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.

Uma análise dos livros de André Perez Y Marin: um momento da história da matemática escolar brasileira no início do século XX

Pós-graduação em Educação Matemática - IGCE

Números Complexos: um estudo histórico sobre sua abordagem na coleção Matemática 2º ciclo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Avaliação na sala de aula de matemática: práticas e concepções

This research aims to understand the assessment practices used by teachers at a public state school in the city of Cunha, Sao Paulo. To this end, we interviewed five mathematics teachers, who answered a questionnaire with five questions. The responses were analyzed according to the rigor of phenomenological research. To understand the investigation region, that is to say, the meaning of evaluation, we proceeded to a review of studies on the subject in authors like Buriasco (2002), Pavanello (2006), Hoffmann (1994), expressive in Mathematics Education that allows us to explain the concept of prevailing interpretation in the area. The phenomenological analysis enabled the development of three categories open revealing the concept of evaluation of teachers investigated. The first shows the review As a way to measure the knowledge acquired by the student. His interpretation leads us to understand that for some teachers, the research subjects, the assessment becomes a method to ' measure ' the knowledge acquired by the student. The second category, expressed by As a way of understanding the student's behavior in class, shows that some of the interviewees understand the evaluation as a medium that reveals and appreciates the ways of the student behave in class. Finally, the third category refers to the evaluation by means of said instruments. On this subject the claim that the assessment is through instruments such that: evidence, exercise lists, among others. In summary, interviews and categories analyzed explain the ways in which the assessment reveals the concept of implicit learning the instruments used in the evaluation practices of teachers interviewed. However, the authors read, evaluation is a necessary and permanent teaching job in teaching, which must follow step by step the process of teaching and learning. It follows, ... (Complete abstract click electronic access below)

Alternative Tasks for the Teaching and the Learning of functions: analysis of an intervention in the High School

In this paper we focus on the application of two mathematical alternative tasks to the teaching and learning of functions with high school students. The tasks were elaborated according to the following methodological approach: (i) Problem Solving and/or mathematics investigation and (ii) a pedagogical proposal, which defends that mathematical knowledge is developed by means of a balance between logic and intuition. We employed a qualitative research approach (characterized as a case study) aimed at analyzing the didactic pedagogical potential of this type of methodology in high school. We found that tasks such as those presented and discussed in this paper provide a more significant learning for the students, allowing a better conceptual understanding, becoming still more powerful when one considers the social-cultural context of the students.

Describing some of the Dimensions that comprise the Profile of the Faculty Staff of Statistics Departments in Brazil

Statistics is a required course in virtually all undergraduate programs in Brazilian universities. In addition, undergraduate programs in Statistics are offered in many public universities. However, despite the importance of this science, there are no systematic studies in the national literature regarding the characterization of the faculty staff, which is responsible for the teaching of statistics in the country. In this context, this paper presents a description of the faculty members of undergraduate courses in Statistics. This description was based on a descriptive sample, related to aspects of their education and scientific production. A prediction of future demand for PhDs in Statistics to fill the vacancies is also provided based on the retirement of faculty members in undergraduate courses in Statistics in the country.

Learning Democracy Together in School? : Student and Teacher Attitudes in Bosnia and Herzegovina

The principal aim of this study is to examine attitudes and values, through questionnaires, among students and teachers in the last grade of primary school (grade 8) regarding issues related to authoritarianism, democracy, human rights, children rights, conflict resolution and legislation in Bosnia and Herzegovina. A second aim is to explore and analyze the role of the international community in the democratization and education processes in the light of globalization in this country through secondary sources of data, site visits and observations. Analysis of the student sample reveals suspicion towards democracy, especially when democracy was associated with politics and politicians. When the issue of democracy was de-contextualized from Bosnia and Herzegovina realities in the questionnaire, students showed more positive attitudes towards it. Students generally agreed with very strong authoritarian statements. High achieving students were more democratic, more socially responsible, more tolerant regarding attitudes towards religion, race and disabilities, and less authoritarian compared to low achievers. High achievers felt that they had influence over daily events, and were positive towards social and civil engagement. High achievers viewed politics negatively, but had high scores on the democracy scale. High achievers also agreed to a larger extent that it is acceptable to break the law. The more authoritarian students were somewhat more prone to respond that it is not acceptable to break the law. The major findings from the teacher sample show that teachers who agreed with non-peaceful mediation, and had a non-forgiving and rigid approach to interpersonal conflicts, also agreed with strong authoritarian statements and were less democratic. In general, teachers valued students who behave respectfully, have a good upbringing and are obedient. They were very concerned about the general status of education in society, which they felt was becoming marginalized. Teachers were not happy with the overloaded curricula and they showed an interest in more knowledge and skills to help children with traumatic war experiences. When asked about positive reforms, teachers were highly critical of, and dissatisfied with, the educational situation. Bosnia and Herzegovina is undergoing a transition from a state-planned economy and one party system to a market economy and a multi party system. During this transition, the country has become more involved in the globalization process than ever. Today the country is a semi-protectorate where international authorities intervene when necessary. The International community is attempting to introduce western democracy and some of the many complexities in this process are discussed in this study. Globalization processes imply contradictory demands and pressures on the education system. On one hand, economic liberalization has affected education policies —a closer alignment between education and economic competitiveness. On the other hand, there is a political and ideological globalization process underlying the importance of human rights, and the inclusiveness of education for all children. Students and teachers are caught between two opposing ideals — competition and cooperation.

The Investigation of the Ways in Which Gender Stereotypes are Perpetuated through Questioning and Assessment Strategies in Inquiry-Based Science Classroom

The purpose of this study was to investigate the questioning strategies of preservice teachers whenteaching science as inquiry. The guiding questions for this research were: In what ways do the questioning strategies of preservice teachers differ for male and female elementary students when teaching science as inquiry and how is Bloom’s Taxonomy evident within the questioning strategies of preservice teachers? Examination of the data indicated that participants asked a total of 4,158 questions to their elementary aged students. Of these questions, 974 (23%) were asked to boys, and 991 (24%) were asked to girls. The remaining questions (53%) were asked to the class as a whole, therefore no gender could be assigned to these questions. In relation to Bloom’s Taxonomy, 74% of the questions were basic knowledge, 15% were secondary comprehension, 2% were application, 4% were analysis, 1% were synthesis, and 3% were evaluation.