Writing In Math Class? Written Communication in the Mathematics Classroom

In this action research study of my seventh grade mathematics classroom, I investigated what written communication within the mathematics classroom would look like. I increased vocabulary instruction of specific mathematical terms for my students to use in their writing. I also looked at what I would have to do differently in my teaching in order for my students to be successful in their writing. Although my students said that using writing to explain mathematics helped them to better understand the math, my research revealed that student writing did not necessarily translate to improved scores. After direct instruction and practice on math vocabulary, my students did use the vocabulary words more often in their writing; however, my students used the words more like they would in spelling sentences rather than to show what it meant and how it can be applied within their written explanation in math. In my teaching, I discovered I tried many different strategies to help my students be successful. I was very deliberate in my language and usage of vocabulary words and also in my explanations of various math concepts. As a result of this research, I plan to continue having my students use writing to communicate within the mathematics classroom. I will keep using some of the strategies I found successful. I also will be very deliberate in using vocabulary words and stress the use of vocabulary words with my students in the future.

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.

Skeletal muscle major histocompatibility complex class I and II expression differences in adult and juvenile dermatomyositis

OBJECTIVE: To analyze major histocompatibility complex expression in the muscle fibers of juvenile and adult dermatomyositis. METHOD: In total, 28 untreated adult dermatomyositis patients, 28 juvenile dermatomyositis patients (Bohan and Peter's criteria) and a control group consisting of four dystrophic and five Pompe's disease patients were analyzed. Routine histological and immunohistochemical (major histocompatibility complex I and II, StreptoABComplex/HRP, Dakopatts) analyses were performed on serial frozen muscle sections. Inflammatory cells, fiber damage, perifascicular atrophy and increased connective tissue were analyzed relative to the expression of major histocompatibility complexes I and II, which were assessed as negatively or positively stained fibers in 10 fields (200X). RESULTS: The mean ages at disease onset were 42.0 +/- 15.9 and 7.3 +/- 3.4 years in adult and juvenile dermatomyositis, respectively, and the symptom durations before muscle biopsy were similar in both groups. No significant differences were observed regarding gender, ethnicity and frequency of organ involvement, except for higher creatine kinase and lactate dehydrogenase levels in adult dermatomyositis (p<0.050). Moreover, a significantly higher frequency of major histocompatibility complex I (96.4% vs. 50.0%, p<0.001) compared with major histocompatibility complex II expression (14.3% vs. 53.6%, p = 0.004) was observed in juvenile dermatomyositis. Fiber damage (p = 0.006) and increased connective tissue (p<0.001) were significantly higher in adult dermatomyositis compared with the presence of perifascicular atrophy (p<0.001). The results of the histochemical and histological data did not correlate with the demographic data or with the clinical and laboratory features. CONCLUSION: The overexpression of major histocompatibility complex I was an important finding for the diagnosis of both groups, particularly for juvenile dermatomyositis, whereas there was lower levels of expression of major histocompatibility complex II than major histocompatibility complex I. This finding was particularly apparent in juvenile dermatomyositis.

Treatment times of Class II malocclusion: four premolar and non-extraction protocols

The purpose of this study was to retrospectively compare the treatment times of Class II division 1 malocclusion subjects treated with four first premolar extractions or a non- extraction protocol and fixed edgewise appliances. Eighty- four patients were selected and divided into two groups. Group 1, treated with four first premolar extractions, consisted of 48 patients (27 males and 21 females) with a mean age of 13.03 years and group 2, treated without extractions, consisted of 36 patients (18 males and 18 females) with a mean age of 13.13 years. Group 2 was subdivided into two subgroups, 2A consisting of 16 patients treated in one phase and 2B consisting of 20 patients treated in two phases. The initial and final Treatment Priority Index (TPI), initial ages, initial mandibular crowding, and treatment times of groups 1 and 2 were compared with t- tests. These variables were also compared between group 1 and the subgroups with analysis of variance followed by Tukey's tests. The treatment times for groups 1 and 2 and subgroups 2A and 2B were 2.36, 2.47, 2.25, and 2.64 years, respectively, which were not significantly different. Treatment times with non-extraction and four premolar extraction protocols are similar.

The identification of the pillars of education in the class comprehensiveness in healthcare

The objective of the present study was to verify, based on the analysis of student portfolio narratives, if the four pillars of education were approached in the class "Comprehensiveness in health care", part of the integrated curriculum of the Baccalaureate in Nursing Program of the University of Sao Paulo at Ribeirao Preto College of Nursing. A qualitative, documental study was performed using 46 portfolios constructed during the classes. Data collection was performed using an assessment tool that contained items addressing cognitive and affective dimensions. The data were submitted to thematic categorical analysis using the pillars of education as predefined categories. The results show that the pillars of education were, apparently, included in the class. Despite the present study findings, no evidence was found that the expected competencies were actually discussed among students and faculty, according to the records regarding the evaluations of each pedagogical cycle of the studied class.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Class-specific metrics for multidimensional data projection applied to CBIR

Content-based image retrieval is still a challenging issue due to the inherent complexity of images and choice of the most discriminant descriptors. Recent developments in the field have introduced multidimensional projections to burst accuracy in the retrieval process, but many issues such as introduction of pattern recognition tasks and deeper user intervention to assist the process of choosing the most discriminant features still remain unaddressed. In this paper, we present a novel framework to CBIR that combines pattern recognition tasks, class-specific metrics, and multidimensional projection to devise an effective and interactive image retrieval system. User interaction plays an essential role in the computation of the final multidimensional projection from which image retrieval will be attained. Results have shown that the proposed approach outperforms existing methods, turning out to be a very attractive alternative for managing image data sets.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.