LSU VIGRE proposal, summary

The central focus of this proposal is the improvement of the mathematical education and training of graduateand undergraduate students as well as their professional development and training. Rapid growth of humanknowledge, particularly in the sciences and technology, brings with it the need for a larger proportion ofthe population to be university educated. Research universities must rise to the challenge of attracting andretaining a wider audience in both research and education. They must reach out to the community, highschools and smaller colleges. And they must serve the leading role in fostering research in pure and appliedscience. New approaches to instruction include increased emphasis on interdisciplinary methods, bridgingtraditional barriers between subject areas, and vertical integration, crossing barriers between undergraduates,graduates, and researchers. The challenge for mathematics departments is to provide students with expertisein diverse specialties while cultivating a sense of unity within mathematics and between mathematics andother sciences.

This ismaximal 1page andshould (a)describe theactivities ifthe proposalis funded, (b)comments onits objectives,people to besupported,and intendedimpact, (c)institutionsinvolved, (d)groups/numberof peopleinvolved,(e+f)intellectualmerit andbroaderimpacts.

The Department of Mathematics at Louisiana State University is organized around 7 research groups inpure and applied mathematics. Nearly 80% of the Department’s PhD graduates have entered University orCollege positions. Only a small percentage of the undergraduate students have entered graduate study inmathematics or science. In recent years the Department has expanded its offerings by introducing a newgroup in Math Education and two new groups in applied mathematics: The Mathematics of Materials Sci-ence and Scientific Computing and Numerical Analysis. The second group is closely tight to LSU’s Centerfor Computation and Technology, which is an interdisciplinary technology center focusing on education, re-search and economic development. At the same time two of the pure mathematics research groups have beenstrengthened through new hires. The changes on faculty level have resulted in increasing research produc-tivity and grants. On the undergraduate level new concentrations in Secondary Mathematics Education andMathematical Statistics have been introduced. These improvements and others in progress are broadeningthe for jobs and for further education for our students and resulting in a strong increase in the number andquality of Mathematics Majors.

The Louisiana State University Department of Mathematics proposes several new initiatives, closelytied to existing initiatives and structures. Our goals are to enhance our graduate, undergraduate, andpostdoctoral programs, and to better prepare our students for their futures in research, education andindustry. The proposed projects build on ongoing initiatives to enhance the training of high quality USmathematician by introducing them early to cutting edge research, using group discussions, research projectsand seminars organized within new research crews. Graduate students will be involved in the mentoring ofundergraduate students in the research crews and in a summer Research Experiment for Undergraduates.The research crews and senior graduate students will interact with incoming students through our newWarm-Up program, which is organized by the graduate students with faculty oversight. Faculty membersand postdoctoral associates interact with the students in the research crews, seminars and related activities.All existing research groups will participate in the program, ensuring maximal faculty participation andintegration of existing structures into new project of learning and training.Intellectual Merit of the Proposed Activity. The grant will strongly support the ongoing educationaland research initiatives of the Department by increasing vertical interaction between faculty members, post-doctoral associates, graduate and undergraduate students. Faculty members have strong research supportedby many federal grants. The VIGRE program will multiply the effect of our research and educational impactby forming research crews in which they can effectively interact with students and post-doctoral assistants.In turn, this will increase the number of US citizens in the mathematical pipeline, contributing to efforts topreserve US scientific leadership.Broader Impact of the Proposed Activity. Teaching and research initiatives at LSU are catalysts forreform efforts at other universities in Louisiana and in the South, having a multiplier effect. Additionally, theyounger generation participants in the proposed VIGRE program will be prepared to communicate betterwith users of mathematics in a variety of disciplines, bridging cultural barriers between mathematics andthe natural sciences. During the summer we will organize activities for undergraduate students from LSUand nearby Universities and Colleges. Special attention will be paid to underrepresented groups.

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Project Description

1 Introduction: Vision, Objectives and Scope

The Department of Mathematics is a core unit of Louisiana State University, with a diverse community ofresearchers, scholars, and students. Through its geographic location in the south and recent growth and

Not morethan 2 pages.Discuss thevision, scope,objectivesandanticipatedimpact of theprogram, atthe localinstitutionand beyond.

diversitification it is well prepared to address workforce enhancement and preparation of young Americans,including minorities, for careers in mathematical research, education and industry. In 2003, the departmentbegan a major structural transformation: the expansion of the number of professorial faculty, graduate andundergraduate students, and a concurrent reduction of the number of instructors balanced by an increasedrole of graduate students in undergraduate education. The Department has enhanced its programs and thequality of graduate students, but much improvement is needed in the postdoctoral research placement of PhDgraduates and in the graduate school placement of undergraduate majors in mathematics. The Departmentis addressing these challenges through ongoing curriculum reforms, stronger recruitment of undergraduatestudents into mathematics and careful investment of new resources being provided by the University.

The mathematical workforce in modern society requires broad training in research and education. Toaddress this need, the Department has built a strong research group in Applied Mathematics with a focus onthe Mathematics of Materials Science and, jointly with CCT, the Center for Computation and Technology, inScientific Computating and Numerical Analysis. It has also built a group in Mathematics Education. Part ofthis group plays a leading role in the Gordon A. Cain Center for Scientific, Technological, Engineering andMathematical Literacy. A second focus is the strengthening of two of our core research groups, GeometricAnalysis and Geometric Topology. The Department has also implemented new mentoring and grant writingprogram for junior faculty leading to increasing NSF grant support. Now about 40% of our faculty membersand all but two of our assistant professors have NSF summer support. At the same time the member of theDepartment are actively participating on other grant activities, including interdisciplinary and educationalgrant.

The graduate program has benefited from the infusion of substantial funding for highly competitiveassistantships and fellowships. The Department implemented a new forum for senior graduate studentsto prepare them for job applications in academics and industry. As one more step to increase verticalintegration of education and research the Department will in August 2007 for the the first time run a Warm-Up program for our incoming students to prepare them for their study at LSU as well as their duties asTeaching Assistants. The Warm-Up will be planned and conducted by the graduate students. We are alsoproposing a new Research Experience for Undergraduate Students with heavy graduate student participation,involving research and outreach. Students from nearby Universities and Colleges in Louisiana and nearbystates will be invited to participate.

Our faculty members are also involved organization of conferences and workshops, in K-12 education,teacher preparation and interdisciplinary research. The Department has organized an annual High SchoolMathematics Contest since 2002, stimulating interest and achievement in mathematics among high schoolstudents in Louisiana. The contest, conducted by a number of faculty members and graduate students, hasbeen a great success.Our Vision and Objectives: Funds are requested for VIGRE support to enhance ongoing activities invertical integration, workforce development, education and student research experience moving the Depart-ment from a solid program to one that can serve as a role model for mathematics departments in the South.The central focus of all planned activities is to improve the mathematical education of our students, bothundergraduate and graduate, and to enhance their post-graduation research prospects. This will be achievedby vertical integration in the form of research crews including postdoctoral associates and students.On the faculty level: Involve faculty members in the work of the research crews and in mentoring

strengthenthisstatement

of postdoctoral associates and students. Enhance the interaction between faculty members and studentsand each of the research groups, by involving faculty, postdoctoral associates, undergraduate and graduatestudents in the work of the research crews;

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On the postdoctoral level: Transform our existing visiting program to a flourishing postdoctoral programthat can be sustained after the duration of the program. Develop a mentoring system that enables ourpostdoctoral associates to compete for research positions and quality positions in industry after their stayat LSU. A distinctive benefit of the inclusion of postdoctoral associates and students in a small crew will beto provide them with the intellectual stimulation and collegial guidance that can be achieved within a smallresearch group, while maintaining the quality-control and the diversity offered by a large department in acomprehensive university. For postdoctoral associates, this will provide valuable experience in teaching andmentoring;On the graduate level: Transform our mathematical culture among our graduate students, increasetheir publication activities, and motivate them to apply for research position after graduation. Increasethe number of our graduate students that accept a postdoctoral position or other form of research positionafter their graduation and enhance the success rate of our US students. The Department has recognizedthat, in addition to traditional reading and classroom lectures, it is important for students to experimentwith group projects and enjoy active research experiences. Students also require training in written andoral presentation. To address these needs, we will change our existing Graduate Student Seminar to aGraduate Student Colloquium. To enhance vertical integration and the responsibility of our students, theseseminars will be organized by the students limited faculty oversight. In tandem with other enhancementgrants, increase the number of underrepresented students, women and of graduate students from the south.Enhance the job prospects of our students through internships and stronger education in applied mathematicsand computation;On the undergraduate level: Enhance classical forms of teaching with more active forms of learningsuch as group projects, technology-assisted learning, and seminars. As LSU plans to decrease the number ofundergraduate students while raising quality, the Department of mathematics will increase the percentageof undergraduate students that majors in mathematics at least by 20% by actively contact strong studentsin our courses. Increase the numbers of majors that go to graduate school in mathematics or other sciences.Strengthen the role of LSU in the south by involving undergraduate students and minorities in our VIGREsupported REU. The undergraduate component of the VIGRE proposal will provide exceptional opportu-nities to prepare undergraduate mathematics majors for mathematical or scientific careers or for graduatestudy.

This proposal describes our strategy for attaining these objectives. The proposal builds on existingstrengths of the Department, on recent initiatives and changes suggested by both external and internalcurriculum review panels, on ideas developed in the preparation of previous VIGRE proposals, and onfeedback from those proposals.Scope: This proposal will engage the entire Mathematics Department at LSU. Each of the existing eightresearch groups will be involved in some aspect of integrating research and teaching, or outreach. Theresearch groups have begun formulating focused plans to guide students’ academic progress, and will assumebroad responsibility for the education and guidance of undergraduate and graduate students, as well as thementoring of VIGRE postdoctoral associates. Overall coordination will be done by the VIGRE committee.Impact at LSU and Beyond: If funded, this proposal will have a great and long-term impact on theDepartment. It will dramatically upgrade ongoing efforts to bring greater vitality and strength to our overallprogram. The Mathematics Department is one of seven enhanced Foundation of Excellence Programs at LSU.In 2003 and 2005, the Mathematics Department and the English Department were the two departments inthe College of Arts and Sciences to receive extra support to hire new professorial faculty and recruit newgraduate students. The vigorous innovation currently underway within the Department and the strongfinancial support now being provided by the University would multiply the effect of a VIGRE grant to createa unique opportunity. The present efforts and institutional financial support will strongly magnify the impactof a VIGRE grant and enable the Department to realize the objectives stated here and to maintain themlong beyond the duration of a VIGRE grant.

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2 Curriculum Review

A living, vital program is never static, but needs constant review and revision. The Department has under-taken several revisions of its graduate program since 1998 in preparation for its first VIGRE proposal in 1999and also resulting from LSU’s external program review the same year. Another external review with a sitevisit took place in September 2004. Of importance for this proposal in these reviews were recommendationsthat the Department should start an Applied Mathematics program, introduce capstone courses for seniormathematics majors, and focus hiring in areas of departmental strength. The steps towards those goalswere formulated in the hiring plan. Also, the impetus of these external reviews led to continuous internalreviews under the auspices of the departmental Undergraduate and Graduate Committees. Consequently,the Department has introduced new undergraduate gateway courses, undergraduate capstone courses, whichcan involve either problem solving or research project related to local industry as well as capstone courserelated to our new concentration in Secondary Mathematics Education. A number of new graduate courses,and a new format for graduate qualifying examinations. As a result of this reform, the total number ofMathematics majors and graduate students has increased, and enrollment in advanced undergraduate andgraduate courses is up, as shown below based on fall enrollments each year.

MAJORS IN MATHEMATICS, ALL LEVELS

2000-2001 2001-2002 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007UG Math Major 88 90 86 103 117 217 218

MS 10 6 5 6 12 11 11PhD 47 56 67 77 77 77 82

In particular, the number of Undergraduate majors increased by 1.33 in 2000/01 to 2000/05 and by a

thosenumbers arenot directly”Curr. Rew”but I think itis good tohave them

factor of 2.48 in 2000/01 to 206/07 compared to a 20% increase proposed in our first VIGRE proposal in1999. A part of that increase is due to the new concentration in Secondary Math. Education. The numbersfrom April 2007 show 219 majors in mathematics. Of those, 57 were in Secondary Education, 46 in PureMathematics, 21 in Actuarial Sciences, 12 in Mathematics/Computer Sciences, 4 in Applied/Discrete Math,2 in Applied Math/Communications Engineering and 78 in had not declared their concentration. Two yearsago the corresponding numbers were: 64 in Secondary Education, 40 in the Mathematics Concentration, 18in Actuarial Sciences, 10 in Applied/Discrete Mathematics, 9 in Mathematics/Computer Sciences, and 76had not declared their concentration. The number of double majors in September 2006 was 24 compared to19 in 2005. In September 2006 the number of minors was 156.

In end of 2006, the Department had 94 graduate students, compared to 53 in 2000 (1.77 increase). Ofthose, 26 are female up from 16 in 2000 (1.63 incrase), 9 are minority, up from 4 in 2000 (2.25 increase), and46 are US citizens, up from 24 in 2000 (1.92 increase).

2.1 The Graduate Program

The graduate offerings are now divided into three categories:(I) Three Core-1 courses in algebra, analysis, and topology for first-year doctoral students. There is also

a one hour course entitled Communicating Mathematics, which is required each semester of the first year asa part of the professional development initiatives of the Department. Each summer we offer a review coursefor students who are preparing to take their the PhD Qualifying exams.

(II) Six Core-2 courses: algebra II, complex analysis, differential equations, differential geometry, graphtheory and topology II. The Department is now considering what changes need to be made because of theincreased size of Applied Mathematics. Each doctoral student selects three of these in the second term ofthe first year, with a fourth required by the end of the second year for breadth. The content of the Core-1and Core-2 courses in algebra, analysis was revised in 2006 and 2007. In particular, the core-1 real analysisis now general measure theory & integration with emphasis on Euclidean space. The core-2 analysis courseis now complex analysis and used to be general measure and integration.

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(III) Advanced courses that are offered at regular intervals. These include annually running second-yearcourses designed to provide breadth of training for every graduate student as well as specialized advancedcourses and seminars that prepare students for research. Each departmental research group has a list of thesecourses on the graduate webpage http://www.math.lsu.edu/grad/gradcurricula.html. Each researchgroup has posted a list of recommended courses, see http://www.math.lsu.edu/dept/grad/gradcurriculaA complete list of courses since 2002 can be found at http://www.math.lsu.edu/dept/grad/cur.grad.cour.

Several other changes have been made or are under consideration. In 2001 the Department introducedthe Graduate Student Picnic and Orientation Conference, a one day event where graduate students meetfaculty members in a relaxed picnic atmosphere and members of some of the research groups present theirwork and the group. Last year two students presented their work and the life as a student at LSU. Based onthe positive feedback the Department is introducing a two week warm-up in August 2007. The Departmenthas also experimented with more seminar style classes, where students read research articles or a part ofa book and then give a presentation. An extension of this idea is proposed in this proposal under thename of research crew. Material to help students prepare for their job applications has been posted at theDepartmental web page http://www.math.lsu.edu/dept/grad/handbook/hb9.

2.2 The Undergraduate Program

Foremost among changes to the undergraduate program is the institution of the Capstone Course, Math4020. This course often runs in conjunction with the Mathematics Consultation Clinic, a highly successfuloutreach program in which the students work on group projects proposed by local industry, government,or businesses. A version of the capstone course devoted to problem solving was offered in Fall 2003, and anew capstone course in Mathematics Education, Math 4004, has recently been introduced. The departmentis also contemplating the institution of sections of the capstone course devoted to research experiences forundergraduate majors.

In Fall 2003, the Department began reducing the number of instructors and, at the same time, redesignedseveral lower level service courses. A very successful form of teaching College Algebra and Trigonometry wasinitiated two years ago. This transition plan was strongly endorsed by the national Roadmap to Redesign(R2R) program, and LSU was accepted as a Phase 2 member of this effort. Now, LSU has become one ofthe leading institutions in this program. The students have one hour lecture each week, but otherwise theywork on problems in a computer lab, where several instructors, graduate students TAs and undergraduatetutors are available for help. We have also introduced large lectures with an intense tutoring program toteach Calculus with Business and Economic Applications. A new course in data analysis, probability andstatistics, to take the place of Math 1100 for non-math and non-science majors, has been developed withgrant support from NSF. An NSF project to develop curriculum materials for use in the training of future

who knowsmore aboutthis?Madden,Perlis?secondary mathematics teachers is also underway. Other changes include the following.

• The institution of three sophomore-level gateway courses to promote recruitment of majors and to facilitatethe transition to higher level mathematics. In these courses, students are introduced to proofs and othermathematical methodologies using selected topics in mathematics.

• The institution of a number of senior-level courses. Among these courses are Math 4050 Interest Theoryfor the Actuarial Sciences concentration, and Math 4700 History of Mathematics.

• Three new courses for the Secondary Mathematics Education concentration. Those courses are runconcurrently with courses offered by the College of Education, and involve tutoring experiences, classroompresentations, and instructional strategies, as well as substantial mathematical content.

• Introduced revisions of Advanced Calculus I and II and introduced a new course in Advanced Calculus ofSeveral Variables, with all three recommended for graduate school preparation.

• Introduced three new concentrations in Actuarial Science, Mathematical Statistics, developed with theDepartment of Statistics and finally Secondary Mathematics with a very strong outreach component ofK-12 activities.

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Proposed Project

3 The Mathematics Department

For more than twenty years, the organization of the department’s faculty was centered on six overlappingresearch groups. Today, the Department’s 54 faculty members are arranged in the following eight groups:Algebraic Number Theory and Algebraic Geometry; Algebraic Topology, Knot Theory, and TopologicalAlgebra; Applied Mathematics in Materials Science; Combinatorics and Graph Theory; Control Theory,Functional Analysis, and PDE’s; Harmonic Analysis and Representation Theory; Probability; and Scien-tific Computation. This last group, recently initiated in cooperation with the Center for Computation andTechnology (CCT), has 4 members, two of them with a joint appointment with the Department of Mathe-matics and CCT. The Department has also formed a new group in Mathematics Education with one hiresplit between Mathematics Education and Topology. Members from all of the research groups and fromthe Departmental administration have been involved in the preparation of the VIGRE proposal and some ofthe meeting of the Vigre committee have been announced to professorial faculty, instructors and graduatestudents, aiming at as wide support for the proposed initiatives as possible.

Each of the traditional research groups organizes a weekly seminar. In recent years, the seminars haveexpanded their focus to include graduate students, who often participate in the presentations. In somecases, series of tutorial lectures on a level suited to advanced graduate students are given. Also, studentsoccasionally give lectures on their work or related topics. Members of the research groups have publishedresearch articles in first-rate international journals, including Annals of Mathematics, Acta Mathematica,Advances in Mathematics, and Inventiones Mathematicae.

The Department is expanding the number of professorial faculty and at the same time redefining the roles- and reducing the number - of instructors. In spring 2005, a new 5-year hiring plan was adopted, focusingon increasing the number of research faculty to 60, and raising research productivity. The hiring plan hasthe following strategic goals:

I Raise the Department’s stature and NRC rankings by hiring strong researchers in the core mathe-matics areas, and concentrating the hiring in two of the traditional groups with strong grant historyand national and international name recognition;

I Increase the size of the computational group by adding two more joint hire with CCT;

I In order to serve the undergraduate population better, the department is reviewing its programs andpersonnel. As part of the Flagship Agenda the department would like to direct more of the undergrad-uate teaching effort of its professors and graduate students into teaching advanced undergraduateswho may use significant mathematics in their careers. The Department will also consider furtherhiring in Mathematical Education;

I Enhance our postdoctoral program as soon as our basic hiring has been done, bringing more freshideas and new connections to the Department.

The Department currently has 14 assistant professors, 4 associate professors, 36 full professors. Seven of I am countingthe new hirethe assistant professor were hired since 2004 as well as three of the full professors. Two of the new facultymembers are former VIGRE postdoctoral associates, the others have several years of research experience,including postdoctoral positions.

Federal grant support for the Department has increased considerably in the last few years:

DEPARTMENTAL GRANT SUPPORT

Year 2001-2002 2002-2003 2003-2004 2004-2005 2005-2006Amount $ 1,308,318 $ 942,455 1,402,683 3,124,125 1,150,592

The numbers are based on grants where the PI is a member of the Department of Mathematics. Severalinterdisciplinary research and educational projects with other departments on campus are underway. In

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particular, the total grant support for educational efforts is now close to $4,550,000. In Spring 2004 andagain in fall 2006, the Department was awarded a three year GAANN grant from the US Department ofEducation. The funding consists of $498,132 federal dollars matched by $124,533 state dollars. These fundsare being used to provide 9 doctoral fellowships to US citizen and Permanent Resident students currentlyenrolled. We expect all the GAANN fellows to participate actively in all VIGRE related activities. GAANNfellows receive stipends set by the Office of Student Aid up to a $30,000 maximum per fiscal year. In additionto the stipends, tuition and fees are paid by the grant funds. Several big grants will start this year or in2006.

In May 2003, a collaborative proposal with Physics to develop a joint course called the Physics/CalculusLearning Community was awarded. The CCT Foundation awarded $15,000 for a workshop, the first of a seriesof three, on 3-D Image Recognition organized by the PI G. Ólafsson (LSU Math), L. Butler(LSU Chemistry),and T. Quinto (Tufts Math). A follow up interdisciplinary workshop took place at the IMA, January 2006,with 111 participants from mathematics and the sciences. Eighteen faculty members were active in organizingspecial session at the joint meeting in New Orleans, in January 2007, and four workshops/conferences havetaken place or are planned to take place at LSU in 2007. The 2003 AMS Southeastern Sectional meeting washeld March 14-16 at LSU with nine Special Sessions organized by faculty in the Department. The Sectionalmeeting will again take place at LSU, March 28–30, 2008. Other projects involve collaboration with membersof the Departments of Civil Engineering, Computer Science, Mechanical Engineering, Biological Sciences,The Cain Center for Education, and the LSU Office of Strategic Initiatives.

The Porcelli Lectures, a three lecture series, are delivered annually by an internationally distinguishedmathematician. The talks are expected to be accessible to senior undergraduate students and graduatestudent. The speaker in 2007 was R. V. Kadison, the Kuemmerle Professor of Mathematics at the Univesityof Pennsylvania and a member of the National Academy of Sciences since 1996. The title of his talks was ThePythagorean Theorem from another, slightly sophisticated, point of view. Other speakers include VaughanF. R. Jones, 1990 Fields Medalist, and 1962 Field Medalist John Milnor.

For the past six years, the Department has organized a Graduate Student Picnic and Orientation Con-ference at the beginning of the fall semester, to welcome new and returning graduate students to the newacademic year. During this social and educational event faculty members from the research groups givesurvey talks about research opportunities for graduate students. In fall 2006 we included two graduate stu-dents as speakers. Graduate student Jens Christensen presented a talk about harmonic analysis concerningthe short time Fourier transform and wavelets, along with the underlying group structures. He also gaveadvice also to new graduate students about how to deal with challenges they will face. An African-AmericanGAANN fellow, Gideon Daspan, spoke on his research on the KP equation. Based on the positive experiencewith the Graduate Student Picnic and Orientation Conference the department is now planning a Warm-Upsession for incoming graduate students to take place in August. The plan will be discussed in detail later, butwe mention here that the organization and lecturing will be conducted mainly by current graduate students.

VIGRE ENHANCEMENTS: A VIGRE grant would strongly enhance both the Graduate Student Picnicand Orientation Conference and the Warm-Up. One of our goals is to increase the number of undergraduatestudents who pursue graduate study in the mathematical sciences. We therefore propose to extend this event,under VIGRE, to include senior undergraduate students. The VIGRE fellows will be required to participatein the organization of the Warm-Up session and actively participate by lecturing and interact socially withthe incoming students. This will be a part of our vertical integration of our students in teaching. GAANNfellows and Board of Regents Doctoral fellows will participate actively in all VIGRE activities, affordingthem new forms of research-related activity.

4 The Graduate Program

Each semester, the Department provides approximately 15 traditional graduate courses, and an averageof 30 individual reading courses and doctoral research sections. Nine of the 28 regular courses per yearare core courses providing a solid foundation for beginning graduate students. The other courses provide

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advanced study in the department’s research specialties. Each student must pass an 11 hour battery ofwritten PhD Qualifying Exams by January of the second year of study. Students must have each semester’scourse selection approved by their Advisory Committee. Every student is required to pass an oral GeneralExam for the PhD by the end of the third year as a condition of receiving financial aid. This exam isconducted by the Advisory Committee, which is chaired by the student’s dissertation advisor and includesat least four additional Department faculty members, together with a Dean’s Representative appointed fromanother department at LSU. In an effort to streamline the path to a doctoral dissertation, each of the researchgroups has complied a course list, including a list of core-1 courses, core-2 courses, and advanced coursesoffered annually or at least every second year, see http://www.math.lsu.edu/grad/gradcurricula.html.Under VIGRE, each research group, in collaboration with the corresponding crew, will be expected to furtherdevelop focused study plans and courses for its students.

In fall 2006 The Mathematics Department had 91 graduate students and 86 in the spring of 2007. Ofthose 27 are first year students and 56 have passed their PhD qualifying exam. Of those exactly the half,or 28, are US citizen. Of those 86 students 34 were US male and 12 US female. The gender distributionbetween international students were 29 male and 13 female students. At the moment there are 2 black USstudent, 2 Hispanic students and one Asian US citizen. Of the first year students 7 are female and 3 of themare US citizens.

In spring 2007 the Department received 170 applications for graduate study: 52 of these from US citizensand Permanent Residents, and 118 from international students. The Department had 13 openings forfinancial aid for new students. 22 offers were issued to fill all the openings, making a 73% success rate in

The followingdata is fromLAST YEAR!New dataavailable afterApril 15!acceptances from the applicants who were the first choices of the Graduate Committee, which represents

all 8 of the Department’s research groups. The 13 recruited students averaged 525 GRE Verbal, 779 GREQuantitative, 3.665 undergraduate GPA, and 3.78 graduate GPA for the 4 students with prior graduatestudy. The average stipend for those 13 students is $23,286 per year. These students will pay no tuition.Seven of the 13 students are US citizens, and 6 are international students. Fifty-two percent of the graduatestudents enrolled are US citizens, and 50% of the already PhD Qualified 56 students are US citizens.

The Department has a solid record of recruiting strong doctoral The Department currently enrolls 86full-time graduate students in mathematics of whom 82 are seeking the PhD. There are enrolled numer-ous graduates of outstanding universities world-wide, including Cornell University, Rutgers University, RiceUniversity, Johns Hopkins University, University of Wisconsin, University of California-Riverside, Cali-

should wekeep this longlist or takemost of itout?fornia Polytechnic, Iowa State University, Virginia Tech, University of Rochester, University of Kentucky,

University of Wisconsin, Amherst College, Harvey Mudd College, Lawrence University, Lehigh University,SUNY-Binghamton, Copenhagen University, the University of Paris, Bucharest University, the University ofScience and Technology of China-Hefei, Nankai University, Wroclaw University, University of Brasilia, SeoulNational University, and many others. As a result, the Department offers students a stimulating intellectualatmosphere in which high standards of achievement are maintained.

The Departments recruitment procedures and holistic methods of evaluation will combine with its individ-ual mentoring procedures to graduate PhDs from under-represented groups at a level far exceeding nationalnorms. During the period 2000-2006 the Departments minority (African-American and Hispanic-American)PhD graduates comprised 8.8% of its 45 PhD graduates. According to the 2002 Annual Survey of the Math-ematical Sciences entitled New Doctoral Recipients, Notices of the American Mathematical Society, Volume50, Number 2, February 2003, pages 238-253 (Also available at http://www.ams.org/notices/200302/02-first-report-updated.pdf) only 2.1% of PhD graduates in the entire US in Mathematics belonged to thesegroups. Thus the Mathematics Department graduated minority PhDs at more than four times the nationalrate. During the same period, 27% of the Departments PhD graduates were women. For example, NormaOrtiz (PhD 2005) was a Hispanic-American Louisiana resident, now a tenure track assistant professor atVirginia Commonwealth University. Uroyoan Walker (PhD 2001) and Angel Cruz (PhD 2000) and GarySalazar are Hispanic-American men: the first two are tenure track at the University of Puerto Rico andthe third at Trinity University in San Antonio. Sam Nelson (PhD 2002) is a McNair Program Economic

Dan Cohenthinks theinformationabout Nelsonis incorrectMinority member and is tenure track at the University of California - Riverside. Said Ngobi (PhD 2000) is an

African US permanent resident and is tenure track at Alabama State University, and Jamiiru Luttamaguzzi

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(PhD 2002) is an African US permanent resident and is tenure-track at Georgia College and State University.Of the 45 PhD graduates in mathematics from August 2000 - August 2006, 7 won research postdoctoral

jobs, 3 entered industry or the Defense Department, and the 34 others entered university or college faculty po-sitions. Of the 45, 18 were US citizens, 12 were women, and 4 were African or Hispanic-American. Job place-ment of all 250 PhD graduates of the Department can be found on-line at http://www.math.lsu.edu/grad.This includes a US student who went from a post-doc at Bonn to a permanent Lectureship at UniversityCollege Dublin, another who went to University of California Riverside. International graduates’ jobs in-cluded a tenure-track position at University Connecticut (Storrs), a research job at Paderborn, supported bythe European Harmonic Analysis Network, and later the International Research Training Group “Geometryand Analysis of Symmetries” Metz and Paderborn as well as a visiting position at the University of Iowa.He just got an article accepted for publication in Journal of Functional Analysis. In 2004, our 1996 alumnus,Yongdo Lim, won a prize from the Korean Mathematics Society for the best research paper of the year bya Korean mathematician. The prize was for his article Birkhoff formula for conformal compressions of sym-metric cones which appeared in the American Journal of Mathematics. The Department puts in efforts tomotivate our graduate and undergraduate students to take an internships to broadening their education andexperience. Our graduate student Tim Breitzman took an internship at Wright Patterson Airbase, followedby a regular semester internship at the same place. Now he is a Senior Scientist permanently employedthere. Simone Flory and Fabiana Cardetti, both women, interned one summer in Baton Rouge with IEM(Innovative Emergency Management) modeling plumes of toxic gases in the atmosphere. Both were offeredpermanent jobs before getting a PhD. However, they completed the PhD first. F. Cardetti got a postdoc-toral position at University of Connecticut and is now in a tenure track position there. S. Flory on the otherhand went into private industry. Complete list of graduates since 1930, with employment information to theextent known, can be viewed at http://www.math.lsu.edu/grad/phdgrads.html.

The recruitment of quality doctoral students is facilitated by large sustainable resources allocated tothe Mathematics Department as one of the University’s seven Foundation of Excellence Programs. Underthis program, Stipend Enhancements, currently $338,500 per year for mathematics graduate students, haveelevated the stipends of most of the departments doctoral students, with incoming offers averaging more than$23,000 per academic year. The University has converted terminated instructorship lines into permanentrecurring funds for graduate stipends in mathematics. Tuition is no longer charged for Graduate Assistants,and the University is preparing to relieve graduate assistants of most of the cost of health insurance. In2006-7, the department’s graduate students are being paid around $1.9 million in stipends, of which $717,000comes from grants. These renewable resources will ensure that programs developed under VIGRE will besustainable.

The aforementioned facts demonstrate that the LSU Mathematics Department has the ability to recruithigh quality graduate students internationally as well as nationally and from within Louisiana. The resourcesmobilized in recent years have greatly increased our ability to draw in US citizen students.

4.1 New Graduate Courses

The Department continuously evaluates its graduate program and improves its programs and course offerings.The syllabi and variety of first year core-1 and core-2 courses have been improved, and new upper-level courseshave been introduced. In particular the content of the three fundamental sequences, Algebra, Analysisand Topology has been revised. As an example, the two course sequences in Analysis is now Math 7311,Real Analysis which treats general measure theory and integration with emphasis on Euclidean space, andMath 7350, Complex Analysis. Each research group runs a weekly research seminar, involving both facultymembers and graduate students. The topic is posted on the Department’s web-page and published in theweekly Departmental calender. These seminars have become more student oriented and are sometimes usedto introduce graduate students to topics courses that will run next semester. It is common for graduatestudents to present results from their dissertation research or other topics of interest. Members of theresearch groups work with students in many individualized reading courses. During the spring 2006 and fall2006 the Department ran seminar style courses as proposed in our previous VIGRE proposals. Here thestudents read research articles, gave presentations on the material and answered questions from the other

9

students and the faculty mentor.A component of the graduate program review has been the formulation and web-publication of a coherent

study plan and list of courses for each research group. Courses offered are divided into three categories:Core-1 fall courses for all incoming graduate students lay a common foundation in Algebra I(groups, rings,modules), Real Analysis I (general measure and integration), and Topology I. Students chose four Core-2spring courses from the list: Algebra II (field theory), Complex Analysis, Ordinary Differential Equations,Graph Theory, Topology II, and Differential Geometry. A wealth of advanced courses is offered on an annualor bi-annual basis according to the plan. Each of the research groups keeps to graduate students updatedon courses related to their speciality http://www.math.lsu.edu/dept/grad/gradcurricula. Some of thenew courses codify topics courses which have been developed during the preceding years. Evaluation ofthe graduate program will continue in the coming years, with the VIGRE Committee acting as a majorcommittee for curriculum review, for the design of new courses, and in the formulation of coherent studyplans and lists of courses for students in various specialties.

Evaluation of the graduate program will continue in the coming years, with the VIGRE Committeeacting as a major committee for curriculum review, for the design of new courses, and in the formulation ofcoherent study plans and lists of courses for students in various specialties. Several faculty members havedeveloped lecture notes related to those courses and posted them on their webpage or a website designed forthe individual research group.

4.2 The Warm-Up program

The Department is developing activities that require more involvement and responsibility of graduate stu-dents. One of the program that has run for several year is the Graduate Student Seminar which is organizedby the graduate students. A new program that will run for the first time in August 2007 is the Warm-UpProgram. This program was an integral part of our previous proposal. We have also studied the successfulWarm-Up Program at the University of Chicago. As a preparation for this program a meeting with thegraduate students was held in March. Here the Chair of the Department, the Graduate Student Advisorand the PI of this VIGRE proposal discussed with the graduate students the Warm up program, the mainidea and the graduate student involvement. During the second half of the meeting several questions aboutthe VIGRE program were also discussed. After the meeting the graduate students formed a committee todiscuss the program and develop new ides.

The Warm-Up program is directed towards incoming mathematics students. The program will primarilybe organized and run by advanced graduate students who will be the guides, teachers, and mentors for theorientation week. Only minimal faculty supervision will be provided. This will already be an exampleof ongoing vertical integration, involving senior graduate students in decision making, development andpresentation of short courses and social interaction with junior students. Its basic goals, which are allstrongly related to the basic goals of the VIGRE program, are as follows.

I to train graduate students in planning and decision making,

I to give senior graduate students the opportunity to develop and present advanced mathematicalmaterial,

I to integrate the incoming students into the departmental life,

I To provide a bridge from undergraduate curricula to the challenging first-year graduate core program;

I to improve the retention rate of graduate students,

I to improve the academic program and environment,

I To introduce new students to advanced students who can provide mathematical and personal resourcesfor them, e.g., begin peer guidance of graduate students;

I To introduce the new students to each other, the department, and Baton Rouge at large. The programwill give support, encouragement and positive reinforcement to students.;

I To indoctrinate students with the basic Mathematics Department philosophy and into the culture of

10

graduate education, and

I To prepare students for the expectations of being a teaching or research assistant: the responsibilitiesof a graduate student including the type and level of work which is expected.

The program will take place during two weeks prior to the start of fall classes. There will be betweenten and twelve two-hour sessions on math (e.g., Set Theory, Analysis in Several Variables, Algebra, etc.)with additional meetings to talk about Baton Rouge, LSU, and graduate students life. There will be socialevents at LSU and downtown. TA training including the technical aspects of the computer systems will beincluded.

The academic sessions are meant to review material, let students see material that may not be explicitlycovered in their courses, which they may be required to learn on their own or in a 4000 level course. andgive a preview of the first year sequence. As an example one could envision the following set of activities:Mathematical Activities: (1) Set Theory (1 session); (2) Point Set Topology (2 sessions); (3) Analysis ofSeveral Variables (2-4 sessions); (4) Linear Algebra (1-2 sessions); (5) Life as a graduate student at LSU;Orientation Activities: (1) Computer Training for TAs and potential TAs (2 sessions); (2) Universityorientation (2 sessions); (3) International Orientation (4 sessions);Social and Evening Activities: (1) Trip downtown and to Shaw Center; (2) Tour of Campus (contactLSU Ambassadors); (3) Introduction to recreational facilities; (4) Dinner and even a Game night.

4.3 Communication skills

During the first year, in addition to the core classes in mathematics, all graduate students are required toparticipate in the Communicating Mathematics course. This course is already a requirement in the graduateprogram and has been in existence and growing in its scope for more than a decade. About half of thecourse focuses on the teaching of mathematics. Students are required to observe the classes of an assignedexperienced mentor, to complete questionnaires on these observations, and to present mini-lectures, firstbefore their graduate peers, and then before their mentor’s undergraduate class. These presentations serveas focal points for in-class discussions of a broad range of pedagogical issues. The other half of the courseconcentrates on expository issues. Each student is required to write a short survey paper, prepared underthe supervision of a faculty member, and then to present a 15-minute talk on this paper to the class andinterested faculty. This project enables the graduate students to meet more faculty members than theywould see in their lecture courses. The talks are presented in conference-style sessions with the speakerusing overhead transparencies or a computer-based slide presentation. This course, the project in particular,introduces students very early in their programs to the tools needed for clear and effective communicationof mathematical ideas.

VIGRE ENHANCEMENTS: The goals of the Warm-up session fit perfectly into our general VIGREgoals of increased students activity and responsibility for organizing educational and research activity andinteract with faculty and other students. We will motivate senior undergraduate students to participate inthe Warm-up session and it will be a requirement for all graduate VIGRE trainee to actively participate inthe session.

5 New Initiatives through the VIGRE program

The Department is proposing several new initiatives to integrate graduates and undergraduates to researchearly, to enhance the scientific education and professional development of our students, and to enhancevertical and horizontal integration of research, education and outreach. Special consideration is devoted to

we have toadd fewcomments on“transition”point highschool ->College

the transition points that meet the students on their way to graduation. Most of those initiatives are builton ongoing curriculum review and the discussion related to our previous VIGRE proposals and are thereforeclosely tied to existing structures and initiatives. Both faculty and graduate students have been involved inthe discussion through open meetings and discussion. The Department has also studied successful VIGRE

11

programs, in particular those at University of Arizona, textitUniversity of Chicago, University of Georgia,and University of Utah. All new activities are based on following principles.

• Provide vertical integration of faculty members, postdoctoral associates and graduate and undergrad-uate students, through the research crews.

• Provide horizontal integration through group projects and integration of several members of the existingresearch groups into each research crew.

• Enhance the mathematical culture and professional development of our graduate students by activeresearch and learning and systematic and stimulating exposure to current research trends in the math-ematical sciences;

• Foster graduate students research contacts at other academic institutions, government, laboratories,and industry through participation in conferences, visits to other departments and internships;

• Provide training in the written and oral communication of mathematics for use at all levels - forteaching, mentoring, and research;

• Help students on all level to pass transition points by mentoring, both individual through the crewsand advisors, and collectively through information material and meetings, as well as review sessionswarm-up sessions. Motivate undergraduate students to major in mathematics through contacting andinformation as well as motivate graduate students to seek research positions after graduation;

• To increase the number of US students, minorities and women through focused recruitment.

5.1 The Research Crews

The Research Crews are the central new part of this proposal. This form of vertical integration has beendeveloped through the discussion around previous VIGRE proposal, through successful research seminars in2006, and the study of the successful implementation of similar structure at the University of Georgia. Thecrews will enrich the ways in which postdoctoral associates and students, both graduate and undergraduate,are mentored, how they learn to interact scientifically with other students, faculty members and postdoctoralassociates. This integration and individual offerings will be coordinated through the existing faculty researchgroups in collaboration with the VIGRE committee and the Graduate committee. Each research crew willconsist of a faculty member or members as a crew leaders and mentors, a postdoctoral associate, if availableand a team of graduate and undergraduate students together with Every VIGRE supported graduate studentas well as the Board of regents and GAANN fellows after their second year will be required to participate in acrew. The first year VIGRE students will be required to take one extra course, which can be a crew, in theirsecond semester. The exception are trainees with Dissertation Year Traineeships (to be discussed later) andfellows that are expected to finish their thesis in one year. Note that all the research groups will continuetheir seminar as before. The crews will run as a 3 credit hour course and require at least 5 students to beable to run for credit.

To obtain maximal flexibility the form of the crews is not fixed, but the objectives are constant: Getstudents involved in mathematical discussion and new, interactive form of learning, writing and presentingmathematics. The role of the faculty mentor is to guide the discussion and learning, to carefully coordinatethe work to make sure all participants participate actively in the work of the crew and involve seniorundergraduate students in a constructive way. The crews can be active for a semester and then give spacefor another crew or, if enough students are interested and the topic require, it can stay alive for severalsemesters. It is proposed to start with at least three crews in the first year of the grant, and increase thenumber as we gain experience and as more VIGRE postdoctoral associates become available. We expect thatat least one of the crews is in applied mathematics/computation. Two main types are crews are seminarstyle learning and discussion and group research projects.

12

Seminar style learning and discussion: Students dig into a specific topic or field, by reading researchShould weput in someexamples.

articles or a research monograph. The students or, if background material is necessary, a faculty memberor postdoctoral associate, present material for the group. The material is discussed and the group tries todevelop new questions and new ideas. The mentor should motivate the students to asking questions, workout and present examples and, if adequate, use computation and programming to attack a problem.Group research projects: Understanding a specific topic or problem. At the beginning a facultymentor would present the problem and some of the basic ideas. The students are divided into smaller groupswith a faculty advisor that work on specific aspects of the problem and then present the results to the fullgroup and point out further directions. The smaller groups will meet several times during the week. Newgoals and tasks are formulated through discussion. If the crew works on the same, extended topic more thana semester, the member of the crew prepare material for new members in the beginning of the semester toenable them to actively participate in future work.

The VIGRE committee may also organize smaller crews with specific, time-limited, duties. For instance,smaller crews may be organized around special tasks such as those related to our K-12 outreach programdiscussed later in this proposal.

5.2 The Graduate student Colloquium

The Department has for several years run a Graduate Student Seminar, organized by the graduate studentsthem self. The speakers are mainly graduate students that are close to graduation. We are planning toupgrade the seminar to a Graduate Student Colloquium are are requesting funds to invite 8 selected speakers

or are 6 = 1each monthenough?

each year. Each of the speaker will say at LSU for at least 3 days to interact with graduate students andfaculty. The colloquium would be organized by graduate students: They find the speakers, contact them,organize the travel and fill out, with appropriate faculty guiding, the forms. One faculty member will actas a mentor and advisor, both to help with the choice of speaker as well as review all forms before they aresubmitted.

5.3 The Research Connections Program

The Department encourage its students to visit other departments and university during their study. Thisprogram was supported for several years by a Board of Regents Grants which covered most or all of thetravel. Through this program students have participated for extended time in programs like Master Class2006-2007, Symplectic Geometry and Beyond, The Netherlands, 2006-2007. Another student visited theUniversity of Vienna for a month to work with members in the Numberical Harmonic Analysis Group there.We plan to extend this program so that graduate students can spend a term, during the spring and inexceptional cases during the academic year on–site at a national laboratory or an industrial or academicinstitution, and participate in projects related to their research. This will provide opportunities for VIGREtrainees and other graduate students to forge research contacts outside LSU, in preparation for postgraduatework. Participation in this program will be coordinated by a designated faculty mentor in the researchgroup. The coordinator will grade the research work done for the trainee’s academic credit. Also under thisprogram, funds will be available for the trainee to attend conferences in his or her area of research interest.The Research Connections Program also complements benefits now available to LSU graduate students atthe Mathematical Sciences Research Institute (MSRI). As an academic sponsor of MSRI, LSU can now sendseveral advanced students to graduate programs organized by MSRI each summer.

5.4 Graduate Traineeships

To attract new students and enhance the training of its American students, the Department of Mathematicsproposes to use the VIGRE grant to create three new types of graduate traineeships for US citizens andpermanent residents. These are the Doctoral Foundation Traineeship (DFT), Doctoral Dissertation Trainee-ship (DDT), and the Dissertation-Year Traineeship (DYT). To obtain a VIGRE support all students, exceptincoming, will have to submit a proposal to the VIGRE committee describing their goals and activity during

13

the time of support. The proposal should contain a one page summary. It should state the beginning andending period for the support, in which research crew the trainee is going to participate, what his or hersresearch and learning goal during the period are. IF travel or other expenses than participant support isinvolved, a budget is also required. The proposal should include a statement about planned interdisciplinarywork or internships as well as expected interaction with undergraduate students. Finally, the proposal hasto contain a description of previous study, previous support if any, a 2-page CV, including a publication listand presentations. The duration of each traineeship is usually 11 month with a possible 11 month extension.The maximum combined traineeship is 33 months. The stipend will be $25,000 per calendar year, and maybe supplemented by $3,000, $5,000, or $8,000 in enhancement/supplement funds awarded by the GraduateSchool to deserving applicants nominated by the Department. All traineeship, except the first year DFT,which is to be administrated by the Department’s Graduate Committee, represented by the Director ofGraduate Studies, will be administrated by the VIGRE committee in collaboration with the Director ofGraduate Studies.Doctoral Foundation Traineeships: One important objective of the VIGRE Program is to recruit promis-ing young American doctoral students, in particular from the Southeast region. To this end, the Departmentwill offer five Doctoral Foundation Traineeships annually to rigorously selected US citizen students and per-manent residents who are not already enrolled in the graduate program in Mathematics at LSU. Specialattention will be paid to underrepresented groups. The initial duration is 11 months, but the trainee cansubmit a request for an extension to maximal 11 more months. The purpose of these traineeships will be tosupport exceptionally promising doctoral students in their initial study at LSU with no duties required otherthan those which enhance the professional preparation of the student and those required by the courses theyare taking, freeing the student’s time and energy for the effort of bridging the gap between undergraduateand graduate study, and to begin forming a solid foundation for a career in mathematical research. Thetrainees will have to take one extra course in the second semester. This course can be a research crew orone of the core two courses.The Doctoral Dissertation Traineeships: Doctoral Dissertation Traineeships will be offered to doctoralstudents who meet all of the following four criteria: (1) Complete the PhD Qualifying Examination success-

if necessary,those detailscan bedeletedfully by January of the second academic year with a grade of distinction on at least two of its four subtests;

(2) Maintain a cumulative GPA of at least 3.25; (3) Pass the General Examination for the PhD before theend of the third academic year; (4) Receive a strong written recommendation from the General Examinationcommittee.

Students supported by the DFT for their first two years are expected to have teaching duties in theirthird year, and will therefore not be eligible for this program until their fourth year at LSU. In most casesthe DDT is expected to be 11 months, but shorter proposal for special research and outreach activities arealso allowed.

Dissertation Trainees will have no regular teaching duties, but their activities during the traineeshipperiod is expected to contain both interdisciplinary component and interaction with undergraduate students.This can consist of aiding group projects, and mentoring VIGRE-supported undergraduate students, assistingin development of new teaching material, helping with extended computer lab work, and assisting withoutreach projects like the Mathematics Consultation Clinic and the VIGRE related summer REU and theWarm-up as well as participation in projects related to our K-12 outreach.The Dissertation-Year Traineeships: Dissertation-Year Traineeships will be offered to two students whohave already had at least one year of teaching experience at LSU and are strongly expected to complete thedoctoral dissertation during the one year of such support.

To apply for the stipend the student must submit to the VIGRE committee the material stated in thebeginning of this subsection as well as a letter from the chair of the advisory committee and signed by allmembers of the committee. This letter must provide convincing evidence that the doctoral dissertation willbe completed successfully during the proposed year of support.

A student who has received a Dissertation-Year Traineeship is not eligible for any further support fromVIGRE funds in case he or she is not able to carry out the plan to complete the Dissertation successfully inone year.

14

6 The Undergraduate VIGRE component

To be written.

6.0.1 The Mathematics Consultation Clinic and Other Outreach Programs

The department operates a highly successful industrial and educational outreach program, the MathematicsConsultation Clinic. Mathematical problems faced by industry (mostly Louisiana based) are analyzed andsolved by teams of graduate and undergraduate students working with faculty guidance. This providesMathematics majors their first opportunity to work on mathematical problems not from textbooks, as wellas their first experience of serious collaborative mathematical work. Recent clients include CII Carbon, achemical company based in New Orleans, Innovative Emergency Management, Inc., a software developerbased in Baton Rouge, Hibernia National Bank, the Louisiana State Lottery Commission, and Our Lady ofthe Lake Hospital. Several summer internships have resulted from this work.

Due to recent changes in high school teacher qualification requirements, the state will soon require largenumbers of mathematics majors to fill its high school mathematics teaching needs. To fill this need, the LSUMathematics Department launched the Secondary Mathematics Education Concentration in the Fall of 2003.Early indications are that there is substantial interest in this concentration. The focus of this concentrationis on excellence in mathematics, with additional training in pedagogy.

The MathVision Laboratory is a relatively new educational outreach unit of the LSU Department of Math-ematics that implements education-research based programs. The mission of the Lab is to help Louisiana’steachers and students excel in mathematics education at all levels. MathVision activities are designed tosupport and accelerate the positive educational changes made in our state during the last six years. The Labhas ongoing projects with the LSU Colleges of Basic Sciences, Engineering, and Education, with Southeast-ern Louisiana University, Southern University Baton Rouge, LSU Shreveport, New Mexico State University,UT Austin, with the Louisiana Resource Center for Educators, and with the East Baton Rouge, Livingstonand Tangipahoa Parish school districts. Current projects aim to:• Revitalize and expand teacher education programs in mathematics and science;• Establish in-school mathematics laboratories in which mathematics, science, and engineering undergrad-

uates and graduate students volunteer to provide tutoring and teaching assistance (Scotlandville MagnetHigh, McKinley Magnet High, Sherwood Middle, Springfield Middle (Livingston Parish), Hammond West-side Upper);

• Provide a coherent, permanent, and sustainable program of professional development for elementary,middle, and high school mathematics teachers (joint initiatives with LRCE, Dana Center (Austin),LDE/LaSIPs Learning-Intensive Networking Communities for Success);

• Investigate the role of mathematics departments state-wide and nationally in teacher preparation, anddevelop, promote, and implement standards-based mathematics curricula and assessment methods in K-16education.

6.0.2 The REU programs

For the past 12 years LSU has continuously run a two-month summer Math REU funded by NSF and

This and thenextsubsection arepart of theundergradu-ate programand willprobably bechanged

Louisiana (LEQSF). The students have come from across the US with many students from elite east andwest-coast institutions. A few others come from the midwest, the west, and the south. These highly-recommended students from non-elite universities are competitive with those from better-known schoolsbut often have taken fewer theorem-proving courses. These REU programs, directed by LSU mathematicsfaculty and involving graduate students as well, have been highly successful and 7 of the participatingstudents decided to do their graduate study at LSU. Topics vary from year to year. Some projects fromrecent years include investigations of braid groups, finitely presented groups, and zeta functions associated tographs. In several cases, REU project work has led to substantial exposure in the mathematical communityfor program participants. For instance, one participant presented his findings on growth functions for braid

15

groups at a Special Session of the American Mathematical Society National Meeting in 2001 and anotherparticipated at the International Congress of Mathematical Physics in Lisbon, 2003.

In addition to the main REU, during the Summer of 2003 faculty from the Department advised threeminority REU students in Environmental Mathematics Projects. These students were supported by an NSFgrant awarded to the Sciences and Mathematics at LSU.

7 The Postdoctoral Program

An active department needs a continuous influx of new ideas, methods, and problems. An effective postdoc-toral program, visiting faculty positions, and frequent hiring of new assistant professors all contribute to theachievement of this objective. The Department of Mathematics has a consistent record of hiring recentlygraduated PhD’s as Visiting Assistant Professors (in addition to hiring tenure-track Assistant Professors).The Department had two Visiting Assistant Professors in 2000-2001, three in 2001-2002, and three in theyears 2002-2006, all supported by CCT and five in 2006/07. In all of those year, the Department had anumber of shorter term visitors. Two of the current postdocs are US citizens, and one of them is a minority.Both of them would therefore be eligible for VIGRE support. A list of visitors and postdoctoral associatesmay be found in the appendix.

As part of the LSU commitment to VIGRE, CCT has agreed to support two half-positions in the nextthree years if the VIGRE proposal is funded. If this program turns out to be fruitful for both the Department

We do nothave thiscommitment

of Mathematics and the CCT, then the support can be extended for the next two years. Otherwise, theDepartment will attempt to secure support from other sources, or, if necessary, use its own professorial lines.The CCT postdoctoral associates will be in computational mathematics and will be affiliated with both theDepartment of Mathematics and the CCT. Furthermore, the College of Arts and Sciences has committedto supporting four half-positions for the duration of the VIGRE grant. It is planned that each position

Question:Will we startwith 4 thefirst year, or2 and then 4?will be for an initial appointment of two years with a possible extension of one more year. A departmental

objective is to maintain at least three permanent postdoctoral positions, to start no later than the end ofVIGRE support. This will be accomplished either by securing new funds from the University, or by usingupcoming retirements and openings to convert existing positions into postdoctoral positions.

Each postdoctoral associate will be a member of a research crew and play a prominent role in its researchand educational efforts. Postdoctoral associates in Mathematics Education will have two advisors, one in amathematical research area, and one in education. All postdoctoral associates will benefit from a reducedteaching load of six hours per year. Part of this teaching may take the form of special educational activitiesof the research crew. In addition, postdoctoral associates will gain experience by serving as mentors forgraduate and undergraduate students supported by the VIGRE program. They will also share responsibilityfor the new seminars initiated by the VIGRE grant.

8 Mentoring and advising

Mentoring is planned in multiple aspects of mathematical life: academic and intellectual guidance for studyand research; oral presentation and writing experience; social integration into departmental and professionallife; and future employment. Accordingly, mentoring of students will be undertaken via an advisor oradvisory committee, web based information, meetings, personal contact with instructors of courses, andthrough informal contact with other students. Vertical integration achieved by means of Research crewsadd a new dynamic to mentoring. It provides a natural venue for undergraduate students to interact withgraduate students and for graduate students to interact with postdoctoral associates. Each group will learnfrom and be motivated by the experience of its seniors.On the graduate level: The social and intellectual mentoring begins during recruitment, even beforethe new student arrives on campus, with communication between prospective students, faculty members,and current graduate students. Mentoring becomes more organized and intense with the beginning of thestudy in Baton Rouge through the Warm-up and again with the Graduate Student Picnic and Orientation

16

Conference. During the the fall semester, the Graduate Director and Assistant Director ask each Core-1course professor to identify any students showing deficiencies to help them with individual mentoring. In thefirst year the graduate students must select a faculty member as a mentor for a communicating Mathematicswriting and speaking project, and an Advisory Committee of three members to help the student with courseselections for future semesters. Mentoring is mandatory and approval required for course selections eachsemester of study. During the summer after the first year of study a Problem Lab course is offered forstudents from Analysis I and Topology I to prepare student for the comprehensive Qualifying Exams.

Some graduate students decide early on a research speciality and select a dissertation advisor who thenchairs the student’s Advisory Committee. That committee is enlarged to 5 faculty members, including atleast one from each traditional core area: algebra, analysis, and topology, when it becomes responsible fordissertation guidance. This must happen by the third year of doctoral study. The dissertation advisorcommonly meets with the student at least once a week, guiding the student through the studies, conductingreading classes with him or her, and introducing the student into mathematical research. The mentor makessure that the student participates in the seminar of his or her field and attends colloquia. Students mustlearn that even colloquia outside the immediate specialty may provide valuable mathematical insights. The I added this.mentor also helps the student to build professional contacts, guides the student to suitable conferences andoutside talks. Finally the mentor helps with job applications by looking over the applications, points outpositions to apply for and persons to contact.

Over 30 of our faculty members chair or have chaired an advisory committee since 2000 and have servedas members of multiple advisory committees. Nearly all professors have mentored students in reading classesor guided them in projects for Communicating Mathematics.

The Department has introduced a Postdoctoral Job Application Resource Center which includes advicefor preparing a vita, submitting a research paper to a journal, and writing a Research Statement and aStatement of Teaching Philosophy. There will be case histories showing how past students succeeded in theirjob searches. In fall 2006 the Department organized a panel discussion between faculty members, the PIof this proposal, the chair, the graduate advisor, one from applied mathematics and two junior assistantprofessor which had postdoctoral experience before coming to LSU. The main topic was how to prepare fora successful job application as graduation approaches. The proposed application procedure for one of thetraineeships will further help student to prepare for applications and later grant submissions. A mentor willread the application before submission and help the student to write a professional proposal.On the undergraduate level: Each undergraduate major has a faculty advisor, who meets with thestudent at least once per semester. Currently 11 professorial faculty members and one instructor with aPhD serves as undergraduate advisor. But LSU and the Department have implemented other, more intense

Is that rightthat theinstructor hasa PhD?form of advising. First on the list are the LSU Chancellor’s Future Leaders in Research. At least 3 have

been mentored in the Mathematics Department, and one of them has been working with the PI for almosttwo year now. Several undergraduate students write honors theses under the guidance of faculty members.For example, Prof. J. Cygan is now guiding D. Guillot, who also has a music advisor, on a thesis on waveletsand music. Another student is writing a honors thesis with Professor D. Sage on Random walks on groups –applications of representation theory in probability. Finally, the Department organizes meetings with seniorundergraduate students to inform them on courses that are needed for graduate study and what their choicesare. In short, almost all faculty members serve as advisors for undergraduate or graduate students and somefor more than one. The Department offers several form of individual mentoring on all aspects in the life ofour students.On the postdoctoral level: Each postdoctoral associate is associated with an advisor in his or her field.The advisor works with the postdoc in regard to teaching, research, grant applications, and a job search.Professor J. Oxley, who initiated and organizes the Communicating Math, or other strongly involved inthe teaching mission of the Department visit their classes and give initial help with their teaching. Thepostdoctoral associate participate in the grant writing meeting with junior faculty and receive the same helpand mentoring during the grant writing process.

17

9 Recruitment and Retention

9.1 Recruitment

The Department of Mathematics has a multifaceted and effective graduate student recruitment program.Recruitment includes both national and global direct paper mailings to universities and to students, followedby direct email to students. The Department exchanges names of mathematics majors with more than 500selected colleges and universities within the US. GRE Search Service is used extensively. Mailings includea full-color poster containing information about the department and the graduate program. It is widelydisplayed on mathematics department bulletin boards, effectively guiding prospective applicants to the De-partment’s graduate website which has been completely redesigned during recent years. This site providesfull, up-to-date information about graduate study, research, and financial aid and an e-mail button for stu-dents to request information. The Department takes a half-page advertisement each year in Assistantshipsand Fellowships in Mathematics, published by the AMSociety. The Department identifies appropriate meet-ings of professional societies at which participating faculty members can publicize opportunities for graduatestudy and faculty members have often recruited new students during travel and visits to other departments.Finally, the Department benefits from the national and international reputations of its faculty members, andfrom its own 250 PhD graduates who frequently recommend the department’s graduate program to theirown students.

With the $1.9 million annual graduate stipend budget from continuing resources identified on page 9, theDepartment currently pays stipends of high as $30,000 per calendar year tuition-free to ten students. Thesestipends are advertised at selected colleges and universities both nationally and globally, raising the visibilityof the graduate program. During the spring of 2007, there are 13 applicants for each opening for financial

need newnumbers for2007

aid. The result has been an increase in both the number and in particular the quality of applicants. TheDepartment succeeded in recruiting a high percentage of its first-round choices: (# soon!)% of the spring2007 first-choices accepted. The recruitment program is primed and ready to include vigorous advertising ofVIGRE Graduate Traineeships in each of its vehicles. The VIGRE Doctoral Foundation Traineeship programwill markedly enhance the recruitment of American students both regionally and nationally.

The Department runs a successful Research Experience for Undergraduates Program each summer. Thisprogram draws excellent advanced undergraduate mathematics majors to LSU for the Summer Term. Manyof the students come from top ranked Universities, Three of the REU graduates are currently enrolled andexcelling in their doctoral studies in the LSU Mathematics Department. Another has accepted a Board ofRegents fellowship and will attend graduate school at LSU fall 2007. Thus, the REU works as a strong tool

We’ll make it2 if Parkheaccepts!!

to attract excellent students to LSU.On the undergraduate level, GK-12 and AP Calculus grants give us valuable contacts with high school

mathematics programs in the state and can be used to direct students to our website and inform themabout study in mathematics at LSU. pEvery fall there’s a meeting at Walker High about the AP calculusgrant program where faculty member go to talk about LSU. And the summer teacher workshops that thegrant supports presents another opportunity to plug the math major. Finally, through our outreach, severalPlus instructors and TA’s hove opportunity to inform students about LSU. A second tool is the annualLSU Mathematics Contest for High School Students, and contacts made with local schools through thatprogram. One of our important tools to recruit good high school students to LSU and into math is our MathContest, p. 2. The Department is also implementing a Undergraduate Recruitment Committee to contactstrong students in our calculus sequence and some other courses and inform them about double major inmathematics. The department will circulate information on its website and in mailing to high schools aboutthe mathematics curriculum and about opportunities to study mathematics in college. We also intend tointroduce a VIGRE student day. This will be a one day recruitment event for undergraduate students to

should wekeep this?Len: I wouldsay yes if youcan fundvisits frombeyond BatonRouge.

take place in April. Information related to the VIGRE program, including financial support information forundergraduates, will be presented by a faculty member or postdoctoral associate and students supported byVIGRE. Finally, we will create a VIGRE webpage, where the program will be advertised and informationabout our initiatives, the scientific and educational efforts of the research crews, and financial support forstudents will be presented.

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Several VIGRE departments have found it difficult to find and compete for highly qualified US citizenpostdoctoral associates. But every year several possible applicants require information about possible post-doctoral positions at LSU to work with selected faculty members indicating that a stronger postdoctoralprogram would likely succeed at LSU. For VIGRE postdoctoral positions, the Department of Mathematicswill rely on recruiting techniques similar to those employed for recruiting new professorial faculty. Further-more, successful recruitment will be conducted via faculty members associated with the various ResearchCrews, who will use their professional connections to informally contact potential applicants related to theirresearch program.Women and minorities: One of the best assets for recruiting minorities is visible production of minorityPhD’s and contacts made through them. The Department of Mathematics has graduated four African-American doctorates, including one who went on to become President of Southern University, the nation’slargest historically black institution. Another won a postdoctoral position at MIT. Four from LSU is asignificant number considering that four is the typical national annual production of Black American PhD’sin Mathematics. The Department has also placed both US and international black PhD graduates asmathematics faculty at historically black colleges in Louisiana and the Southeast. It has been common forinternational African PhD graduates to become permanent residents or citizens of the US, making them newminority citizens and role models for American minority students. The department sends representatives,including its two African-American tenured professors, to meetings of minority mathematical societies forthe purpose of recruiting minority graduate students. Targeted recruiting literature is mailed to a list it hasdeveloped of historically black institutions. The Department has also graduated many Hispanic AmericanPhD’s, including two who are now professors at the University of Puerto Rico and another is tenure-trackat Virginia Commonwealth University. In all, our efforts the last year have resulted in considerable increaseof minority students, from 3, or 4% of our graduate students in 2002/03, to 9, or just below 10% in 2006/07.GAANN currently supports a Hispanic-American woman and an African US Permanent Resident minority.Both GAANN and BOR Fellowships recently or currently support Sino-American Women minority studentsas well.

Women are an under-represented group in mathematics. In Fall 2006/07, around 28% of the Department’sgraduate students are women. In 2005/06 5 out of 11, or almost 50%, of the PhD graduates from LSU werewomen! Women have held many of the department’s most prestigious doctoral fellowships.

9.2 Retention

High retention is promoted by individual mentoring of students and a warm student/faculty working rela-tionship which is characteristic of the program. Both factors will be enhanced by the new Warm-up sessionand the integration of graduate students into Research crews. Two weeks after the start of the fall semester,the Graduate Director and Assistant Director ask each Core-1 course professor to identify any studentsshowing deficiencies. Individual mentoring is provided to such students. During the summer after the firstyear of study, students are invited to take a summer Problem Lab course to gain more supervised experiencesolving problems in Real Analysis-1 and Topology-1 if needed. During the first year of study, each studentforms an Advisory Committee of three faculty members whose approval is required for the student’s courseselections each term. After PhD Qualifying, the student arranges to work with a major professor, who thenchairs the Advisory Committee. At the dissertation stage of study, the Advisory Committee is enlargedto include 5 faculty members, including at least one from each core areas: algebra, analysis, and topology.There is also a Dean’s Representative. The Committee administers the (oral) General Exam for the PhDand the Dissertation Defense.

Using published AMS data, the Department has tabulated the ratio of 3-year PhD graduation totals tototal graduate enrollment for 28 state university math programs ranked above LSU by the NRC. The averageratio in 2004-5 for that group was 0.22. LSU’s ratio for that period was 0.21. However, LSU’s enrollment hadincreased from 1999 to 2004 from 53 to 90, and the number of its graduates for 2004-5 was really determinedby the 53 enrollment, not the larger figure of 90. Using the older enrollment figure, LSU’s ratio for 2004-5would have been 0.32, ranking LSU just below the top 5 in the table.

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I have not worked on the following parts. We need to think more about the life after VIGRE.

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10 Organization and Management Plan

The research and educational efforts of the VIGRE program are centered around the Department’s research to berewrittengroups and the new research crews. The VIGRE Committee, headed by the Program Director, will coordinatethese efforts. The multifaceted vertical integration of education and research will be integrated into theexisting structures at the Department. The graduate program is lead by the Director of Graduate Studies,Professor L. F. Richardson, and the Graduate Committee. The Graduate Committee makes recommendationsfor curriculum changes, decides upon the course offering each semester, and discusses the progress and needsof individual graduate students as appropriate. The Graduate Committee also assists in the selection ofrecipients for financial aid for graduate study and in the recruitment and campus visits of students whoare selected. The Department provides financial assistance to facilitate visits by recruited students. Theundergraduate program is lead by the Associate Chair for Instruction, Professor G. Cochran, supported bythe Undergraduate Studies Committee, the Mathematics Majors and Minors Committee and the Committeeon Instructors. The VIGRE Committee will work closely with these administrative units in the overalleducational aspects of the program and the anticipated curriculum review.

The VIGRE Committee will include a member of each of the research groups. Each crew will be chairedby its representative on the VIGRE Committee. Crew chairs may be assisted by a postdoctoral associateworking with the crew. Initially, the members of the VIGRE Committee will be the PIs and senior personnelof this propos