marley during the 2009 spring semester at the University of Nebraska-Lincoln. The notes loosely follow the treatment given in Chapters 8 and 9 of Cohen-Macaulay Rings, by W. Bruns and J. Herzog, although many other sources, including articles and monographs by Peskine, Szpiro, Hochster, Huneke, Grith, Evans, Lyubeznik, and Roberts (to name a few), were used. Special thanks to Laura Lynch for putting these notes into LaTeX.

Class Notes for Math 918: Local Cohomology, Instructor Tom Marley

Topics include: Injective Module, Basic Properties of Local Cohomology Modules, Local Cohomology as a Cech Complex, Long exact sequences on Local Cohomology, Arithmetic Rank, Change of Rings Principle, Local Cohomology as a direct limit of Ext modules, Local Duality, Chevelley’s Theorem, Hartshorne- Lichtenbaum Vanishing Theorem, Falting’s Theorem.