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.

Germline-Specific MATH-BTB Substrate Adaptor MAB1 Regulates Spindle Length and Nuclei Identity in Maize

Germline and early embryo development constitute ideal model systems to study the establishment of polarity, cell identity, and asymmetric cell divisions (ACDs) in plants. We describe here the function of the MATH-BTB domain protein MAB1 that is exclusively expressed in the germ lineages and the zygote of maize (Zea mays). mab1 (RNA interference [RNAi]) mutant plants display chromosome segregation defects and short spindles during meiosis that cause insufficient separation and migration of nuclei. After the meiosis-to-mitosis transition, two attached nuclei of similar identity are formed in mab1 (RNAi) mutants leading to an arrest of further germline development. Transient expression studies of MAB1 in tobacco (Nicotiana tabacum) Bright Yellow-2 cells revealed a cell cycle-dependent nuclear localization pattern but no direct colocalization with the spindle apparatus. MAB1 is able to form homodimers and interacts with the E3 ubiquitin ligase component Cullin 3a (CUL3a) in the cytoplasm, likely as a substrate-specific adapter protein. The microtubule-severing subunit p60 of katanin was identified as a candidate substrate for MAB1, suggesting that MAB1 resembles the animal key ACD regulator Maternal Effect Lethal 26 (MEL-26). In summary, our findings provide further evidence for the importance of posttranslational regulation for asymmetric divisions and germline progression in plants and identified an unstable key protein that seems to be involved in regulating the stability of a spindle apparatus regulator(s).

Dynamic networks, text analysis and Gephi: the art math

In numerosi campi scientici l'analisi di network complessi ha portato molte recenti scoperte: in questa tesi abbiamo sperimentato questo approccio sul linguaggio umano, in particolare quello scritto, dove le parole non interagiscono in modo casuale. Abbiamo quindi inizialmente presentato misure capaci di estrapolare importanti strutture topologiche dai newtork linguistici(Degree, Strength, Entropia, . . .) ed esaminato il software usato per rappresentare e visualizzare i grafi (Gephi). In seguito abbiamo analizzato le differenti proprietà statistiche di uno stesso testo in varie sue forme (shuffolato, senza stopwords e senza parole con bassa frequenza): il nostro database contiene cinque libri di cinque autori vissuti nel XIX secolo. Abbiamo infine mostrato come certe misure siano importanti per distinguere un testo reale dalle sue versioni modificate e perché la distribuzione del Degree di un testo normale e di uno shuffolato abbiano lo stesso andamento. Questi risultati potranno essere utili nella sempre più attiva analisi di fenomeni linguistici come l'autorship attribution e il riconoscimento di testi shuffolati.

Traduzione per il web nelle istituzioni europee. Proposta di localizzazione di una sezione di sito della dg azione per il clima

The aim of this dissertation is to provide an adequate translation from English into Italian of a section of the European Commission's site, concerning an environmental policy tool whose aim is to reduce the EU greenhouse gas emissions, the Emissions Trading System. The main reason behind this choice was the intention to combine a personal interest in the domain of sustainability development with the desire to delve deeper into the knowledge of the different aspects involved in the localisation process. I also had the possibility to combine these two with my interest in the universe of the European Union. I therefore worked on the particular language of this supranational organisation and for this reason I had the opportunity to experience a very stimulating work placement at the Directorate-General for Translation in Brussels. However, the choice of the text was personal and the translation is not intended for publication. The work is divided into six chapters. In the first chapter the text is contextualised within the framework of the EU, and its legislation on multilingualism. This has consequences on the languages that are used by the drafters of the official documents and on the languages used by translators. The text originates from those documents, but it needs to be adapted to different receivers. The second chapter investigates the process of website localisation. The third chapter offers an analysis of the source text and of the prospective target text. In the fourth chapter the resources created and used for the translation of the text are described. A comparison is made between the resources of the translation service of the European Commission and the ones created specifically for this project: a translation memory, exploited through the use of a CAT tool, and two corpora. The fifth chapter contains the actual translation, side-by-side with the source text, while the sixth one provides a comment on the translation strategies.

Create Math Recital

Guest musicians: Heather Lingle and Mark Hayden

Gute Arbeit gibt herrlichen Lohn, in einer Predigt über das Evangelium am Sonntage Septuagesimae, Math. XX. 1. - 16. in der Kirche St. Leonhard in Stutgard, 1738 : mit einer eingeflossenen Anweisung, wie die vorsehende Execution des verurtheilten Juden, Joseph Süß Oppenheimers, christlich anzusehen und zu gebrauchen seye, ...

von Georg Cunrad Rieger

A total variation discontinuous Galerkin approach for image restoration

The focal point of this paper is to propose and analyze a P 0 discontinuous Galerkin (DG) formulation for image denoising. The scheme is based on a total variation approach which has been applied successfully in previous papers on image processing. The main idea of the new scheme is to model the restoration process in terms of a discrete energy minimization problem and to derive a corresponding DG variational formulation. Furthermore, we will prove that the method exhibits a unique solution and that a natural maximum principle holds. In addition, a number of examples illustrate the effectiveness of the method.