American Institute Of Mathematics

Programs: Aim research conference center (arcc): a model for collaborative researcharcc hosts focused workshops in all areas of the mathematical sciences. Arcc focused workshops are distinguished by their emphasis on a specific mathematical goal, such as making progress on a significant unsolved problem, understanding the proof of an important new result, or examining the convergence of two distinct areas of mathematics. Aim focused workshops provide an ideal forum for a team of researchers working together to map out strategies, set priorities, work toward a solution, and set in place a framework for progress on important mathematical problems. The leaders in each field are involved in the planning of the workshops, and junior scientists and graduate students are active participants. Special attention is devoted to facilitate collaborations which include women, minorities, and researchers at primarily undergraduate institutions. The purpose of aim's research program called squares (structured quartet research ensembles) is to allow a dedicated group of four to six mathematicians to spend a week at aim in san jose, california with the possibility of returning in following years. A square could arise as a follow-up to an aim workshop or it could be a free-standing activity. Aim will provide both the research facilities and the financial support for each square group. Aim will solicit square proposals in all areas of pure and applied mathematics. Preference is given to groups which contain a mix of junior and senior researchers and to groups which have participants from north america. Squares usually meet during weeks when there are no arcc workshops scheduled. Twenty-two workshops were held in 2017 involving 539 participants. Forty squares workshops were held in 2017 involving 186 participants.

directed grants:the following directed grants were active during 2017:1. Research experiences for undergraduate faculty (reuf)the goals of reuf are (a) to rekindle or enhance a love of doing original mathematics among undergraduate faculty participants, (b) to prepare participants to engage in research with undergraduate students at their home institutions, in some cases using the problems presented, (c) to involve some participants in long-term research collaborations, and (d)to establish a network of faculty at primarily undergraduate institutions together with faculty at research universities who support collaboration and undergraduate research. Progress continued through 2017 by the pi. 2. Open resources for the mathematical curriculumthis exploration project will (1) provide materials such as textbook content, videos, interactive applets, and instructor guides; (2) identify optimal methods for building comprehensive, quality-controlled, and curated libraries of freely reusable instructional materials for college-level mathematics courses; and (3) investigate the impact of such a library on faculty adoption of evidence-based teaching practices. The materials will be created and curated collaboratively, and the project will provide training in the development and use of such content. The project will explore how this new approach enables instructors to locate and utilize a variety of curricular materials in the classroom. Progress continued through 2017 by the pi. 3. Analytical theory of l-functionsthis research project centers on the connections between number theory and random matrix theory. In particular, the study of prime numbers and divisors is now influenced by the work of physicists in modeling high energy systems by understanding the statistics of random matrix theory. This project explores the relationship between these apparently independent areas of research. The work studies the analytical theory of l-functions, which are fundamental objects in number theory that encode arithmetic information. Progress continued through 2017 by the pi. 4. Collaborative research: aim & icerm research experience for undergraduate faculty (reuf)enabling more americans to earn undergraduate degrees in science, technology, engineering and mathematics (stem) is important to improving american innovation capabilities. Participating in research as undergraduates improves retention in stem majors and encourages students to pursue graduate degrees. Faculty at colleges and universities that focus on undergraduate education are critical to this mission, yet in many cases such faculty receive little support to do research with the students they teach or continue their own research, and doctoral programs often fail to train their graduates to mentor undergraduate research. To address this need, the american institute of mathematics and the institute for computational and experimental research in mathematics will conduct a series of four annual research experiences for undergraduate faculty (reuf) workshops during the summers of 2016, 2017, 2018 and 2019. Progress continued through 2017 by the pi. 5. Collaborative research: utmost: undergraduate teaching in mathematics with open software and textbooksthe utmost 2. 0 project will design, develop, and study innovative approaches to the teaching and learning of undergraduate mathematics using open software and electronic textbooks. This project will study students' use of electronic textbooks when these are made freely available in a variety of formats and on a variety of devices. These textbooks will support interactive computation through a seamless integration of sage, the leading open-source computing system for mathematics. The main vehicles for this integration with sagemathcloud, a rich online environment for computation and collaboration between students and their course instructor, and sage cells, self-contained interactive calculation modules that can be embedded in any web page while requiring no software installation or prior knowledge of sage, because the commands are pre-loaded. Additionally, utmost 2. 0 will support the further adoption of mathbook xml, an authoring platform that enables the creation of highly functional, open-source textbooks - in particular, textbooks which can exist both in print and in an online format that contains sage cells. The project includes technical improvements to sage cells which will make it easier for instructors to create their own sage cells for their particular course needs. A catalog of sage cells will be curated, which will further lower the barrier to widespread adoption. Progress continued through 2017 by the pi. 6. Math festivals & math outreach projectsvarious activities and projects that support locally organized events that inspire k-12 students to expore mathematics through collaborative, creative problem-solving.

investigating the impact of math teachers' circles on mathematical knowledge for teaching and classroom practice:the math teachers' circle 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 mathematical teachers learn by participating in the workshops and how teachers use what they have learned in their mathematical teaching. Progress continued through 2017 by the pi.