Anne Dougherty - US grants

This project investigates combined visual and haptic (touch) interfaces to display multi-dimensional data generated by computer models of physical systems. The focus is on data features that are difficult to convey visually, such as scalar data which fills volumes, vector fields, and tensor fields. First, tests are conducted to better understand the perception of haptic rendering elements: virtual surfaces and constraints, forces and torques, and mechanical impedances. Second, new haptic rendering modes are developed which can convey multi- dimensional data via combinations of haptic rendering elements. These modes are tested using representative visualization problems in fluid dynamics, electromagnetics, and solid mechanics. Third, visualization puzzles are developed which quantify the perceptual added value of haptic rendering modes. Both cooperative and complementary visual/haptic rendering are explored. The project seeks to discover synergistic rendering modes which produce understanding more easily than visual rendering alone. An improved visual/haptic interface enables intuitive debugging of computer models, efficient visualization of modeling results, and improved physical understanding. Such a capability benefits the conduct of scientific research in many fields, the design and analysis of engineered systems, and the education of future scientists and engineers.

The MCTP: Colorado Advantage proposal will build on existing programs and efforts within the department as well as on campus (e.g. SMART program). MCTP: Colorado Advantage will continue to attract numbers of underrepresented students to the mathematical sciences by actively collaborating with the Colorado Diversity Initiative. Support from NSF-funded MCTP: Colorado Advantage will allow the department to develop and implement strategies for sustainability, such as time for re-tasking existing department resources, working with the Deans (Engineering and Arts & Sciences Deans) and Provost to gain additional resources as well as working with successful donors capable of endowing undergraduate scholarships. The 17 faculty members in the department strongly endorse this MCTP proposal. The intellectual merit of this proposal is to introduce a large number of undergraduates to the excitement of research and to stimulate their interest in furthering their mathematical education. The ability of the Department to meet this objective can be inferred from its record with its previous VIGRE grant, which began in 1999, and trained 54 undergraduates.

Among the broader impacts of the MCTP: Colorado Advantage program are that it will significantly increase the number of students who take more advanced mathematics courses; the number of majors who have the transformative opportunity of working on serious longer term projects and research projects; and the number of students who graduate from the Department of Applied Mathematics and are well prepared for graduate school and the scientific workforce. Further its multiplier effect on other undergraduates at the University through the creation of a culture of undergraduate research activity will have longer-term implications for the University as a whole. An additional impact will be on graduate students and faculty who become involved in these critical mentorship activities as they pursue their own careers. Finally, the MCTP: Colorado Advantage proposal is a model that can be used at any research university that has a graduate program, faculty committed to undergraduate education and a will to transform itself.

Mathematics (21) This collaborative project addresses a problem that occurs in many mathematics and mathematics-related courses at the university-level across the US: high failure rates in important early college mathematics courses, especially in Calculus I. The teaching strategy being used and tested is based on the idea of using Enhanced Conceptual Development through Focused Oral Discourse, or Orals. The current work is analyzing and extending earlier work that has been focused on helping students identified as at risk of failing calculus. Based on the earlier success of reducing failure rates using effective teaching strategies, including Orals, the project team is now applying these teaching strategies to diverse users in several new settings: to classes taught in different STEM (science, technology engineering, and mathematics) departments, at a different college, and at different educational levels.

The goals of this project are to: 1) Refine, implement, and test Orals with diverse groups of learners and in diverse education settings; 2) Provide training, coaching and evaluation for facilitators of Orals including Instructors, Teaching Assistants and Undergraduate Learning Assistants; 3) Provide extensive assessment artifacts of the implementations; 4) Create a database and website of new learning materials (Orals questions for diverse courses); and 5) Improve the retention and understanding of STEM students.

Intellectual Merit: The importance of discourse in the mathematical sciences classroom has already been shown for K-12. A potentially important impact of this proposal will be to contribute to the national dialogue by conducting careful experiments that assess one method of increasing discourse: Orals. In particular, the project team will conduct proof of concept studies of Orals, in moving from small classrooms (the original setting) to large lecture sections.

Broader Impact: Many STEM majors require successful completion of a calculus sequence; however, many university students do not achieve their career goals because of their inability to pass the introductory calculus courses. This project will address this important national issue. The new work will not only be in a larger variety of mathematics courses, but also in introductory Aerospace and Mechanical Engineering courses, and at a local high school in a two-year algebra course.

The Data Cubed project will prepare students for the challenges posed by the analysis of large datasets. As governmental, scientific, and business enterprises collect, store, and process more data, many technological challenges are encountered. The analysis of big datasets requires a collaborative effort between mathematicians, statisticians, computer scientists, and domain experts. Computation (including algorithmic development), modeling (including dimensionality/complexity reduction), and visualization are all needed. The Data Cubed project will identify talented students early in their academic career and give them appropriate mentoring and increasingly advanced statistical and computational coursework. The students will proceed to data discovery research under the guidance of faculty members and partner scientists. The ultimate goal of the Data Cubed project is to increase the number of highly qualified undergraduate students who are able to apply their skills as they enter the scientific workforce and data analytics careers and to share the results of this project with the broader community.

Students will learn mathematical and statistical techniques and software systems to collect, generate, store, analyze and visualize large amounts of data. In the Data Cubed project, several new courses will be created to train students in the core computational and statistical areas that underpin the analysis of large datasets; the students will be provided with significant research opportunities in the areas of geophysical modeling, analysis of unstructured social media data, and dimensional reduction techniques and modeling. One of the research projects will use large geophysical datasets from the National Center for Atmospheric Research (NCAR) and will involve modeling heat stress in urban environments and its relationship to public health. Another will examine the role of oceans as a primary reservoir of heat for our planet, which plays a significant role in the dynamics of climate change. Yet another project will combine heuristics of social media data (e.g., tweets) during times of mass emergency with a user's social graph to develop a more comprehensive picture of the situation. These and other projects all require fundamental knowledge and understanding of how to analyze large datasets.