On Monday September 15th at 3:30 in Math 357, Dr. Matt Beauregard will be talking about “Surgical Splitting”. This talk will be interactive and interesting to all levels of students. Students with exposure to differential equations or numerical methods are especially encouraged to attend.
Abstract: Time dependent mathematical models are often written in terms of partial differential equations. The spatial derivatives can then be approximated to develop a system of first order differential equations in time. The solutions can formally be written in terms of an evolution operator. A final approximation can be formulated through approximating the underlying matrix exponential. Approximating the matrix exponential can be time-consuming, especially for high dimension problems. Is it possible to split the problem? If so, how is this influenced by forcing terms, nonlinearities, or geometric considerations? We’ll be investigating these questions with some toy problems. Students with exposure to differential equations are especially encouraged to attend! Come prepared with a few pieces of paper, pen/pencil, and water to stay hydrated as we sweat through this surgical splitting procedure. (flyer in PDF form)
On Monday April 28th at 3:30, Dr. Kalanka Jayalath will be talking about “Geometrical Pattern Identification Using a Bayesian Paradigm.”
Abstract: Identifying spatially distributed point patterns plays an important role in many scientific areas including pattern recognition, computer vision, image processing and some geological applications. Current methods of identifying conic structures depend solely on algebraic or geometric distances and are known as algebraic or geometric fits respectively. This talk focusses on a novel circle and ellipse fitting technique which elicits a Bayesian philosophy on geometric distance. Statistical methods will be discussed to investigate whether the spatial pattern is reasonably attributable to a circular or elliptical pattern. We compare classical and novel circle fitting methods under various error structures. In particular, we focus on their accuracy of estimates when in the presence of noisy data, a topic that is poorly documented in the literature. Finally, our findings will be applied to a pre-historic archeological site to identify the evident geometrical structure. (Flyer in PDF form)
On Monday April 14th at 3:30 in Math 357, Dr. Lynn Greenleaf will be talking about “Estimation and Analysis of Atmospheric Vortices”.
Abstract: Intense atmospheric vortices occur in dust devils, waterspouts, tornadoes, mesocyclones and tropical cyclones. Tangential wind models have been proposed that approximate the observed tangential wind profile of at atmospheric vortex for the purpose of data analysis and prediction. Data analysis is required to demonstrate in an objective way that a parameterized tangential wind model provides an acceptable description of the tangential wind profile of an atmospheric vortex and determine if the model can be used to make accurate predictions. Using the methodology of Information Theory and Sensitivity Analysis, information content of the parameters of a vortex model show that both parameters are essential in estimation of the tangential wind profile. Uncertainty in radial, tangential and vertical winds were examined and can be used effectively to predict these quantities and their uncertainties. (flyer in PDF form)
As part of his campus visit, on Thursday April 10th at 3:30 PM in Math 357, Dr. Mathew Beauregard will be giving a talk “Numerical Linear Algebra: Can you point me in the right direction?” This talk will be geared toward undergraduates and interesting to students with linear algebra or numerical analysis background.
Abstract: Numerical approximations to time-dependent differential equations often require spatial and temporal adaptive methods to resolve the solution accurately. In such methods, the numerical solution is advanced upon solving a, potentially large, linear algebraic system of equations. The adaptation in space and time generates new matrices at each iterate. Nevertheless, changes in the matrices are nominal, while the structure of the matrices often remains the same. GMRES is a common numerical linear algebraic solver, developed in the 1990s, that approximates the solution to a linear system. In this talk, a modified GMRES method is presented. The new method takes advantage of eigenvector information obtained from prior linear algebraic solves and then uses this to increase the rate of convergence in future linear solves. (flyer in PDF form)
As part of a campus visit on Monday February 24th at 3:30 PM, Rebecca-Anne Dibbs from the University of Northern Colorado will be talking about “The Effects of Formative Assessment on Students’ Zone of Proximal Development in Introductory Calculus”.
Abstract: One of the challenges of teaching introductory calculus is the large variance in student backgrounds. Formative assessment can be used to target which students need help, but little is known about why formative assessment is effective with adult learners. The purpose of this mixed methods study was to investigate which functions of formative assessment that enable instructors to provide the scaffolding needed to engage students in an introductory calculus course within their Zones of Proximal Development during weekly group labs. By regularly collecting information from low-stakes opportunities for students to demonstrate their current understanding, instructors were able to target subsequent class discussion on critical scaffolding for student growth. The formative assessments also enabled students to evaluate their own progress and ask clarifying questions and, provided students who would not ordinarily ask questions during class opportunities for legitimate peripheral participation. (flyer in PDF form)
On Monday at 3:30 in Math 357, Kedar Nepal will be talking about “College Algebra Students’ Perceptions on Computer-aided Instruction & An Investigation of Novice College Mathematics Instructors’ Teaching Philosophies”.
Abstract: I will split this talk into two parts. During the first half, I will talk about College Algebra students’ perceptions on a computer-aided college algebra course, a redesigned model from a traditional lecture-based instruction. Students’ beginning-of-semester and end-of-semester responses were analyzed using a constant comparative method of analysis (Strauss & Corbin, 1998). During the second half, I will talk about novice college mathematics instructors’ teaching philosophies, and how their philosophies evolved over time during the pre-service and in-service phases. Three teaching philosophy statements were collected from each participant at different stages of a pre-service program ‘Seminar and Practicum in the Teaching of Collegiate Mathematics’, and three one-on-one interviews were conducted during the in-service phase. Some of the factors that influenced these novice instructors and their teaching philosophies will also be discussed. (flyer in PDF form)
On Thursday February 27th at 3:30, as part of his campus visit Dustin Owen Smith will be talking about “Eliciting Early Elementary School Students’ Informal Inferential Reasoning through Storytelling”.
Abstract:One growing area of research on statistical learning is Informal Inferential Reasoning (IIR). Makar and Rubin (2009) describe IIR as having three components: expressing uncertainty, making and evaluating claims, and drawing explicitly from the data when making or evaluating claims. There is limited research about IIR at the early levels of elementary school but this type of informal reasoning can be a powerful precursor to formal statistical learning in the middle grades (English, 2012). This presentation will discuss a method for providing opportunities for young children (Grades K, 2, and 4) to make informal inferences about data through Storytelling-Questioning. Storytelling-Questioning consists of the researcher reading students a story, and asking strategic questions, that are grounded in the story’s context and content. To understand IIR and the impact of Storytelling-Questioning, this study was built around the following research questions:
- What does Storytelling-Questioning reveal about the similarities and differences in students’ Informal Inferential Reasoning within and across grades K, 2 and 4?
- How can Storytelling-Questioning be leveraged to help early elementary school students engage in Informal Inferential Reasoning?
- What types of questions are most/least effective in engaging students in IIR?
- What types of stories and contexts are most/least effective in engaging students in IIR?
This work has potential to contribute to the description of IIR in the early grades as well as provide a practical pedagogical approach for addressing IIR in the classroom in a way that represents a new way of using storytelling to teach mathematics. Here is a flyer in PDF form