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 921/922: Real Analysis, Instructor Mikil Foss

Topics include: Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon- Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration, Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon-Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration.

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

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: Cohen Macaulay Modules, Instructor Roger Wiegand

Topics covered are: Cohen Macaulay modules, zero-dimensional rings, one-dimensional rings, hypersurfaces of finite Cohen-Macaulay type, complete and henselian rings, Krull-Remak-Schmidt, Canonical modules and duality, AR sequences and quivers, two-dimensional rings, ascent and descent of finite Cohen Macaulay type, bounded Cohen Macaulay type.

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.

Class Notes for Math 871: General Topology, Instructor Jamie Radcliffe

Topics include: Topological space and continuous functions (bases, the product topology, the box topology, the subspace topology, the quotient topology, the metric topology), connectedness (path connected, locally connected), compactness, completeness, countability, filters, and the fundamental group.

What Business Reference Librarians Need to Know about Intellectual Property: Presentations sponsored by the Patent and Trademark Depository Library Association (PTDLA) at the American Library Association Annual Conference, New Orleans, June 25, 2006

Presentations sponsored by the Patent and Trademark Depository Library Association (PTDLA) at the American Library Association Annual Conference, New Orleans, June 25, 2006 Speaker #1: Nan Myers Associate Professor; Government Documents, Patents and Trademarks Librarian Wichita State University, Wichita, KS Title: Intellectual Property Roundup: Copyright, Trademarks, Trade Secrets, and Patents Abstract: This presentation provides a capsule overview of the distinctive coverage of the four types of intellectual property – What they are, why they are important, how to get them, what they cost, how long they last. Emphasis will be on what questions patrons ask most, along with the answers! Includes coverage of the mission of Patent & Trademark Depository Libraries (PTDLs) and other sources of business information outside of libraries, such as Small Business Development Centers. Speaker #2: Jan Comfort Government Information Reference Librarian Clemson University, Clemson, SC Title: Patents as a Source of Competitive Intelligence Information Abstract: Large corporations often have R&D departments, or large numbers of staff whose jobs are to monitor the activities of their competitors. This presentation will review strategies that small business owners can employ to do their own competitive intelligence analysis. The focus will be on features of the patent database that is available free of charge on the USPTO website, as well as commercial databases available at many public and academic libraries across the country. Speaker #3: Virginia Baldwin Professor; Engineering Librarian University of Nebraska-Lincoln, Lincoln, NE Title: Mining Online Patent Data for Business Information Abstract: The United States Patent and Trademark Office (USPTO) website and websites of international databases contains information about granted patents and patent applications and the technologies they represent. Statistical information about patents, their technologies, geographical information, and patenting entities are compiled and available as reports on the USPTO website. Other valuable information from these websites can be obtained using data mining techniques. This presentation will provide the keys to opening these resources and obtaining valuable data. Speaker #4: Donna Hopkins Engineering Librarian Renssalaer Polytechnic Institute, Troy, NY Title: Searching the USPTO Trademark Database for Wordmarks and Logos Abstract: This presentation provides an overview of wordmark searching in www.uspto.gov, followed by a review of the techniques of searching for non-word US trademarks using codes from the Design Search Code Manual. These codes are used in an electronic search, either on the uspto website or on CASSIS DVDs. The search is sometimes supplemented by consulting the Official Gazette. A specific example of using a section of the codes for searching is included. Similar searches on the Madrid Express database of WIPO, using the Vienna Classification, will also be briefly described.