Physical Sciences and Mathematics Commons^™

Homology Of Artinian Modules Over Commutative Noetherian Rings, Micah J. Leamer

Department of Mathematics: Dissertations, Theses, and Student Research

This work is primarily concerned with the study of artinian modules over commutative noetherian rings.

We start by showing that many of the properties of noetherian modules that make homological methods work seamlessly have analogous properties for artinian modules. We prove many of these properties using Matlis duality and a recent characterization of Matlis reflexive modules. Since Matlis reflexive modules are extensions of noetherian and artinian modules many of the properties that hold for artinian and noetherian modules naturally follow for Matlis reflexive modules and more generally for mini-max modules.

In the last chapter we prove that if the Betti …

Groups And Semigroups Generated By Automata, David Mccune

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups ``expanding automaton semigroups''. We show that this class strictly contains the class of automaton semigroups, and we show that the class of asynchronous automaton semigroups strictly contains the class of expanding automaton semigroups. We demonstrate that undecidability arises in the actions of expanding automaton semigroups and semigroups …

On A Family Of Generalized Wiener Spaces And Applications, Ian Pierce

Department of Mathematics: Dissertations, Theses, and Student Research

We investigate the structure and properties of a variety of generalized Wiener spaces. Our main focus is on Wiener-type measures on spaces of continuous functions; our generalizations include an extension to multiple parameters, and a method of adjusting the distribution and covariance structure of the measure on the underlying function space.

In the second chapter, we consider single-parameter function spaces and extend a fundamental integration formula of Paley, Wiener, and Zygmund for an important class of functionals on this space. In the third chapter, we discuss measures on very general function spaces and introduce the specific example of a generalized …

Extremal Trees And Reconstruction, Andrew Ray

Department of Mathematics: Dissertations, Theses, and Student Research

Problems in two areas of graph theory will be considered.

First, I will consider extremal problems for trees. In these questions we examine the trees that maximize or minimize various invariants. For instance the number of independent sets, the number of matchings, the number of subtrees, the sum of pairwise distances, the spectral radius, and the number of homomorphisms to a fixed graph. I have two general approaches to these problems. To find the extremal trees in the collection of trees on n vertices with a fixed degree bound I use the certificate method. The certificate is a branch invariant, …

Packings And Realizations Of Degree Sequences With Specified Substructures, Tyler Seacrest

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation focuses on the intersection of two classical and fundamental areas in graph theory: graph packing and degree sequences. The question of packing degree sequences lies naturally in this intersection, asking when degree sequences have edge-disjoint realizations on the same vertex set. The most significant result in this area is Kundu's k-Factor Theorem, which characterizes when a degree sequence packs with a constant sequence. We prove a series of results in this spirit, and we particularly search for realizations of degree sequences with edge-disjoint 1-factors.

Perhaps the most fundamental result in degree sequence theory is the Erdos-Gallai Theorem, characterizing …

Annihilators Of Local Cohomology Modules, Laura Lynch

Department of Mathematics: Dissertations, Theses, and Student Research

In many important theorems in the homological theory of commutative local rings, an essential ingredient in the proof is to consider the annihilators of local cohomology modules. We examine these annihilators at various cohomological degrees, in particular at the cohomological dimension and at the height or the grade of the defining ideal. We also investigate the dimension of these annihilators at various degrees and we refine our results by specializing to particular types of rings, for example, Cohen Macaulay rings, unique factorization domains, and rings of small dimension.

Adviser: Thomas Marley

Making Connections Between Science And Equity: A Motivation To Teach Science In Elementary Grades, Grinell Smith, Colette Rabin

Faculty Publications

Teacher quality is among the strongest correlates of student outcomes. However, only about a quarter of the nation’s elementary teachers consider themselves qualified to teach science. In this descriptive and exploratory study, we investigated whether helping pre-service teacher candidates explore connections between science and issues of equity, particularly around sustainability issues, could help them see the importance of teaching science to their students more often. Qualitative and quantitative data were collected from 59 students enrolled in revised science methods courses at a large public university. Our findings suggest that positioning science instruction thusly was perceived as a strong motivator to …

The Theory Of Discrete Fractional Calculus: Development And Application, Michael T. Holm

Department of Mathematics: Dissertations, Theses, and Student Research

The author's purpose in this dissertation is to introduce, develop and apply the tools of discrete fractional calculus to the arena of fractional difference equations. To this end, we develop the Fractional Composition Rules and the Fractional Laplace Transform Method to solve a linear, fractional initial value problem in Chapters 2 and 3. We then apply fixed point strategies of Krasnosel'skii and Banach to study a nonlinear, fractional boundary value problem in Chapter 4.

Adviser: Lynn Erbe and Allan Peterson

Collaborative Strategic Board Games As A Site For Distributed Computational Thinking, Matthew Berland, Victor R. Lee

Instructional Technology and Learning Sciences Faculty Publications

This paper examines the idea that contemporary strategic board games represent an informal, interactional context in which complex computational thinking takes place. When games are collaborative – that is, a game requires that players work in joint pursuit of a shared goal – the computational thinking is easily observed as distributed across several participants. This raises the possibility that a focus on such board games are profitable for those who wish to understand computational thinking and learning in situ. This paper introduces a coding scheme, applies it to the recorded discourse of three groups of game players, and provides qualitative …

Iowa Academy Of Science: The New Bulletin, V07n1, Spring 2011, Iowa Academy Of Science

New Bulletin

Inside This Issue:

--Message from the Executive Director

--123rd Annual meeting of the Iowa Academy of Science

--Candidates for Iowa Academy of Science President

--Candidates for Iowa Academy of Science Board of Directors

--Candidate for Iowa Science Teaching Section Vice Section Chair

--Iowa Science Teaching Section Fall Conference

--Iowa Academy of Science – Election 2011

--Welcome Corporate Members

--IAS Corporate Memberships

--2011 IAS Speaker Series at the Saylorville Visitor Center

--IAS Welcomes Executive Assistant, Debbie Dean

--Wanted: Saylorville Gift Shop Coordinator

--Announcements, Events & Deadlines

Astr 404: Stellar Astrophysics, Edward Schmidt

Department of Physics and Astronomy: Syllabi

Syllabus for ASTR 404: Stellar Astrophysics for Spring 2011 semester.

Epistemic Strategies For Solving Two-Dimensional Physics Problems, Mary Elyse Hing-Hickman

Physics Theses & Dissertations

An epistemic strategy is one in which a person takes a piece of knowledge and uses it to create new knowledge. Students in algebra and calculus based physics courses use epistemic strategies to solve physics problems. It is important to map how students use these epistemic strategies to solve physics problems in order to provide insight into the problem solving process.

In this thesis three questions were addressed: (1) What epistemic strategies do students use when solving two-dimensional physics problems that require vector algebra? (2) Do vector preconceptions in kinematics and Newtonian mechanics hinder a student's ability to apply the …

Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette

Department of Mathematics: Dissertations, Theses, and Student Research

In this work, I offer an alternative presentation theory for C*-algebras with applicability to various other normed structures. Specifically, the set of generators is equipped with a nonnegative-valued function which ensures existence of a C*-algebra for the presentation. This modification allows clear definitions of a "relation" for generators of a C*-algebra and utilization of classical algebraic tools, such as Tietze transformations.

Wind For Schools: Fostering The Human Talent Supply Chain For A 20% Wind Energy Future, Ian Baring-Gould

Publications (E)

As the United States dramatically expands wind energy deployment, the industry is challenged with developing a skilled workforce and addressing public resistance. Wind Powering America’s Wind for Schools project addresses these issues by:
• Developing Wind Application Centers (WACs) at universities; WAC students assist in implementing school wind turbines and participate in wind courses
• Installing small wind turbines at community “host” schools
• Implementing teacher training with interactive curricula at each host school.

Education In The Environment: A Strategy For Continued Interagency Outdoor Education Programming: Quarterly Progress Report: Period Ending February 28, 2011, Margaret N. Rees

Reports (PLI Education)

Highlights of the university’s focused efforts during the past three months include the following:

• One Families in Nature events was held, benefitting approximately 25 people.
• Presentations were given about the Nevada Children’s Outdoor Bill of Rights to senior staff at Clark County Parks and Recreation and to the Southern Nevada Regional Open Space and Trails working group.
• A total of 12 people completed all requirements and successfully graduated from the Nevada State Certification in Environmental Education and Interpretation program.
• Forever Earth was scheduled for 29 days and served 975 people.

How Do Mathematicians Make Sense Of Definitions?, Laurie O. Cavey, Margaret T. Kinzel, Thomas A. Kinzel, Kathleen L. Rohrig, Sharon B. Walen

Laurie O. Cavey

It seems clear that students’ activity while working with definitions differs from that of mathematicians. The constructs of concept definition and concept image have served to support analyses of both mathematicians’ and students’ work with definitions (c.f. Edwards & Ward, 2004; Tall & Vinner, 1981). As part of an ongoing study, we chose to look closely at how mathematicians make sense of definitions in hopes of informing the ways in which we interpret students’ activity and support their understanding of definitions. We conducted interviews with mathematicians in an attempt to reveal their process when making sense of definitions. A striking …

How Do Mathematicians Make Sense Of Definitions?, Laurie O. Cavey, Margaret T. Kinzel, Thomas A. Kinzel, Kathleen L. Rohrig, Sharon B. Walen

Margaret T. Kinzel

It seems clear that students’ activity while working with definitions differs from that of mathematicians. The constructs of concept definition and concept image have served to support analyses of both mathematicians’ and students’ work with definitions (c.f. Edwards & Ward, 2004; Tall & Vinner, 1981). As part of an ongoing study, we chose to look closely at how mathematicians make sense of definitions in hopes of informing the ways in which we interpret students’ activity and support their understanding of definitions. We conducted interviews with mathematicians in an attempt to reveal their process when making sense of definitions. A striking …

The Complexity Of Reform Efforts In Science Curriculum And Instruction: A Case Study Of The Illinois Mathematics And Science Academy Chemistry Teacher, Tang Wee Teo

IMSA History

This study explores how teacher-initiated site-based reform in a specialized STEM school is conceptualized and enacted, how and why curriculum reform ideas change in the process of enactment, what qualities of teacher agency are entailed, how these qualities are acquired, interplayed, become generative, and/or are influenced to effect different curriculum reform outcomes, and how different conditions support and further teacher agency to make a more defensible curriculum.

In a critical case study of a highly experienced and qualified science teacher, I follow a teacher who initiated efforts to reform the advanced chemistry curriculum. This teacher wanted to make the curriculum …

Predictors Of Student Outcomes In Developmental Math At A Public Community And Technical College, Linda Darlene Hunt

Theses, Dissertations and Capstones

With the wide range of abilities of community college students, proper course placement is crucial. Therefore, having better predictors of success can help improve placement of students for their achievement. This study analyzed student predictors, instructor predictors, and classroom predictors in relation to student final exam score and student final grade in Elementary Algebra and Intermediate Algebra classes. Student predictors included gender, ACT math score, SAT math score, community college enrollment, math pretest score, and ASC grade. Instructor predictors included gender, employment status, Mozart music use, and ALEKS software use. Classroom predictors included time of day, number of class meetings …

Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee

Mathematics Faculty Publications

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …

Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave

Faculty Publications

The Oregon Mathematics Leadership Institute (OMLI) project served 180 Oregon teachers, and 90 administrators, across the K-12 grades from ten partner districts. OMLI offered a residential, three-week summer institute. Over the course of three consecutive summers, teachers were immersed in a total of six mathematics content classes– Algebra, Data & Chance, Discrete Mathematics, Geometry, Measurement & Change, and Number & Operations—along with an annual collegial leadership course. Each content class was designed and taught by a team of expert faculty from universities, community colleges, and K-12 districts. Each team chose a few “big ideas” on which to focus the course. …

Metaphors, Metonymies, Modes And Linear Algebra, Persis Samanta Beaven

Open Access Theses & Dissertations

The analysis focused on the presence of different thinking modes, metonymies, and metaphors found on the interview responses to questions related to linear independence, span, and spanning sets of four students taking their first linear algebra course at the college level. The findings provide insight of how first year linear algebra students move from one thinking mode to another and what kind of metonymies and metaphors are used to construct new knowledge. The main purpose of this research was to document and determine the main characteristics that categorize the four students' reasoning.

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti

Mathematics Faculty Publications

This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.

On The Betti Number Of Differential Modules, Justin Devries

Department of Mathematics: Dissertations, Theses, and Student Research

Let R = k[x₁, ..., x_n] with k a field. A multi-graded differential R-module is a multi-graded R-module D with an endomorphism d such that d² = 0. This dissertation establishes a lower bound on the rank of such a differential module when the underlying R-module is free. We define the Betti number of a differential module and use it to show that when the homology ker d/im d of D is non-zero and finite dimensional over k then there is an inequality rank_R D ≥ 2ⁿ. This …

Impulse-Momentum Diagrams, David Rosengrant

Faculty Articles

Multiple representations are a valuable tool to help students learn and understand physics concepts. Furthermore, representations help students learn how to think and act like real scientists. These representations include: pictures, free‐body diagrams, energy bar charts, electrical circuits, and, more recently, computer simulations and animations. However, instructors have limited choices when they want to help their students understand impulse and momentum. One of the only available options is the impulse‐momentum bar chart. The bar charts can effectively show the magnitude of the momentum as well as help students understand conservation of momentum, but they do not easily show the actual …

Flood Frequency Estimation By Neyman-Scott Rectangular Pulse Rainfall Model And Topmodel, Richard Bernatz

Journal of the Iowa Academy of Science: JIAS

A spatial-temporal Neyman-Scott Rectangular Pulse (NSRP) stochastic rainfall model is developed for seasonal-continuous simulation to project annual discharge probabilities from a relatively small watershed, the 1395 km2 Upper Iowa River watershed upstream from Decorah, Iowa. NSRP rainfall data is used as rainfall input to TOPMODEL, a conceptual, semidistributed rainfall runoff model, to calculate river discharge at a site common to the United States Geological Survey (USGS) gauging station in Decorah, Iowa. Annual peak flows based on simulated rainfall are used to fit a log-Pearson type III distribution to project 1 %-, 0.2%-, and 0.1 %-annual discharges. These results are compared …

Current Status Of Lichen Diversity In Iowa, James T. Colbert

Journal of the Iowa Academy of Science: JIAS

No abstract provided.

Editorial Board & Iowa Academy Of Sciences Officers And Directors

Journal of the Iowa Academy of Science: JIAS

No abstract provided.

Table Of Contents (Back Cover)

Journal of the Iowa Academy of Science: JIAS

No abstract provided.

Cover

Journal of the Iowa Academy of Science: JIAS

No abstract provided.