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Palo Alto, CA, United States

Agency: NSF | Branch: Standard Grant | Program: | Phase: | Award Amount: 282.91K | Year: 2010

The UTMOST Project (Undergraduate Teaching in Mathematics with Open Software and Textbooks) is coupling the use of Sage - comprehensive free open source mathematics software - with existing free open textbooks, to make it possible for faculty and institutions to more easily bring the power of mathematics software to their students. Authors of open source software and open textbooks provide licenses that permit free copying and editing of their work, allowing others to adapt or extend them to suit their needs or make improvements. A major project activity is to convert existing open textbooks into web-based dynamic e-texts that integrate traditional mathematical exposition with Sage code and hands-on demonstrations. The intellectual merit of this project lies in its use of the innovative Sage environment and its active community of users and practitioners. Eight diverse undergraduate institutions are helping to test and refine these materials using a comprehensive, professional evaluation procedure. The main goal driving this project is to create technical and pedagogical tools and methods that greatly simplify the deployment and use of powerful software to increase learning and experimentation in undergraduate mathematics. The potential broader impacts of this project are strong given the distributed nature of both development and deployment.

Agency: NSF | Branch: Standard Grant | Program: | Phase: | Award Amount: 224.44K | Year: 2012

The American Institute of Mathematics (AIM) will conduct a series of three annual Research Experiences for Undergraduate Faculty (REUF) workshops during the summers of 2013, 2014, and 2015, and additional activities for participants afterwards to support continuation of research engagement sparked by the workshop. At each REUF workshop four senior mathematicians (leaders) who have experience doing research with undergraduate students will present problems in a variety of areas, after which the participants and leaders will divide into groups and work on the problems; the workshop will conclude with group presentations of each project. Most of the time will be spent doing mathematics, but there will also be whole group discussions about topics such as best practices in undergraduate research led by the organizers. Since numerical experiments and computational investigations are crucial to much of the research done with undergraduates, the workshop will also include instruction in using the free open-source mathematics software Sage. AIM directors will facilitate the management of the workshop, and participants will receive full funding.

The REUF workshop and ongoing activities will provide faculty participants whose undergraduate institutions have limited research activity with a research experience investigating open questions in the mathematical sciences and equip them to engage in research with undergraduate students at their home institutions. In addition, some participants will become involved in long-term research collaborations with other faculty at the workshop. The recruitment efforts for REUF will particularly focus on faculty at minority-serving institutions as well as underrepresented minority faculty at undergraduate colleges. The REUF project will lead to more and better undergraduate research experiences for students of the faculty participants, and greater engagement in mathematical research by the faculty participants, thus expanding and diversifying the mathematical workforce.

Agency: NSF | Branch: Continuing grant | Program: | Phase: MATHEMATICAL SCIENCES RES INST | Award Amount: 10.04M | Year: 2012

The American Institute of Mathematics (AIM) Research Conference Center will continue in its mission of promoting focused collaborative research on important topics from all areas of the mathematical sciences. These workshops are distinguished by their emphasis on identifying key problems in a given field and in establishing teams of researchers to work collaboratively toward resolving these problems. The workshop topics encompass outstanding fundamental problems as well as important applied and interdisciplinary problems facing 21st century mathematical scientists. In addition to conducting 20 workshops annually, AIM will run 30 Structured Quartet Research Ensembles per year; these are groups of four to six mathematical scientists who have an ambitious research goal and meet for a week at a time at AIM, multiple times over a multi-year period. AIM has committed to increasing diversity in the mathematical sciences workplace and has put a structure in place to ensure that such diversity occurs in all of AIMs programs. In addition, AIM holds special workshops that directly address workforce issues and strives to ensure that the discipline has a healthy pipeline to the future.

The American Institute of Mathematics was founded with the goal of fostering mathematical research through collaboration. AIMs guiding premise is that collaboration is essential to the development of modern mathematics, where the depth and breadth of fields have become so great that understanding the connections between various mathematical areas is increasingly difficult, yet many of the most important and interesting developments occur at the confluence of different research areas. AIM has created a collaborative model for workshops that facilitates collaboration, bridging the gap between the various subject areas and between the different mathematical communities. This model is complemented by the Structured Quartet Research Ensembles (SQuaREs) program, which hosts smaller groups of four to six participants to work on ambitious projects over a three-year period. The American Institute of Mathematics Research Conference Center will host 20 AIM-style workshops (each with up to thirty participants) and 30 SQuaREs per year.

Agency: NSF | Branch: Standard Grant | Program: | Phase: DISCOVERY RESEARCH K-12 | Award Amount: 449.98K | Year: 2011

The Math Teachers Circles project (MTC) is connecting mathematicians and mathematics teachers in middle schools by offering summer workshops and continued communication throughout the year. The workshops focus on mathematical problem solving and include activities that offer multiple entry points. The goal of the workshops is to increase teachers knowledge of mathematics for teaching and to help teachers use their knowledge to improve student learning of mathematics. In addition to conducting workshops, researchers are investigating what mathematics teachers learn by participating in the workshops and how teachers use what they have learned in their mathematics teaching. The American Institute of Mathematics (AIM) is facilitating Math Circles in 26 states with research sites in Albuquerque, Denver and San Francisco Bay area. Their research questions include: (1) How is the MTC model being implemented at local sites? (2) What are the effects of participation in a MTC on Teachers Mathematical Knowledge for Teaching? (3) What is the impact of MTC involvement on teachers approaches toward mathematics and classroom practice? Twelve case studies, based on classroom observations, are offering insights into how teachers use their mathematical knowledge in planning, implementing, assessing, and reflecting on their instruction.

Math Teachers Circle leaders and participants are connected by a digital network organized by AIM. Workshops are offered for mathematicians who would like to be leaders and organizers of local Math Teachers Circles, and help is provided to local Circles. The purpose of the local workshops is to develop teachers content knowledge, problem-solving skills, and mathematical habits of mind. The Math Circles supplement other professional development efforts that focus on pedagogy. The MTC model includes five criteria: content focus, active learning, coherence, approximately 50 hours of professional development, and collective participation. Participants are expected to continue to work within the networked community to develop their mathematical knowledge. The research effort is measuring teachers mathematical knowledge and conducting case studies to investigate the impact of the MTC on mathematics teaching. They are videotaping lessons and using the Mathematical Quality of Instruction observation protocol. The project evaluator is from Colorado State University.

Agency: NSF | Branch: Standard Grant | Program: | Phase: | Award Amount: 91.43K | Year: 2011

Award: DMS-1105837
Principal Investigator: Sikimeti Mau

A-infinity algebra structures have recently emerged in symplectic topology and will be investigated and extended by these projects. The principal investigator intends to study these algebraic structures in concrete examples based on Hilbert schemes of points on complex curves or complex surfaces. Part of the goal will be to extend the structures to higher categorical structures, using symplectic constructions closely related to the string diagrams of physicists. The extended algebraic structures are motivated by constructions in algebraic geometry for the same Hilbert schemes, which should have symplectic analogues by mirror symmetry. Two examples in particular that have been well studied on the symplectic side, and can function as guides, are the Heegaard Floer theory developed by low-dimensional topologists, and Seidel-Smiths symplectic Khovanov homology, a symplectically constructed invariant of knots and links. The short-term objective is to find concrete illustrations, and potential applications, of a new theory that is largely abstract, but has the potential to explain algebraic phenomena in these fields. The broader goal is to describe as much of the algebraic structure of Lagrangian Floer theory as possible in a single algebraic language coming from quilts, a recent technique in symplectic topology due to Wehrheim and Woodward.

A symplectic structure is the geometric face of Hamiltonian mechanics, in which the position and momentum coordinates of a system of moving particles are tracked and used to write out equations of motion that correspond to Newtons laws. Spaces that carry such structures are always even-dimensional, and their underlying geometry is about two-dimensional area and higher-dimensional volume rather than about length and angle, which are at the root of much of familiar geometry. New methods are coming into symplectic geometry from other subjects such as low--dimensional topology, and it appears that an algebraic formalism can be devised to carry a number of these new constructions and to reveal useful properties of them. ˇ

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