The traditional organization of NSF annual reports is not very well-adapted to VIGRE activities, so we replace it with a single narrative about our project so far. GRADUATE PROGRAMS Operations Shortly after the recommendation to award was announced, we called for proposals for graduate fellowships for fall 2006 and spring 2007. As always, proposals are solicited from students in Mathematics and Applied Mathematics and are reviewed by a panel of faculty from both units. Students have a chance to revise their proposals once based on feedback from the panel. In this round, twelve proposals were received and 11 were fully or partially awarded. Proposed academic goals included finishing the dissertation, passing comprehensive oral exams, giving papers at conferences, and taking independent studies to explore potential dissertation topics. Professional development activities ranged from the traditional summer qual study leadership, super TA positions, and seminar organization to a Sonia Kovalevsky high school math day, development of web resources for vector calculus, and participation in a course in mentoring which among other things prepared graduate students to be mentors for the 2007 Arizona Summer Program. First-summer fellowships were awarded to 8 first-year graduate students to support study for the qualifying exams. Three of the 4 Math students and 1 of the Applied Math students passed at the highest level and the others passed at the intermediate level. Thirteen of 14 incoming PhD students in Math participated in the Integration Workshop. On the basis of that experience, 2 were placed on two-year cores and the other 12 started all three core courses. Several students took and passed at least one of the three parts of the qualifying exams before classes began. Of the 12 students on a traditional core program, 11 have chosen to stay in Tucson during summer 2007 and study for quals and 6 of these have first-summer fellowships to support their studies. (The others are foreign and are supported with departmental resources.) For 2006/07 the Program in Applied Mathematics recruited a class of 7 students including 3 females and 1 minority (a Hispanic male). In keeping with Program practices a careful assessment of the new class is made at the beginning of the Fall semester to determine the choice of a one or two year core. These decisions and the design of the two year program of study are made in close consultation with the students. Of the 2006/07 class, two students were put on a two year core. All new Applied Mathematics students (independently of whether they are on a one or two year core) participate in a special professional development seminar which, in the first semester, involves novel laboratory based projects designed to introduce them to the methodologies of research in applied mathematics including data acquisition and analysis, literature searches, presentation skills, etc. In mid-fall 2006, there was a call for proposals for spring and summer fellowship funding. Five proposals were received and 4 of them were funded. One student used VIGRE funding combined with other support to spend the spring semester with his advisor on sabbatical at the Ecole Normale Superieure in Lyon, France. Travel awards were made on a rolling basis to 15 graduate students, who used them to attend conferences and schools. Several students gave talks or presented posters. In mid-spring 2007, there was a call for proposals for summer, fall, and spring funding. Sixteen proposals were received and all were fully or partially funded. In addition to the mix of academic and professional development goals seen in previous competitions, several of the spring 2007 proposals involved mentoring of undergraduate students in the Arizona Summer Program. Notable Successes The graduate students have been very creative and energetic in proposing new professional development activities. Among them are the Sonia Kovalevsky day mentioned above, participation in the New Start program for underrepresented minority freshmen, and design of web materials for vector calculus. The students are clearly aware of that VIGRE funding allows them to develop new activities aligned with their individual goals and interests. Although the number of graduates was relatively small, placements were excellent: there were two Math PhDs previously supported by VIGRE; one of them will be a post-doc at the Max-Planck-Institut in Bonn and the other will be a tenure-track assistant professor at Stony Brook. Graduates from the Applied Mathematics Program previously supported by VIGRE have achieved some notable professional successes including an NSF postdoc at Princeton, an NRC Research Fellowship at the Naval Research Laboratory, an Assistant Professor at the University of Connecticut, as well as a variety of postdoctoral positions and junior faculty positions at four-year colleges. We foresee relatively modest numbers for the next two years, then a definite ramp up in the number of graduates. Aided by VIGRE funds, we had an excellent year for recruiting, both in terms of quality and diversity. The Math program recruited a class of 14 PhD students, 5 of whom were in the top 10 of our rankings. The incoming class includes 3 African-Americans, two of them female, and one Hispanic who comes from a member of the Southwestern Network, namely the University of Texas Pan American. The Applied Mathematics Program also had an excellent year for recruitment and will bring in a class of 11 students for 2007/08. This includes some of our top choices and overall is one of the stronger groups recruited over the past few years. The new class includes 2 females and 2 minorities (1 African American and 1 American Indian). Two of the students are from a major industrial employer in Tucson (Raytheon) who offer their employees a fellowship program to enable them to continue with graduate studies while working part time with the company. The inclusion of such industrial fellows in an incoming class is a first for the Program. Challenges We found ourselves frequently giving the same feedback on student fellowship proposals and so we have put in place a more detailed "solicitation" which we hope will give students a more clear idea of what a VIGRE fellowship proposal should look like. UNDERGRADUATE PROGRAM Operations URA program: In the last year we have had 18 semester-long undergraduate research projects in which our mathematics majors have worked with faculty, post-docs, and graduate students on research projects from diverse areas of mathematics and its applications ranging from number theory and geometry to nonlinear optics and biology. Some of these projects were continuations across more than one semester. Fourteen of those projects were sponsored using VIGRE funding, the remainder were funded with NSF REU money or with departmental funds. This summer we expect to fund 2-4 projects. During the Spring semester we ran an undergraduate research seminar in which research projects are presented to students who have an interest in getting involved in the program. We had presentations in (among other things) mathematical genetics, number theory, singular limits, and topology and geometry in biology. Three of our current and one of our former participants presented their research at the AMUC undergraduate conference on mathematics this Spring at Western New Mexico State University. The level and quality of many of the projects was particularly impressive this year: The majority of the students are working on projects at a graduate level, and several of these have potential to lead to publications. We still have some work to do to bring up the participation numbers in the program, and we hope to increase the recruiting that we do in the Fall, but overall the URA program is producing very good work. UTA program: In the fall of 2006, there were 9 UTA's; most of them were assigned to lower-division core courses, ranging from Trigonometry to Vector Calculus. Additionally, a couple of our most talented majors were assigned to upper-division courses, one to Abstract Algebra and another to Graph Theory. One particularly interesting project was undertaken by Christina Birch, under the supervision of Rick Cangelosi in Vector Calculus: Christina dedicated much of her time to compiling examples of applications of the course content to physics, engineering, and chemistry. Her work added a layer of depth to the course that would have been difficult for an instructor working alone to achieve. During the spring of 2007, there were 11 UTA's; the increase was partly due to the securing of additional funding via the Lusk scholarship. This semester, we focused the assignments on the core courses that our majors find particularly challenging: Calculus II, Vector Calculus, Linear Algebra, and Introduction to Formal Reasoning. These are all multi-section courses, but in many cases, time invested by the UTA's (for example, office hours and problem sessions) could benefit students in all sections of the course, and not merely the section to which they were assigned. This model proved to be successful, and we will continue it in future semesters. The UTA program has been particularly popular among our majors who are considering careers in education, both at the high school and university level. In that sense it provides a unique opportunity within the math department, as it offers students a chance to gain real classroom experience, beyond the routine of grading papers and tutoring. High School AP class outreach: This year teams of faculty, graduate students, and undergraduates visited 8 schools in the region, speaking to students about the possibilities for those with advanced training in mathematics and opportunities at the University. Seven faculty, 7 graduate students, and 6 undergraduates participated. Recruiting high schools and undergraduates is an ongoing difficulty. Next year we plan to move more of the visits to the fall semester, where they may have a greater impact on students' decisions about college. Notable successes We ended the academic year with 505 mathematics majors (an increase of 7% over the preceding year), of whom 167 (33%) were females, 11 (2.2%) were African-American, 11 (2.2%) were Native American, and 72 (14%) were Hispanic. About 3.5% of the undergraduate population at Arizona is majoring or minoring in mathematics. In recent years we have typically produced fewer than 65 bachelors in Mathematics. This year the number of graduates will be about 87 (including 24 females and 12 minorities). At least 22 of this year's Mathematics graduates (5 of them minority students) will pursue graduate or professional studies. At least 44 Mathematics undergraduates will participate in REU, internship or tutoring employment activities over the summer, an increase of 16% over the preceding year. Challenges The percentage of females among our undergraduate major population has been at 33% for many years and does not seem to be increasing. POSTDOCTORAL PROGRAM Operations We hired three VIGRE post-docs who will begin work in August, 2007: one in Applied Mathematics, one in Mathematics, and one funded jointly by VIGRE and a Howard Hughes Medical Institute grant. For 2007/08 the Program in Applied Mathematics recruited one VIGRE postdoc. Of the short-listed candidates, four were invited out for interviews (at the expense of the Program). The position was offered to and accepted by Paul Dostert, a graduate student in mathematics at Texas A&M specializing in numerical analysis and scientific computation (dissertation title "Uncertainty quantification using multiscale methods and stochastic finite element methods for porous media flows"). His research interests and internship experience at Lawrence Livermore make him well suited for interdisciplinary collaborations with the hydrology and geosciences groups at the University of Arizona. Jing Long Hoelscher is the Mathematics VIGRE postdoc. Dr. Long Hoelscher is a recent graduate of the UPenn Mathematics Department whose research interests include Galois theory, algebraic number theory, and arithmetic geometry. These interests mesh well with many themes of our algebra, number theory, and geometry research groups and we expect that Jing will play a role in inspiring our graduate students to pursue research in these areas. In particular, she will be teaching our foundational, second-year course in algebraic number theory in the fall. Chris Bergevin is our VIGRE-HHMI postdoc. This hybrid position is supported by funding from the VIGRE grant and the Biological Sciences/Medical School's Howard Hughes Medical Institute grant. The postdoc holding this position is expected to have a strong research focus and promise in the area of Mathematical Biology and also an interest in developing novel curricula and educational experiences for undergraduates at the interface between mathematics and biology. Dr. Bergevin is an excellent fit for these criteria. He is a graduate of the prestigious Harvard-MIT Speech and Hearing Biosciences and Technology Program. His research involves comparative modeling and analysis of otoacoustic emissions in mammals, amphibians, reptiles and birds. We expect Chris to help foster novel interdisciplinary research and educational collaborations between the departments of Mathematics and Biology. SOUTHWESTERN NETWORK AND SUMMER PROGRAM Operations In the fall, we implemented a web site and list-serve for the Southwestern Network. On October 21, we held a one-day meeting of network representatives which included panel discussions on undergraduate research, the Arizona Summer Program, recruiting undergraduates, inputs and outputs of network graduate programs, and what students should know about the academic job market; a CV feedback session for Spring 2007 graduates; and a tour of the Applied Mathematics laboratories. Two network members expressed interest in participating in the Arizona Summer Program as visiting faculty members and one of them (Cristina Villalobos from UT Pan American) will be a mentor in the 2007 program. The workshop also fostered recruiting relationships and at least one hispanic student who probably would not have known about our programs will commence a PhD in Fall 2007. The Arizona Summer Program in 2007 will be on the topic of mathematical modeling. The modular format of the program is inspired by an undergraduate course at Arizona. Participants will work in teams on modeling projects based on articles recently published in the research literature. Each team will be supervised by a graduate or faculty mentor. The program will use the resources of our two applied mathematics laboratories and of one of our computer classrooms. A brief ethics component, visits to local scientific institutions, as well as social activities will also be included. There were 40 applicants, 14 of whom will attend. Among the attendees are 7 women and 7 men, at least 3 minority students, and 6 students from our network, 3 o them from the University of Arizona. Notable successes: Network Activities lead to a faculty member from a network partner participating in the Arizona Summer Program and one of her students enrolling in the PhD program in Mathematics. Challenges: Our summer program is like an REU, but not officially an REU and so we had some trouble getting it advertised in the places students typically search for an REU program. On the other hand, the network partners were able to spread the word on their campuses and we had an adequate number of applicants. We may consider other media such as direct mailings next year. OTHER ACTIVITIES Evaluation: in late September, our evaluation expert Vicki Brown resigned to pursue other opportunities. We quickly replaced her with Mende Davis, an evaluation specialist who holds a doctorate in Psychology and joint appointments in Pediatrics, Biostatistics, and Epidemiology. She has been working on a very thorough base-line study which will result in a wealth of data with which comparisons can be made later in the project. She has also shepherded our proposal through various phases of human subjects review and worked with staff members to improve our databases and design data collection instruments. We expect to have more quantitative findings to report next year. Faculty participation: Defining "participation in VIGRE" as in our proposal (at the bottom of page 7), at least 46 tenured or tenure track faculty (72% of the total) have been involved in VIGRE just in the last year. We expect that taking a three-year average when that becomes possible will yield an even higher number. Dissemination: The Arizona PIs have participated in a number of VIGRE- and workforce-related events recently, including the Seattle meeting in April, the NSF discussion panel in New Orleans in January, and several workforce advisory panels and reviews at NSF (including VIGRE, MCTP, Graduate fellowships, and the NAS study). We are included in and cooperating with the Cozzens project. One of our most important dissemination activity is the Arizona Summer Program discussed above. Diversity experts and minority speakers: During the academic year 2006-2007, there were presentations by at least 6 diversity experts and high-profile minority or female scientists in our colloquiua, not to mention the weekly research seminars. Additional funding: The Arizona graduate programs have been aggressively pursuing funding complementary to VIGRE in order to improve the success of our first-year students and our competitiveness in recruiting. In particular, we have submitted a proposal for 4 years of S-STEM funding to be used to reduce the teaching load of all incoming domestic students to .25 time, thereby allowing them to focus more on their academic work in the first year. This effort was aided by a one-time infusion of UA Graduate College funds of support recruitment of underrepresented minority students from our network and a transition to the reduced teaching load plan. Management: Our management structure has been functioning smoothly and effectively, due in part to the long collective experience of the management team in running large training and infrastructure projects. It is expected that the project will continue without problems during the 2007-2008 academic year when PI Douglas Ulmer will be on sabbatical in Europe and co-PI Michael Tabor will be acting director of VIGRE.