This is an online version of a special report that appeared in the AWM Newsletter, Volume 27, Number 6, NovemberDecember 1997. This special report was written by AWM President Sylvia Wiegand and edited, organized and laid out by AWM Newsletter Editor Anne Leggett. Tamara Kolda prepared the online version. AWM is very grateful to the Mathematics, Computer and Information Sciences Division of the Office of Naval Research for their support of the workshop program and of the printing of the Newsletter insert. Thanks also to SIAM for their cooperation and help with the workshop and to the AWM members who volunteered their time and expertise. Special thanks go to Suzanne Lenhart for serving as organizer of this workshop and to Dawn Wheeler for handling all the details of scheduling, correspondence, and publicity. Finally we thank the participants and speakers for making the workshop so interesting. Format of the WorkshopThe Association for Women in Mathematics (AWM), in conjunction with the Society for Industrial and Applied Mathematics (SIAM) and with funding from the Mathematics, Computer and Information Sciences Division of the Office of Naval Research (ONR), held an outstanding work shop July 1315, 1997 at the SIAM Annual Meeting. The workshop was the latest in a series that AWM offers twice yearly to promote and encourage women advanced graduate students and recent postdoctoral mathematicians. This workshop featured 21 talented new women mathematicians from all over the United States, with the state of Maryland best represented by five of them. The participants in the July '97 event felt that hearing others' research, meeting other graduate students and postdocs, and meeting senior mathematicians (particularly women) were extremely valuable activities for them. The opportunity to attend a meeting was also important. The sessions focused on the reporting of research results and the mentoring of graduate students and postdoctoral mathematicians. Most of the sessions at the Workshop were open to the public, and some events attracted a large number of other mathematicians. The program included an informal discussion period for mentors and participants, a banquet with keynote speech, an outdoor lunch, graduate student poster sessions, an AWM minisymposium on "Presenting Your Work and Yourself to the World: A Focus on Written Communications," a panel discussion on research and funding opportunities, and three research minisymposia featuring postdoctoral women: I. Mathematical modeling, II. Optimization, and III. PDE's and Applications. In addition to our publication of this Newsletter insert, SIAM plans to publish the "Presenting Your Work" and "Grantwriting" portions of the program as a guide for young professionals. Graduate student participants and posters
Donna Calhoun (University of Washington) displays her poster to Barbara Lee Keyfitz (University of Houston). Calhoun's poster, "A Cartesian Grid Method for 2d Stefan Problem," involved "tracking the moving interface that separates two phases (liquid and solid) of a material and solves the heat equation in both regions." Donna organized a studentrun Numerical Analysis Journal Club at UW.
Maria Sosonkina Driver (Virginia Tech University) presented the poster "Sparse Approximate Inverses in Preconditioning of Distributed Linear Systems." Driver's research area is numerical linear algebra and scientific computing, specifically in methods to solve difficult nonlinear systems of equations. She is originally from Ukraine. Carolyn Hill Coleman (Case Western Reserve University) stands with Svetlana Rudnaya (University of Minnesota) at Rudnaya's poster, "Application of Genetic Algorithms in Diffractive Optics Design." Rudnaya is interested in industrial applications of mathematical modeling and optimization techniques; currently she is collaborating with scientists at 3M on an optimal design problem arising in optics.
Coleman's poster on software she has developed to perform analyses of diagnostic information was titled "Expanding Generalized Receiver Operator Characteristic (ROC) Analysis." This has applications in medicine to complications stemming from very low birth weight. A former high school teacher, Coleman is married and has a 15yearold son.
Anna V. Georgieva (Duke University), shown with her poster "Nonlinear Particle Chains with Alternating Masses," studies wave propagation in this context and proves rigorously the existence of periodic traveling waves. She describes her research as "a wellbalanced mixture between abstract mathematical theory and concrete calculation."
Ruth Pfeiffer (University of Maryland) worked on "A Threshold Estimation Problem for Stochastic Processes with Hysteresis." Pfeiffer, who has held NASA and Fulbright fellowships, is originally from Austria. She has been the cochair of the University of Maryland Women in Mathematics seminar. Her main research interest is in the modeling of scientific data; for example she has been studying rainfall in the tropics and estimating rain rates (a joint project between the U.S. and Japan).
Ivonne DiazRivera (Arizona State University) explains her poster, "The Dynamics of Queues of Reentrant Manufacturing Systems," to Rudy Home (University of Colorado) and Debra Polignone Warne (University of Tennessee). DiazRivera is enthusiastic about this research using recent developments in dynamical systems and chaos theory; it's "an exciting ex ample of the use of mathematics in solving industrial problems." She has been Chairperson of a Women in Math group at ASU and was VicePresident of the Hispanic Club while at AT&T.
Kristen S. Moore (University of Connecticut) presented the poster "On a Singular Semilinear Elliptic Boundary Value Problem with Boundary Blowup." Moore is interested in applying qualitative and quantitative methods to nonlinear partial differential equations which arise from mechanical problems. She has previously been an actuary.
Misha E. Kilmer (University of Maryland)
stands at her poster, "Cauchylike Preconditioners and 2D Ill posed
Problems." The integral equations that model processes in seismography,
tomography, and signal and image processing are often illposed in that small
changes in data can cause arbitrarily large changes in the solution. Kilmer has
worked on finding a regularized solution. She has also studied underwater
acoustics. Postdoctoral mathematiciansI. Minisymposium on Mathematical Modeling Organized by Suzanne M. Lenhart (University of Tennessee), this minisymposium included a variety of mathematical models and applications. Both continuous and discrete models were considered.
Gabriella A. Pintér (Ph.D. Texas Tech University, now at North Carolina State University) spoke on "Global Attractors for Damped Abstract Nonlinear Hyperbolic Systems." These systems arise in the study of smart material structures (elastomers, which are used in the development of active and passive vibration devices). Pinter brought her threemonthold daughter, Anna, to the workshop. Debra Polignone Warne (Ph.D. University of Virginia, now at University of Tennessee) discussed "Nonsymmetric Deformations in Incompressible Nonlinear Elasticity," research in continuum mechanical modeling and related areas. She studies gross material behavior and governing principles of such behavior in solids and fluids. The topic of Kathleen A. Rogers (Ph.D. University of Maryland, now at University of Minnesota) was "Stability Properties of Equilibria within a Continuum Mechanics Model of DNA Minicirdes." The motivation for these results arose from a problem in the study of DNA structure. Hong Zhou (Ph.D. University of California, Berkeley, now at University of North Carolina) spoke about "The Effect of Dynamics Surface Tension on the Oscillation of Slender Elliptical Newtonian Jets." Her research is in computational fluid mechanics and mathematical modeling of fibers and liquid crystal polymers.
II. Minisymposium on Optimization This minisymposium, organized by Margaret H. Wright (Bell Laboratories), presented a variety of optimization problems with varied applications. There were also illustrations of the impact of scientific computing on these problems. Dana Bedivan (Ph.D. from and presently at the University of Texas at Arlington) spoke on "Least Squares Methods for Optimal Shape Problems." Her work has been motivated by problems that arise in semiconductor design. She has also been an editor for a Romanian mathematical journal. Tamara G. Kolda (Ph.D. University of Maryland, now at Oak Ridge National Laboratory) discussed "Information Retrieval via LimitedMemory Matrix Methods," where she says, "the goal in information retrieval is to match documents against a user's query." Kolda has chaired Maryland's Women in Mathematics group.
Lianfen Qian (Ph.D. Michigan State University, presently at Florida Atlantic University), is a statistician working on nonlinear time series analysis. Her work, "On Maximum Likelihood Estimators for a Threshold Autoregression," involves various phenomena such as limit cycles, harmonic distortion and chaos. In many cases, for example the temperature of the sea surface and pollen concentration at various depths of a lake, the associated functions are discontinuous, and it is helpful to study a maximum likelihood estimator. Zhiyun Yang (Ph.D. University of Washington, now at Pacificorp) spoke on "The Solution of the Elliptic Boundary Value Problems on Irregular Regions." She has focused on a wavelet approach to solving elliptic problems arising from computational chemistry. III. Minisymposium on PDE's and Applications Joyce R. McLaughlin (Rensselaer Polytechnic Institute) organized this minisymposium, in which several different PDE models were discussed, along with a variety of physical and biological applications and some methods for analyzing them. Xin Chen (Ph.D. at Rensselaer Polytechnic Institute, now at University of Illinois) works in systems and control; she applies her mathematical skills to a broad spectrum of engineering problems. Her presentation was on "Worst Case Linfinity to Linfinity Gain Minimization via State Feedback."
Dawn A. LottCrumpler (Ph.D. Northwestern University, now at New Jersey Institute of Technology) spoke on "The Quasilinear Wave Equation Governing Compressional Wave Motions of Nonlinearly Elastic Bodies: A Numerical Approach." This problem arose from physical phenomena in solid and fluid mechanics. She also studies the formation of shear bands in metals, a phenomenon that occurs because straining the metal increases its temperature and the increased temperature weakens the material.
Elsa Newman (Ph.D. Emory University, now at Marymount University) spoke on "Axisymmetric Flow in Transonic Aerodynamics." Newman's work, related to transonic flight, deals with equations that arise in the design of fuelefficient axisymmetric bodies and the study of axisymmetric jet flows. Transonic flow is flow with speed close to the speed of sound. Much commercial flight (e.g., 747's) is in this range, so there is much interest in this topic. Originally from North Carolina, Newman is married and has a twoyearold daughter. Barbara Niethammer (Ph.D. University of Bonn, now at Courant Institute, NYU) is interested in equations which describe phase separation in binary alloys and elasticity. She spoke on "Derivation of the LifshitzSlyozov Theory for Coarsening by Homogenization Methods." An example of coarsening is solid formation in undercooled liquid: the system evolves to minimize surface area. Due to surface tension, large particles grow at the expense of the smaller ones which shrink and disappear.


On Sunday afternoon, at the beginning of the workshop, the participants and four senior mathematicians gathered for a introductory gettogether. The senior mathematicians, Rosemary Chang, Margaret Cheney, Marsha Berger and Suzanne Lenhart, each told about her own job or situation when a student. Then the senior mathematicians gave advice about success in careers, such as:

Make a strong contribution in one research area to get tenure. Do not spread yourself too thin at first.

Pick your fights carefully. Fights take time and effort, and you do not want to be known as someone who fights on every issue. Decide what issues are worth fighting about.

Introduce yourself to colleagues at conferences. Collect and hand out business cards. Send followup email messages and try to maintain contacts.

Try not to teach in the summer. Go to conferences and get some research done in the summer.
 Get two mentors (if possible), one inside your department and one outside your department. Try to find someone to answer your "stupid" questions (which are probably not that "stupid").
The participants also raised some issues and questions. The issue of finding a job seemed crucial. Elsa Newman suggested that you should be wellinformed about calculus reform and have some opinions on reform before going on an interview.
You should also think about other curriculum issues such as standards and cooperative learning. Possibilities of postdoctoral fellowships were discussed. Balancing family and work was an issue of interest With a supportive spouse, the group was optimistic about achieving this balance and being successful in a career.

On Sunday evening, Pam Cook, Chair of her department at the University of Delaware, spoke at the AWM banquet on "Thoughts from a chair(person)." When she first went to Delaware 15 years ago she was the only woman with a tenured or tenure track position; now there are four such women in a faculty of 36. Still Cook is one of very few women chairs of Ph.D.granting math departments, roughly four out of 156. This clearly indicates that we still have a long way to go. She was emphatic that senior faculty ought to mentor junior female faculty; she has benefitted greatly as Chair from mentoring by a female Dean. Her position on the SIAM board is a networking aid.
She also told the participants of five rules for being a successful woman mathematician given by Audrey Terras in the MayJune AWM Newsletter: (1) Don't ever give up, (2) Keep learning and teaching, (3) Network, go to' meetings, give talks, collaborate, (4) Do useful math, and (5) Have a (good) life! Cook added that it's important to be flexible and to expand your area of expertise.
Originally from Ontario, Canada, Cook received her Ph.D. from Cornell University and is married with two children. She and her husband had a difficult time resolving the twobody problem, which she didn't explain because "it would take a whole page!" She's interested in transonic aerodynamics.
Dianne O'Leary, a mentor at the workshop, received her Ph.D. from Stanford University and is now a professor of Computer Science at the University of Maryland. Married with three children, she and her husband solved the twobody problem by "looking in metropolitan areas." Her fields of interest are numerical analysis, computational linear algebra, optimization, and illposed problems.
The ability to communicate is a key to success in academia and industry. This was the focus of the Monday morning minisymposium "Presenting Your Work and Yourself to the World: A Focus on Writ ten Communications," organized by Linda R. Petzold (University of California, Santa Barbara). The author must clearly display the relevance of technical work, even of excellent technical work. How to write journal articles and grant proposals was also discussed.

Petzold is currently Professor in the Departments of Computer Science and Mechanical and Environmental Engineering and Director of the Computational Science and Engineering Program at Santa Barbara. She spoke on "Overcoming Proposal Phobia." Although writing a proposal may seem overwhelming, it is an opportunity to clarify, plan and prepare for your future research, to communicate your excitement and to explain the importance of your work. Applying for a grant involves selling your project and yourself, being a salesperson. Some questions to ask yourself: What do you want to do? Why? What good is it? (Talk to others about it and convince them, and then you will convince yourself.) Are there problems that could be solved better as a result of this work? To get over the initial writer's block, use a successful proposal for a model. Some don'ts: Don't use a small font to fit your proposal into the page limits. Don't be overly pedantic. Don't forget to mention other's work. Don't be too negative about the potential difficulties.
Petzold, who received her Ph.D. in Computer Science in 1978 from the University of Illinois, was awarded the Wilkinson Prize for Numerical Software in 1991. She has served as SIAM Vice President for Publications since 1993 and as Editor in Chief of the SIAM Journal on Scientific Computing, 19891993. Her research interests include numerical ordinary differential equations, differential algebraic equations, partial differential equations, numerical optimization, parameter estimation and optimal control for PDE systems, mathematical software, parallel computing and scientific computing.

Lloyd (Nick) Trefethen, now associated with Oxford, spoke on "How I Write"; he has always loved to write and finds it to be one of the pleasures of academic life. Trefethen's talk was amusing, sprinkled with little poems by Piet Hein, a Danish poet wellknown for his "grooks," for example: "If no thought/ your mind does visit/ make your speech/ not too explicit."
Trefethen especially emphasized his habit of endlessly polishing his papers. He described the iterative procedure of taking a draft, using a red pen, and producing an improved draft "you keep going until f(x)=x." But he admitted that he "can't rest until it's utterly simple and utterly clear," that he wants the "best theorem and the best proof." This never quite happens, so his projects take a long time. (His students once made a point of presenting him with a large box of red pens!)
Trefethen has worked on various problems in applied mathematics and numerical analysis. In 1988 he married Anne Daman, from England, also a Ph.D. in numerical analysis. In 1985 he won the first Fox Prize in Numerical Analysis, and in 1986 he received a Presidential Young Investigator Award. More recently his work concerns eigenvalue problems and their applications in fluid mechanics and other fields.
Margaret Wright's title, "Writing: A String that Makes the Necklace," came from a quote of Gustave Flaubert: "Ideas are the pearls/ But writing/ Is the string that makes/ The necklace." Wright, who is at Bell Labs, emphasized the importance of writing skills for almost every successful career, although she cautioned that there is no single magic formula for writing well. Some of the general principles she mentioned were similar to advice she has given for delivering research talks: (1) Practice, practice, practice! (2) The content matters but isn't enough. (3) Know you're in charge; know what you want to say and make sure you say it. She also mentioned revising endlessly and suggested consulting references for grammar and style.
After receiving her Ph.D. from Stanford University, Wright remained there for twelve years in the Department of Operations Research. From 1988 to the present, she has been at Bell Labs. Wright, who served as President of SIAM in 199596, is interested in optimization, linear algebra, numerical analysis, and scientific computing.

Deborah Lockhart spoke in the Writing Minisymposium on "Preparation of Research Grant Proposals," particularly for the National Science Foundation, where she has been a program director for nine years. Lockhart earned a Ph.D. in mathematics from Rensselaer Polytechnic Institute in the area of continuum mechanics. In her talk, she included suggestions for the effective presentation of ideas as well as proposal development, preparation, format, and style. Her main points were: (1) Have a great idea, (2) Know your audience, (3) Follow instructions, and (4) Ask for help. She emphasized particularly that you should know the ground rules, the scope and mission of the funding source, and how they evaluate and that you should talk to the program officer. Key questions to ask yourself: What do you intend to do? Why is this research important? What has already been done? (Give the background and list all relevant research.) How are you going to do the work? Al Thaler, also at NSF and in the audience, also stressed calling the program officer; you can get candid information.
Later on Monday in the panel discussion on funding and research, Lockhart described several relevant NSF programs, including the POWRE program (Professional Opportunities for Women in Research and Education), Postdoctoral Research Fellowships, the Faculty Early Career Development program, the Research in Undergraduate Institution (RUI) program, and Research Opportunity Awards submission, as well as the regular program.
As examples of research opportunities, Fadil Santosa, the associate director of the Minnesota Center for Industrial Mathematics, described three workshops at the IMA of possible interest to participants: Dynamical Systems, Mathematics and Biology, and Reactive Flows. He also mentioned opportunities for rewarding collaborative research with industry. Santosa, who also oversees the graduate degree program in Industrial Mathematics offered at Minnesota's School of Mathematics, received his Ph.D. from the University of Illinois in 1980; he works in several areas of applied mathematics including inverse problems, imaging, optimization, wave propagation and nondestructive evaluations.

John Tague of the Office of Naval Research spoke on winning grantsmanship. Tague emphasized that along with writing an effective proposal, it is important to develop a good working relationship with the program officer and stay in touch with the program officer after the award has been received. In Tague's opinion, "star" performers are those who deliver what they promise and take the initiative in finding out what problems the program officer wants solved. They are active participants in the program, communicate with the program officer regularly, and send paper preprints and slides describing the objectives and results of the project.
Workshop Organizers
Suzanne Lenhart, the Organizer of this work shop, received her Ph.D. in mathematics from the University of Kentucky. Lenhart has also kindly agreed to organize the SIAM Workshop to be held in Toronto in 1998. In addition to her faculty position at the University of Tennessee, Lenhart has been a parttime employee of Oak Ridge National Laboratory since 1987. She was the Sonia Kovalevski Guest Professor at the University of Kaiserslautern, Germany, in the spring of 1994 and gave an AWM invited lecture at the MAA meeting in Atlanta in August of 1997.
Lenhart's research area is partial differential equations and optimal control. Her current emphasis is on environmental and population models. Her application areas have ranged from robotics to managing beaver populations to optimal nutrient delivery strategies for bioreactor models for hazardous waste remediation. Her work on optimal control for chemotherapy strategies for AIDS models is the first work on optimal control in AIDS biologicalmathematical research. She has done research in the areas of optimal control of competitive population models and viscosity solutions for systems. Lenhart, who directs a Research Experiences for Undergraduates (REU) summer program and has organized AWM Sonia Kovalevsky High School Days and Postdoc and Graduate Student Workshops, is a former president of the local Association for Women in Science chapter.

A driving force behind previous AWM/SIAM workshops, Joyce McLaughlin, who has been Ford Foundation Professor of Mathematics at Rensselaer Polytechnic Institute since 1992, not only organized the workshops, but she also prepared the successful proposals which provided the funding. McLaughlin, who earned her Ph.D. from the University of California, Riverside, describes her main research interests as inverse problems and optimization; she studies the use of spectral data in design and identification. This work requires defining special data sets which yield wellposed problems and for which accurate algorithms can be obtained. The problems are nonlinear and have a wide range of application in nondestructive testing, manufacturing, and geophysics.
McLaughlin has recently given seven major invited addresses, including the Plenary Lecture at the SIAM 1996 annual meeting. McLaughlin's professional activities include her position as Chair of the SIAM Board of Trustees (1996present) and her positions on several editorial boards, including serving as Associate Editor for the Journal of Mathematical Analysis and Applications.
Future Workshops

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