This report covers the activities of our VIGRE project from June, 2007 through May, 2008. GRADUATE PROGRAMS Operations As a result of the fellowship competition held in Spring 2007, 15 continuing (second year or later) students were awarded summer fellowships. Of these, 4 were for summer and fall of 2007 and 3 were for summer plus the full academic year 2007-2008. In addition to the usual assortment of professional development activities, mentoring in the the Arizona Summer Program was part of the proposal of several students and 4 of them were selected as mentors for this program. Eight summer study fellowships were awarded to first-year students studying for the qualifying exams and 3 students were partially supported in the summer to run exam study sessions. All 12 incoming Mathematics PhD students participated in the Integration Workshop, which was organized by acting Associate Head Ken McLaughlin. On the basis of that workshop, three students were advised to pursue a two-year core. One of the took the advice and two did not. Unfortunately, the student who took the advice and one who did not had large difficulties during the fall semester (academic, social, and medical) and did not continue in the program past the first semester. The third student, who did not start in a two-year core, had some difficulties in the core courses and is effectively carrying out a two-year core. In August 2007 5 Applied Mathematics students out of a class of 6 took their qualifying exam (the sixth student is on a 2-year core) and all passed at the PhD level (high pass) at the first attempt. This is the first time the Program has seen a 100% success rate. In Fall 2007 the Program admitted a class of 11 students. All the full-time students were placed on the 1-year core track. Two of the class are on a work/study program the Raytheon Corporation and require two years to complete the core as a consequence of company work requirements. All students successfully completed their core-sequence and will be taking their qualifying exam in August 2008. Course grades, 2nd semester term papers, and instructor reports indicate that all but one student are performing at a high level. In the fellowship competition held in Fall 2007, 10 students applied for VIGRE fellowships for Spring (and in some cases summer). Of these 6 were funded, all for the Fall semester. Travel awards were made to a rolling basis to 16 students to support conference attendance, with an emphasis on cases where the student would be making a formal presentation. The average travel award was about $300. In the fellowship competition held in Spring 2008, there were 24 (!) applications for funding for some combination of Summer 2008, Fall 2008, and Spring 2009. Nine of these applications were funded fully, 10 were partially funded, and 5 were not funded. The process of receiving serious feedback and possibly a decision not to fund continues to be an excellent growth experience for most of our students. Notable successes The graduate students made an excellent contribution to the Arizona Summer Program which is described in more detail below. There was a small number of graduates from the Math program (2), one of whom accepted prestigious position Los Alamos National Lab. We expect significant ramp-up in graduates from the Math program starting next year. In the Applied Math Program, 1st year student John Pate (a Native American) was awarded a National Defense Science and Engineering Graduate Fellowship. Three students received Achievement Rewards for College Scientists (ARCS) Scholarships. One student (Serina Diniega) won first prize in the SIAM "Math Matters: Apply It" modeling competition. Three students graduated going on to postdocs at Rensselaer Polytechnic Institute and the University of Canterbury (New Zealand), and to an Assistant Professorship at Framingham State College, Massachusetts. Aided by VIGRE and S-STEM, the Math program recruited an incoming class of 9 students, of whom 4 are women. First indications are that the average quality of the students is high, but with less variation than in the previous year. The Applied Mathematics Program recruited an incoming class of 11 full-time students and 1 student on the work/study program with Raytheon. All the full-time students are on the 1-year core and the first indications are that this is another strong class. Challenges As noted above, two of our students, both minorities, were unable to complete the first year of the program. In at least one case, there seems to be a misperception on the part of network colleagues about the background and motivation needed to succeed in our PhD programs. An upcoming network workshop, described more fully below, is partially aimed at remedying this problem. Moreover, we continue to monitor all of our students' progress and intervene as needed, especially in cases of students who may be at risk due to cultural factors. UNDERGRADUATE PROGRAM Operations URA program: There were 6 URA projects this year, on topics ranging from group theory to numerical analysis and mathematical biology. (There seems to be some cyclicity, as the numbers for the preceding year and for Fall 2008 are much larger.) Reports from most of these projects are available on our web site. We continue to offer an undergraduate research seminar. UTA program: There were 20 UTAs this year, assisting with courses across the range of our undergraduate offerings. The program continues to be very popular with both students and faculty. High school visits: This program seems to be struggling in that we are not seeing a large interest on the part of local high schools. Only 4 visits took place in 2007-2008. We are considering making some modifications such as moving the visits earlier in the year where they may have more of an effect on students' plans for college. Notable successes The number of math majors at Arizona has increased to 564, up from 505 last year. 22% of these are minority students! 81 mathematics undergraduates completed their degrees this year, 17% of these being underrepresented. Of the 81 graduates, 12 went into teaching and 15 pursued post-graduate studies, 7 of these in mathematics. In summer 2007, 57 math majors had internships, a substantial increase over previous years. Challenges As noted above, the high school visit program has been struggling and may need to be rethought. We continue to receive generous donations from one donor to the Lusk fund, but we have not yet had a a great deal of success in increasing the number of contributors to this fund or other resources for the URA and UTA programs after VIGRE funding ends. We do however have a large proposal in with a local technology company which would help address this issue. POSTDOCTORAL PROGRAM Summary of activities of VIGRE post-doctoral fellows: Chris Bergevin Chris is supported jointly by funding from VIGRE and the Howard Hughes Medical Institute (HHMI). His responsibilities in regard to the latter are to assist a joint committee of mathematics and biology faculty in designing mathematics curricula for biology majors that will meet the future needs of those planning for research careers in the biological sciences. Chris has been a regular participant in the HHMI Biomath Committee meetings and has taken the CITI training (for human subjects). In Fall semester 2007, Chris assisted Jim Cushing, who taught a pilot version of MATH 250A (advanced placement second semester calculus) for freshman Biochemistry majors. Chris ran a problem session once a week for the students enrolled in Prof. Cushing's class. He also worked with Prof. Cushing on all aspects of the course: he attended lectures, graded the homework, participated in writing exams, etc. In Spring semester 2009, Chris taught his own section of MATH 129 (regular second semester calculus) while continuing to assist Prof. Cushing, who was teaching MATH 250B (advanced placement ordinary differential equations). Chris ran problem sessions, attended classes, etc., as before, but also worked on the development of student projects for this course. Chris's principal VIGRE mentor was Joceline Lega. Prof. Lega met with Chris once a week to discuss pedagogical issues such as reasons for teaching a particular topic or the best way to present specific material or how to deal with problematic students. In particular, she gave him advice on how to set up his course policy and prepare for the Math 129 class of which he was solely in charge. She also checked his exams and visited his classes on several occasions providing written constructive advice on how to involve students in solving problems or answering questions in class. Over the course of the semester she reported good improvement in Chris's teaching style. Prof. Lega also familiarized herself with Chris's research. She read and provided constructive criticism about a small grant proposal he wrote and he showed her the poster he presented at a conference in Phoenix during the past Spring semester. Over the course of the past year Chris has worked (with success) on publishing papers related to his thesis work on otoacoustic emissions. He has also started thinking about mathematical modeling aspects of his research on the mechanics of the auditory periphery. Chris is very active within the Department's Mathematical Biology research group and has future projects, integrating research and education, planned with Cushing, Lega, Secomb, and Watkins. Beside his activities in teaching and research, Chris has also pursued a number of outreach activities which included mentoring a group of students taking the Math Modeling (MATH 485) course taught by Kevin Lin last Spring and supervising an undergraduate student (URA), Andrew Binder, on a research project. Paul Dostert Paul is supported jointly by funding from VIGRE and the Applied Mathematics Program. Paul's teaching experiences this past year were centered on Math 124. This is a 5 unit first semester calculus course (most of our courses are 3 units) that Paul taught in the Fall semester. Alain Goriely was Paul's principal VIGRE mentor. He had a few talks early on with Paul about students' (and faculty) expectations and reported that Paul seems to understand the philosophy and idea of teaching really well. Prof. Goriely also looked at the first couple of Paul's exams and concluded that he knew what he was doing. He also noted that Paul's office hours were always very busy and that he was taking a lot of time to interact with his students. In conclusion Professor Goriely reported that Paul's student evaluation scores for the course were around 4.8 (out of 5) which was much higher than the comparison group and the second highest score for that course in Fall 2007 semester. Paul has so far mainly concentrated on finishing his PhD work and extending it in collaboration with outside scientists. He is currently participating in a working group on Uncertainty Quantification. This theme is closely related to Paul's thesis topic. He has planned future projects on stochastic modeling with Juan Restrepo and Shankar Venkataramani. Jing Long-Hoelscher Last year the Department, with the approval of the Number Theory research group, asked Jing to teach Math 514, which is a year-long graduate course on Algebraic Number Theory. Dinesh Thakur was her principal VIGRE mentor in the Fall semester. He met with her in the beginning of the semester and discussed her plans for the graduate course in algebraic number theory, her syllabus, and gave her copies of his own notes and exams for the course to help her calibrate. He attended several of her classes and provided feedback and suggestions throughout the semester. During the Spring semester, when Professor Thakur went on sabbatical, Bill McCallum took over the principal mentoring responsibilities. He talked to Jing a couple of times about her class and helped her plan out the second semester's work. He visited her class and talked to the graduate students in the class. Jing is a regular participant in the Number Theory research group. She joins the weekly Number Theory lunch, which provides the opportunity to informally discuss her research with other number theorists. She met weekly with Professor Thakur to discuss the papers she was working on. He suggested corrections and gave her advice. Professor McCallum continued this consultation in the Spring semester and Jing regularly sent Professors McCallum and Thakur updates of her manuscripts for comment. On her own initiative Jing also initiated a research interaction with Al Cuocco, a number theorist and educator who was visiting our Institute for Mathematics and Education last Spring. Andrea Young Andrea is a new VIGRE postdoc joining our Department this Fall. Her research interests are in the area of geometric evolution equations. She will be joining the Geometric Analysis research group but will undoubtedly interact with a broad spectrum of analysts and geometers in the Department. David Glickenstein will be her principal VIGRE mentor. We hope that she will become involved in planning for and organizing the VIGRE summer program in 2010. SOUTHWESTERN NETWORK AND SUMMER PROGRAM The Southwestern Network was relatively quiescent during this academic year, perhaps because one VIGRE PI was on sabbatical and another was on leave. A network meeting will take place on September 27th. Part I of the meeting will consist of short and informal presentations by Network partners about the latest initiatives at their home institutions to develop the "pipeline" in the mathematical sciences. Part II of the meeting will consist of a Workshop on the Teaching of Proof in the undergraduate curriculum (sponsored by the Institute for Mathematics and Education at Arizona). This meeting may lead to a proposal for a larger, funded workshop on the topic. The 2007 Arizona Summer Program was on Mathematical Modelling and was very successful. What follows is a report from Professor Lega, the organizer: The 2007 Arizona Summer Program was held from July 2nd to July 27th. We had 12 VIGRE participants plus one student from Mexico. We started with 13 VIGRE participants, but one of them had to leave in the middle of the program due to personal circumstances. Students worked in teams of 3 or 4, under the supervision of a graduate or faculty mentor. We had 3 graduate mentors (David Morales, Predrag Punosevac and Mark Robertson- Tessi). They all did a wonderful job in mentoring their groups. David Morales also organized many social activities, which helped with the cohesion of the group. The fourth mentor was Cristina Villalobos, a faculty member at the University of Texas Pan American. Students learned how to read a research paper, reproduce and extend the results, write a report in LaTeX, a presentation in Beamer, and a poster in PowerPoint. They also learned how to use MATLAB, how to write a resume, and how to create group and personal web pages in HTML, using cascading style sheets. They attended research seminars given by faculty and graduate students, had sessions in the Applied Mathematics Laboratory, and visited the UA Mirror Lab, Kitt Peak and the Biosphere 2. Prior to their arrival in Tucson, they were asked to take an online quiz (that I had set up on D2L), which guided them through understanding ethical issues related to plagiarism and self-plagiarism. Please consult the web site, at http://projects.math.arizona.edu/~sp2007/sp.html, for a list of projects, group web pages prepared by the students (with links to all written and oral reports and, for some of the group pages, movies of numerical simulations), a detailed schedule (including information on all of the seminars and group activities), as well as a list of participants and all personnel involved in the program. All in all, it was a lot of work but I think it went very well. I was very impressed by and proud of the students' accomplishments. I believe they got a lot from the time they spent here. Mende Davis, our external evaluator, should provide us with a report on the official student evaluations, which were administered at the end of the program. Professor Lega produced a further, quite detailed list of practical considerations and suggestions for improvements. A report of the survey of summer program participants will be available during the site visit in Fall 2008. The 2008 Arizona Summer Program was on Computational Group Theory and was also very successful. A detailed report will appear in the 2008-2009 annual report on the grant. Preliminary information is available at http://math.arizona.edu/~klux/2008Info.html. OTHER ACTIVITIES Evaluation: Mende Davis, the evaluation specialist we hired after the resignation of Vicki Brown continues to work on several long-term evaluation projects. In particular, a very complete base-line graduate student database is nearly finished, and we have post-workshop and follow-up data for the summer program participants. An alumni survey is planned for this fall. Managing the evaluation specialist and the human subjects issues has been a time-consuming challenge, but we hope that the resulting data will be a valuable resource for years to come. We will certainly be in a position to address all of the Standards for Success crieria in Section 6.2 of the proposal at the site visit. Faculty participation: As detailed in the accompanying spreadsheet, at least 44 members of our tenure-track and tenured faculty participated in the VIGRE project, which represents a participation rate of 72%. This does not include temorary faculty and faculty from other units on campus (many of whom supervise dissertations in Applied Mathematics). Underrepresented speakers: At least 20 women and 3 members of underrepresented groups spoke in our colloquia and seminars in 2007-2008. Additional funding: VIGRE co-PIs Tabor and Ulmer were awarded a 4-year S-STEM grant to support first and second year students in our two PhD programs by reducing their teaching load. There is obviously a strong interaction and reinforcement between S-STEM and VIGRE. Qualifying exam and attrition results for the first year indicate that S-STEM has been a success and contributes to VIGRE and general workforce enhancement goals.