Preparing for opportunities was the theme of a workshop on Minorities and Applied Mathematics -Connections to Industry, held October 4--6, 1996 at the Institute for Mathematics and its Applications (IMA), University of Minnesota. Approximately sixty invited minorities in mathematical sciences attended the workshop. Of these, forty were Ph.D. students from mathematical sciences departments in North America; the other twenty participants represented a range of professional experience from postdoc to senior scientist. Also attending were Avner Friedman, Director of the IMA; Robert Gulliver, Associate Director of the IMA; and Barry Cipra, a science writer.

The workshop was arranged by the IMA Director and the organizers to provide an atmosphere in which minority graduate students could hear about the research and careers associated with applying mathematics to real-world problems. The real-world problems presented to students involved mathematics at all levels from elementary to technical, and showed students the need to communicate across disciplines with scientists and engineers having sophisticated mathematical training. Students began that communication process (listening and speaking) at this workshop. Their careers will be enhanced by this type of exposure; they were encouraged to seek similar opportunties at their home insitutions and in their home regions. Each graduate student attending the workshop agreed to return to their home institution and make a presentation about the workshop, so that its benefits would not be limited to those who attended.

The composition of the workshop--- a relatively small group, mostly graduate students--- was based on the model used at the workshop for women at the IMA in February, 1996 and was intended to create a comfortable and relaxed environment. The workshop contained four components:

1. Overview talks by senior participants about their technical work and career experiences;
2. Technical talks about the applications of mathematics associated with various real-world problems;
3. Focused small-group discussions charged to produce action items for colleges and universities, government laboratories, funding agencies and professional organizations;
4. An after-dinner talk by Earl Barnes of Georgia Tech describing how the discovery of Karmarkar's algorithm affected IBM's business strategy and the relationship between further developments in the mathematics and changes in strategy by IBM and its competitors.

The minority mathematics community is small, and the workshop was the first opportunity for many of the students to network with minority professionals sharing their interest in mathematics.

The technical talks were uniformly of high quality, and covered a range of applications, including manufacturing of semi-conductors, microstructure of materials, design of a chemical vapor deposition reactor, mathematical problems arising in biology including freezing of tissues for biomedical engineering, dynamics of proteins in aqueous solutions, transport of solutes across cell membranes and reconstruction of images in tomography. The mathematics involved included wavelets, Markov processes, optimization, partial differential equations and computer models. (Abstracts of all the talks are in Section IV below.)

The small-group discussion sessions were also modelled on the program held for women in February. Each group included about twelve people, typically eight graduate students and four senior mathematicians. One or two people served as coordinators to assure that everyone had a chance to speak and to assure that the group covered all relevant topics. One person was designated as recorder to prepare notes of each group's discussions. Another member of each group was asked to present the group's recommendations at the final assembly of all workshop participants. Student volunteers introduced speakers after the morning session, providing another chance for them to practice their communications skills.

The organizing committee was extremely pleased with the workshop. Participants were so enthusiastic that one of their primary suggestions was a request to meet again to see how people had carried out the suggestions made to them. They wanted to use another meeting to practice skills suggested at this workshop, where graduate students would give more of the talks, and would receive advance help in order to make maximum use of the conference.

The primary value of workshops like this is the students' exposure to people like themselves with interests like theirs, who have accomplished what they are striving to accomplish. All mathematicians are members of many communities--- minorities, women, men, analysts, geometers, topologists, applied mathematicians. Workshops like this do not substitute for the specialized meetings of those communities; they serve to demonstrate the existence of a minority mathematics community which is not visible to students isolated in their graduate programs.

The meeting was valuable because minority mathematicians have an unparalleled opportunity. Mathematics research and education are rapidly changing. The minority mathematics community did not prosper under the old model; there is a willingness in our community to consider other models of preparation for a career in research. This workshop showed that minority students are eager to prepare themselves for twenty-first century opportunities.

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    AGONAFER, DEREJE       IBM Corporation 
    AQUINO, LESLIE         Rensselaer Polytechnic Institute 
    ARREDONDO, MIGUEL      Purdue University 
    BARNES, EARL           Georgia Institute of Technology 
    BLAYNEH, KBENESH       Florida A & M Univ.
    BRANA-MULERO, FRANCIS  Shell Development 
    CANTU, SERGIO          Purdue University 
    CLARK, ANTWAN          Rensselaer Polytechnic Institute 
    DONALDSON, JAMES       Howard University 
    ECHOLS, CARRAE         University of Kentucky
    FOSSER, CECILIA        University of Arizona 
    GARCIA, ANGEL          Los Alamos National Laboratories 
    GILYOT, DUANE          University of California-Berkeley 
    GOMEZ, ELVIA           Texas Tech Univ.
    GOWARD, RUSSELL        University of Missouri-Columbia 
    GRAHAM, MERIDITH       Rensselaer Polytech Institute 
    GREENE, DAVID          Florida A & M Univ.
    HANSEN, BEN            Univ. of California, Berkeley 
    HAYES, LINDA           University of Texas-Austin  
    HOUSTON, JOHNNY        Elizabeth City State University
    HUNT, FERN             Nat. Inst. of Standards and Technology  
    INNISS, TASHA          University of Maryland-College Park  
    JACKSON, MONICA        University of Maryland 
    JOHNSON, RAYMOND L.    University of Maryland 
    JONES, FLETCHER        IBM 
    KEEVE, MICHAEL         Georgia Institute of Technology  
    LIAMBA, LUKEMBA        University of Wisconsin-Milwaukee
    LIVINGSTON, ALICE      Florida State University         
    LONDONO, JAIME         University of California-Riverside 
    LOPEZ, GILBERTO        Northwestern University 
    MACK, IRIS             Associated Technologies 
    MAIR, BERNARD          University of Florida 
    MARTINEZ, MONICA       Rice University  Univ. of Texas 
    MASON, TOM             Florida A&M Univ.
    MCINTYRE, CLAUZELL     Clark Atlanta University 
    MEJIA, RAYMOND         National Institutes of Health
    MEZA, JUAN C.          Sandia National Laboratories 
    MOLEFE, DANIEL F.      Northern Illinois Universitiy
    MOORE, JOY             University of Cincinnati   
    NIGUSSIE, YARED        Ohio State University 
    PERRY, STEPHANIE       North Carolina A & T Univ.
    PHILLIPS, ALFRED       Cornell University 
    RAMIREZ-GOMEZ, EDGARD  Virginia Tech    
    SARKAR, SHYAM          Centura (Gupta) Software Corp. 
    SIMON, TAMMY           North Carolina State Univ.
    ST. MARY, DONALD       Univ. of Massachusetts-Amherst 
    TATE, CALANDRA R.      Xavier University of Louisiana 
    TAYLOR, KEVIN          University of Iowa
    TURNER, JAMES          Florida A&M University
    TWUM-DANSO, NANAYAA    Harvard Unversity
    WALLACE, ALTON         Institute for Defense Analysis
    WATKINS, BOYCE         University of Kentucky
    WHITAKER, SHREE        North Carolina State 
    WRIGHT, PAUL           Bell Laboratories  
    ZAMORA, PAOLA          Univ. of North Carolina 
    ZEIGLER, DAVID         Texas A&M University 

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Mathematical problems arising in industrial applications typically embody complicated, interdisciplinary issues of formulation, analysis and solution. Minorities in mathematical careers are often attracted to areas in which their results can have a societal impact. There are manuy opportunites provided by real-world problems for high-quality research, contributions to practical results, and rewarding scientific careers. The purpose of the weekend workshop is to show examples of people and problems from industrial settings and to develop a set of concrete action items that individuals and agencies can carry out and help minority scientists at all levels and in varied environments become involved with industrial problems.

The first goal will be achieved through technical talks by selected participants chosen based on their success with real-world problems. The collection of action items will build on suggestions received at earlier workshops.

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Each breakout group was asked to discuss the following topics:

1. Undergraduate and graduate education in mathematical sciences
   • Transition from undergraduate to graduate work;
   • Curricular issues;
   • Uses of technology.
2. Preparing for opportunities
   • Bridging the gap between academia and industry;
   • Breadth of training;
   • Role of interdisciplinary work;
   • Role of internships;
   • Entrepeneurs and the global ecnonomy.

Although each group took a slightly different perspective on the main issues, many common elements were cited. Means of overcoming difficulties faced by students at the transition points (undergraduate to graduate, graduate to work) were subjects of numerous suggestions. Since members of the minority community frequently work in isolation, most of the recommendations were actions for individuals to undertake to prepare themselves better. The key to increasing the number of minority mathematicians is individual inititative on the items discussed below.

The main recommendations from all breakout groups are listed here in four groups; recommendations for faculty and students, recommendations for students, recommendations for academic mathematical sciences departments and recommendations for the professional societies. (Some recommendations are listed under more than one heading.)

A.     Actions for everyone

1. Get connected; have and use e-mail and internet access
2. Make departmental presentations about this workshop; invite students from other departments
3. Take advantage of computer center resources (C, C++, software packages, LATEX, UNIX, EXCEL)
4. Encourage the Department to invite speakers who can give talks about applications of mathematics (and to make contacts with local industry)
5. Attend seminars in other departments
6. Contribute information to Internet sites for minorities (information about internships, co-ops, programs, etc.)
7. Become aware of other minority/professional organizations
8. Look for internships and summer appointments in industrial settings
9. Keep in contact with mentors
10. Set up a Web site on the Internet containing:
    1. Profiles of minority industrial mathematicians
    2. Names and research areas of minority graduate students who are working toward the Ph.~D.~degree; thesis topics when completed
    3. Profiles of minority businesses
    4. Listing of available internships
    5. Profile of tools needed for successful graduate experience (C, C++, Hypertext, GAMS, presentation skills, LATEX)
    6. Profile of conference abstracts, speakers, e-mail addresses, as in AARMS at http://www.wam.umd.edu/~rlj/aarms.html ; contribute to such sites
    7. Information on how to subscribe to minority e-mail lists
    8. Current sources of minority scholarships
    9. List of industrial and academic mentors
    10. Support for budding entrepeneurs, such as information on how to get started, information about others interested in starting businesses and information about writing proposals and reviewing proposals
    11. Information about getting involved with ``virtual" companies
11. Use the Web to foster Applied Math team projects
    1. Identify hot areas in applied mathematics
    2. Recruit students
    3. Encourage students to form teams around these areas
    4. Support students planning and executing their chosen project
    5. Encourage student presentations on their projects at conferences

B.     Actions for students

1. Set a goal and remain focused on it
2. Spend some time learning how to learn mathematics; take responsibility to prepare yourself
3. Explore academic offerings of other departments to broaden research opportunities: take a computer course; perhaps minor in some area of engineering, science, business, etc.
4. Develop facility with written/spoken language
5. Get computational experience; learn a computer language and how to apply it to your problem
6. Request a cross-departmental math modeling class with strong industry involvement
7. Start an interdisciplinary journal club (students getting together to read articles from journals) or a graduate student seminar
8. Get involved with a project involving applications or integrating math with other disciplines
9. Make contact with other (minority) graduate students for possible collaboration on research-seek out a ``like-minded" group
10. Discuss with advisor ``what lies ahead"
11. Always keep your resume in mind
    1. Go to conferences (for example, SIAM conferences including SIAM's Diversity Day during the SIAM meeting at Stanford, July 14-18, 1997) and take a leadership role
    2. Prepare for conferences by reading abstracts, deciding on talks you will attend and contacting authors of articles in which you are interested
    3. Do things inside and outside of school to make yourself more marketable
    4. When working on a project, always think about what part or extensions will be publishable
12. Make an all-out effort before graduating and looking for a job
    1. Network at every opportunity--- attend seminars, attend conferences, e-mail authors of articles
    2. Contact all your mentors and professors as you near completion of your M.S. or Ph.D. degree, asking them to get the word out that you are close to graduating
    3. Ask professors and mentors to send recommendations; those based on personal contact are particularly important
    4. Send letters/resumes "out of cycle" when the majority of letters/resumes are least likely to come (this is less effective in academe than in industry)
    5. Always follow up contacts
    6. Continually update your resume
    7. Stay aware of current events to facilitate conversations during job interviews
    8. Call ahead to determine which areas of research are of interest to the company with which you are interviewing--- meet industry halfway by showing them you are a good match with their needs

C.     Actions for academic mathematical sciences departments

1. Organize student-to-student forums conducted by graduate students for undergraduate student math majors to talk about the transition to graduate school
2. Have a ``strategies to get a job" seminar (for undergraduates and/or for graduate students). Invite employers of all types--- community colleges, four-year colleges, industry and government representatives
3. Recognize and support students who plan to enter the job market with a B.~S.~or a M.~S.~degree
4. Forward all job listings to all graduate students at all levels
5. Offer a math modeling class where students can work on problems from industry--- expose students to working in teams and learning how to approach problems
6. Make the modeling class interdisciplinary by cross-listing it with other departments
7. Encourage students who want to take courses outside the Mathematics Department
8. Invite speakers from industry to talk about real-world problems
   1. Contact graduates who work in industry
   2. Set up an Advisory Committee with invited representatives from local industry to provide another source of speakers
9. Improve advising for graduate students; some groups even suggested development and use of a placement exam
10. Offer support to students other than teaching assistantships; research internships in industry would prepare students to begin industrial careers as teaching assistantships encourage them to pursue teaching
11. Be aware of students in other disciplines, such as EE, who take lots of mathematics, as sources of double majors and graduate students
12. In industry, mathematics departments should explain their usefulness to the company; in academe, mathematical sciences departments should explain their usefulness to allied departments

D.     Actions for professional societies

1. Encourage student participation at meetings
   1. Organize events for students
   2. Support students' attendance at society meetings (as is done by the Society for Mathematical Biology)

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