School of Mathematics Newsletter - Volume 10 - 2004
In This Issue...
Welcome to Incoming Faculty and New Postdoctoral Appointees
|It is a pleasure to welcome the new members of the School of Mathematics--Assistant Professors Ezra Miller and Duane Nykamp. We also welcome the new Dunham Jackson Assistant Professor Chian-Jen Wang.|
||Assistant Professor Ezra Miller earned his Ph.D. in 2000 from UC Berkeley where his honors, while a graduate student, included a Alfred P. Sloan Doctoral Dissertation Fellowship, a Julia B. Robinson Fellowship and the Charles B. Morrey Award. During the period 2000 - 2002 he was an NSF Postdoctoral Research Fellow at MIT. Ezra joined our department in September 2002, but took a leave of absence to spend the 2002 - 2003 academic year as a visiting researcher at MSRI Berkeley. His research areas are algebraic geometry, combinatorics, commutative algebra and mathematical physics.|
|Assistant Professor Duane Nykamp earned his Ph.D. in 2000 from the Courant Institute of Mathematical Sciences. As a graduate student, his honors included an NSF Graduate Research Fellowship, Dean's Dissertation Fellowship, and Henry Mitchell Mac Cracken Fellowship. During the period 2000 to 2003 he was an NSF Postdoctoral Fellow and Computational Applied Mathematics Assistant Professor at UCLA. In addition, he held a Margaret and Herman Sokol Postdoctoral Research Fellowship and was a recipient of an NSF Grant. In his research Duane studies neural networks, both through modeling as well as through analysis of experimental data.||
|Dunham Jackson Assistant Professor Chian-Jen Wang earned her Ph.D. in 2003 from Ohio State University. Her research areas are automorphic forms and representation theory.|
From the Department Head
On July 1, 2003, Naresh Jain stepped down as Head of the School of Mathematics, after eight successful and effective years in that office. Since then, I have been trying to grasp the intricacies of the job, determine what my own style will be, and keep out of trouble! The faculty and staff have been supportive and patient. The change in administration has had a natural domino effect. David Frank took over my previous position as Director of Undergraduate Studies. He was in that spot once before, and I very much appreciate the experience that he brings, as well as his obvious dedication to our undergraduate teaching mission. Rick Moeckel kindly agreed to become the Associate Head, taking over the job from Bernardo Cockburn, who was on leave for part of this year. Administration is a new thing for Rick, but he has done well, and it has been very enjoyable working with him as we both try to figure out what we are doing. I am grateful to Paul Garrett, who was persuaded to stay on another year as the Director of Graduate Studies. It was important to me to have someone in that role who is an expert. Paul will be leaving that job at the end of this year. Scot Adams will be our new DGS, and I look forward to working with him.
The past few months have been busy. We have just completed our “normal” hiring season, and we are pleased that two strong young mathematicians have accepted our offers to become tenure-track assistant professors in the School. Daniel Spirn is an applied analyst who will be joining us from Brown University. He works on nonlinear PDE’s, particularly in connection with fluid motion. Gilad Lerman, currently a postdoc at Courant, will be involved in our Minnesota Center for Industrial Mathematics (MCIM). He has been applying methods of harmonic analysis to problems in bioinformatics. As we look to the future, we will be trying to fill several more positions. We will particularly focus on trying to increase the diversity in our faculty by seeking strong female and under-represented minority candidates. This will be an ongoing effort that is not restricted to any particular time of year, and I have asked that the entire faculty be engaged.
There are a couple of other changes in the works. Significant modifications of our computer system are underway, including the hiring of additional staff to keep up with the huge workload. We have started a new Ordway Lecture Series, which will bring world-class mathematicians here for a week of special lectures, once or twice a year. Our first Ordway lecturer was Hillel Furstenberg, who gave three lectures on ergodic theory that were well-attended by faculty and students, including some enthusiastic undergraduates. Our next Ordway Lecturer will be Maxim Kontsevich, on April 20-23, 2004. We have hopes of obtaining a “VIGRE” grant from the NSF (the site visit occurred on March 11). This grant would have a tremendous impact on our program, particularly regarding postdocs, grad students, and undergrads. Special thanks go to Willard Miller for his work in writing the proposal and preparing us all for the site visit. And finally, our faculty keeps changing. Morty Harris and David Storvick have retired. There will be a retirement dinner for them on April 29th of this year. And Avner Friedman and John Lowengrub decided to leave us: Avner to continue as Director of the Mathematical Biology Institute at Ohio State, and John to take a position at UC Irvine. Such changes can be difficult, at times, as we try to keep up. At least for me, it has kept my life very interesting.
Awards and Recognitions
NICOLAI KRYLOV AWARDED STEELE PRIZE
Ordway Professor Nicolai Krylov was awarded the 2004 Leroy P. Steele Prize for Seminal Contribution to Research. He shares the prize with Lawrence C. Evans of the University of California, Berkeley. They were honored for their fundamental contributions to the theory of fully nonlinear elliptic equations. Presented annually by the American Mathematical Society, the Steele Prize is one of the highest distinctions in mathematics. The prize was awarded at the Joint Mathematics Meetings held in January in Phoenix, Arizona.
The Prize Citation states in part: "The Steele Prize for Seminal Research is awarded ...for the "Evans-Krylov theorem".... Fully nonlinear elliptic equations are of interest in many subjects, including the theory of controlled diffusion processes and differential geometry. These authors, independently and with different arguments established ...a result now known as the Evans-Krylov theorem. The Evans-Krylov theorem was both a capstone on fundamental contributions of the recipients and others and a harbinger of things to follow from the community. ...both recipients have made a variety of distinguished contributions to the theory of nonlinear partial differential equations." Further information may be found at http://www.ams.org/prizes-awards. All of us join in congratulating Professor Krylov on this great honor.
HUMBOLDT RESEARCH AWARD FOR HANS OTHMER
The Alexander von Humboldt Foundation, Germany, presented the Humboldt Research Award to Professor Hans Othmer. The award honors his academic achievements, especially in the field of mathematical biology. Professor Othmer was invited to carry out research projects in cooperation with his colleagues from Germany for a period up to one year. The award carries an amount of 50,000 Euro. We congratulate Professor Othmer on this major recognition. An interview with Professor Othmer by Professor Peter Webb who is one of the Newsletter editors appears below.
DISTINGUISHED MCKNIGHT PROFESSORSHIP FOR VICTOR REINER
Professor Victor Reiner is one of the recipients of the Distinguished McKnight University Professorship Award. This is a very high recognition of Professor Reiner's accomplishments as a researcher and a teacher. The only other Distinguished McKnight University Professor in the School of Mathematics is Professor Vladimir Sverak. We congratulate Professor Reiner on this well deserved honor.
OFER ZEITOUNI AWARDED HENRI POINCARE INSTITUTE PRIZE
Professor Ofer Zeitouni was awarded the 2003 Prix de l’Institut Henri Poincare for his paper “Cut points and diffusive random walks in random environment”. This award is made every year for a paper that has appeared in the Annals of the Institut Henri Poincare - Probability and Statistics.
He shares the award with E. Bolthausen and A. Sznitman.
BEST IT MATH PROFESSOR AWARD FOR ARTHUR LIM
Visiting Professor Arthur Lim received the "Best IT Math Professor" award for two consecutive academic years: 2001 - 02 and 2002 - 03. The award is given by the IT Student Board. We congratulate Professor Lim for this recognition of his excellent work.
Distinguished Ordway Visitors (2003-2004)
The following leading mathematicians accepted our invitations to visit the School during the current academic year under the Distinguished Ordway Visitors Program. The program brings highly distinguished mathematicians to Minneapolis for prolonged periods, significantly enhancing the creative environment of the School. The visitors typically give several lectures, including a colloquium lecture and several seminars, and the exchanges of ideas with our faculty and students often result in research collaborations.
Jim Douglas, Jr., Purdue University, numerical analysis L.
Craig Evans, University of California, Berkeley, partial differential equations
Hillel Furstenberg, Hebrew University, dynamical systems
Guy Henniart, University of Paris XI, number theory
Thomas G. Kurtz, University of Wisconsin, Madison, probability theory
Jean Lannes, Ecole Polytechnique, algebraic topology
Michel Ledoux, University Paul-Sabatier, Toulouse, probability theory
Boris L. Rozovsky, University of Southern California, probability theory
Professor Douglas will give a colloquium lecture about locally conservative Eulerian-Lagrangian methods for transient systems and applications to porous media problems. He will also give two additional, more technical, lectures which will be of interest to people working in numerical analysis of partial differential equations and applied mathematics. His visit will take place during the month of May.
Professor Evans' visit takes place during the second half of March. He will give several lectures about his work.
Professor Furstenberg will deliver three lectures on the following topics: Non Conventional Ergodic Averages, Nilpotent Groups, and the Long-Term Memory of Dynamical Systems. His visit will take place in February 2004.
Professor Henniart delivered eight lectures on The Local Langlands Correspondence for GL(n) and Higher L-functions, Local-Global Principles, and Langlands' Conjectures, in late September and throughout October 2003.
Professor Kurtz is visiting the department and the Institute for Mathematics and its Applications (IMA) as a Distinguished Ordway Professor for the entire 2003 - 4 academic year. He serves as Chair of the Organizing Committee for the IMA's current annual scientific program on "Probability and Statistics in Complex Systems: Genomics, Networks, and Financial Engineering".
Professor Lannes spoke on Sturm sequences and H lower 2 of the Hyperbolic homomorphism at the Algebraic Topology Conference which took place here September 19-21, 2003, and he also played an important role in organizing the conference. In addition, he talked four times in the topology seminar. He visited for one month, September 15 - October 15, 2003.
Professor Ledoux delivered two lectures. On November 13, 2003, he spoke at the colloquium on "The concentration of measure phenomenon" and on November 14, 2003, he spoke in the probability seminar on "Spectral measures of orthogonal polynomial ensembles and small deviation inequalities".
Professor Rozovsky will give three lectures on stochastic fluid mechanics, Wiener Chaos, and financial mathematics. His visit takes place from March 20 to April 20, 2004.
Continuing Postdocs and Visiting Faculty
Bernard Badzioch, Dunham Jackson Assistant Professor (Ph.D. University of Notre Dame, algebraic topology and homotopy theory)
Jesus Carrero (Ph.D. UCLA, partial differential equations)
Jamylle Carter (Ph.D. UCLA, image processing, computer graphics)
Mehdi Hakim-Hashemi (Shiraz University, algebraic topology, homotopy theory)
Junho Lee, Dunham Jackson Assistant Professor (Ph.D. Michigan State University, symplectic geometry and Gromov-Witten invariants)
Christof Melcher, Dunham Jackson Assistant Professor (Ph.D. Max-Planck-Institute, partial differential equations, continuum mechanics, materials science)
Simon Morgan (Ph.D. Rice University, geometric measure theory, harmonic maps)
Ralf Schmidt (Saarland University, number theory, automorphic forms, representation theory)
Jennifer Wagner (Ph.D. UCSD, algebraic combinatorics)
Raja Sridharan (The Tata Institute of Fundamental Research, commutative algebra, algebraic geometry)
Alexei Zhubr (Syktyvkar State University, algebraic topology)
Postdoctoral Associates and Postdoctoral Fellows, including IMA Postdoctoral Associates who participate in the teaching activities:
Olga Brezhneva (Ph.D. Computing Center, Russian Academy of Sciences, Moscow, optimization, numerical analysis)
Mihail Cocos (University of British Columbia, differential geometry, geometric analysis)
Chetan Gadgil (Ph.D. in chemical engineering, University of Minnesota, mathematical modeling in biology)
Balaji Gopalakrishnan (Ph.D. Georgia Tech, algorithms, combinatorics and optimization)
Marshall Hampton, NSF Postdoctoral Fellow (dynamical systems, celestial mechanics, image processing)
McKay Hyde, NSF Postdoctoral Fellow (numerical solutions of partial differential equations, fast algorithms, spectral methods)
Huiqiang Jiang (Ph.D. Courant Institute, partial differential equations)
Jeremy Martin, NSF Postdoctoral Fellow (Ph.D. UCSD, combinatorics and algebraic geometry)
Greg Rampala (University of Louisville, probability theory)
Tamon Stephen (Ph.D. University of Michigan, Ann Arbour, combinatorics and optimization)
Magdalena Stolarska (Ph.D. Northwestern University, applied mathematics, mathematical biology) Jun Zhao (Ph.D. Texas A&M University, numerical analysis)
Other Visiting Scholars:
Inkyung Ahn (Korea University, partial differential equations)
Josep Alvarez (Universitat Politecnica de Catalunya, Barcelona, commutative algebra)
Hyeong Ohk Bae (Ajou University, dynamical systems and partial differential equations)
Yassine Boubendir (Universite Paris 13, applied mathematics)
Jay Fillmore (Professor Emeritus, UCSD, geometry)
Michael hardy (Statistics, foundations of probability theory)
Chetan Gadgil (Ph.D. in chemical engineering, University of Minnesota, mathematical modeling in biology)
Bosu Ko (Cheju University, partial differential equations)
Boris Levitan* (Professor Emeritus, Moscow State University, functional analysis, differential equations)
Saadet Ozer (Institute of Science and Technology, Istanbul, mathematical physics)
Kimun Ryu (Korea University, partial differential equations)
Thomas Schwartzbauer (Assoc. Professor Emeritus, OSU, probability)
Tobias Weth (University of Giessen, numerical analysis)
Thomas Wihler (ETH Zurich, numerical analysis)
*Deceased, April 4, 2004. An obituary will appear in the next issue of the newsletter.
The Sixth Riviere-Fabes Symposium on Analysis and PDE was held at the School of Mathematics from April 25th to the 27th, 2003. Professor's Ronald Coifman (Yale University) and Michael Christ (Berkeley) each delivered two lectures describing beautiful and varied applications of harmonic and functional analysis. Coifman's two talks centered on approximation in high dimensions, in particular various issues involved in approximating empirical functions of a large number of parameters (e.g. geometric analysis of data sets embedded in high dimensions.) Michael Christ spoke on recent ill-posedness results for nonlinear Schrodinger equations, and also recent work on the d-bar Neumann problem, magnetic Schrodinger operators, and the Aharonov-Bohm phenomenon. Other speakers were Alex Iosevich (Missouri), "Analysis and combinatorics of distances set"; Gerd Mockenhaupt (Georgia Tech), "On the Hardy-Littlewood majorant property"; Camil Muscalu (UCLA), "Multilinear singular integrals"; and Mikhail Safonov (Minnesota), "Mean value theorem for harmonic functions: some unusual applications". The conference dinner was Saturday evening in the newly renovated Campus Club in Coffman Union. We were fortunate to be joined there by Esther Fabes.
The organizing committee consisted of Fernando Reitich, M. Carme Calderer, Markus Keel, Carlos Kenig (U of Chicago), and Walter Littman.
The conference was expertly managed by Harry Singh and Kathy Swedell.
This Symposium was established in memory of our colleagues Nestor M. Riviere and Eugene B. Fabes. Both of them were analysts and did their graduate work together at the University of Chicago. After finishing his Ph.D. under Alberto Calderon in 1966, Nestor joined the School of Mathematics the same year. Gene finished his Ph.D. under Antoni Zygmund in 1965 and spent two years at Rice University before coming to Minnesota in 1967. The two started a new era in classical analysis at Minnesota. Unfortunately for us, cancer claimed Nestor's life at the young age of 38 in 1978, ending a brilliant career. The department established the Nestor M. Rivire Lecture in his memory. Every year a highly distinguished mathematician delivers a lecture in the broad area of analysis. Gene usually took care of the organizational work and the Rivire Lecture was supported by a fund established by donations from friends of Nestor. In 1997 another tragedy struck. Gene passed away just after he turned sixty and was still at the peak of his productive career. A list of his mathematical achievements can be found in his obituary in the Amer. Math. Soc. Notices, v. 45 (1998), pp. 706-708, and in the Journal of Fourier Analysis and Appl., v. 4, no. 4/5 (1998). Former colleagues, students and friends of Nestor and Gene from all over the world expressed the sentiment that we should establish an annual symposium in their memory. Families of Nestor and Gene fully endorsed the idea of turning the Nestor M. Rivire Lecture into the Rivire-Fabes Symposium. With financial support from interested people the symposium was formally established in 1998.
THE SEVENTH RIVIERE-FABES SYMPOSIUM ON ANALYSIS AND PDE,
APRIL 23-25, 2004.
Two one-hour lectures will be delivered by Professors H. Brezis, Rutgers University, and S.R.S Varadhan, Courant Institute. In addition, the following speakers will each give a one-hour talk: J. Pipher, Brown University, S. Wu, University of Michigan, Ann Arbor, and A. Nagel and A. Kiselev, University of Wisconsin, Madison.
Organizers: Nicolai Krylov (Chair), Carlos Kenig, Walter Littman, Fernando Reitich, Ofer Zeitouni
|SMALL ALGEBRAIC TOPOLOGY CONFERENCE, SEPTEMBER 19-21, 2003|
A conference in algebraic topology was organized to coincide with the visit of Jean Lannes (Ecole Polytechnique) as Ordway Visiting Professor in the Mathematics Department. The speakers were W. Chacholski (Minnesota), A. Adem (Wisconsin), P. Goerss and S. Priddy (Northwestern), H. Sadofsky (Oregon), J. Morava and S. Wilson (Johns Hopkins), F. Cohen (Rochester), N. Kuhn (Virginia) and J. Strom (Western Michigan) as well as Prof. Lannes himself. The overall theme of the talks tended to reflect the powerful algebraic techniques in use in topology, some of them pioneered by participants at the conference, and in which many conference participants were expert. The occasion provided an opportunity for interaction in this interdisciplinary area of algebra and topology, between researchers who know each other quite well but see each other infrequently, and also between several of the graduate students in the department and the visitors.A conference dinner was held in the Jewel of India' on Saturday night,September 20. The conference was privately funded, and the organizers were Professors Badzioch, Feshbach, Gershenson, Kahn, Voronov and Webb. The conference was judged by the participants to be a total success!
THE 52nd MIDWEST CONFERENCE IN PARTIAL DIFFERENTIAL EQUATIONS
NOVEMBER 15-16, 2003
The Conference, hosted by the School of Mathematics, was attended by over50 participants, including more than 25 out of town visitors, who heardsome very interesting talks from the following speakers: John Lewis (Kentucky), Yi Li (Iowa), Igor Rodnianski (Princeton/IAS), Mikhail Safonov (Minnesota), Sylvia Serfaty (Courant), Gieri Simonett (Vanderbilt), Daniel Tataru (UC Berkeley), and Kevin Zumbrun (Indiana). The conference dinner was held Saturday evening at the Sawatdee Thai restaurant. Special thanks to Kathy Swedell and Harry Singh for their management of the conference. (To give just one example: Harry's acrobatic negotiating skills produced not one but two (!!) desserts on the banquet table Saturday night.) Thanks also to Rhonda Dragan for a beautiful and useful web-site and to Kate Houser and Leanne Hewitt for timely advice on conference planning. The organizers of the conference were M. Keel, N. Krylov, W. Littman, P. Polacik, and V. Sverak.
CONFERENCE ON "NEW DEVELOPMENTS IN NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS",
JUNE 23 - 25, 2004
Professor James Serrin is organizing a workshop to be held June 23 - June 25 at the University of Minnesota on the topic "New Developments in Nonlinear Partial Differential Equations". The workshop is supported by the Participating Institutions of the IMA and also by the University of Minnesota Foundation.
Speakers will include Filippo Gazzola, Hans-Christoph Grunau, Giovanni Leoni, Gary Lieberman, Enzo Mitidieri, Patrizia Pucci, Marco Rigoli, Guido Sweers, Moxun Tang, Grozdena Todorova, Hans Weinberger, and Henghui Zou. For further information please contact James Serrin.
SECOND YAMABE MEMORIAL SYMPOSIUM
The Second Yamabe Memorial Symposium is being planned for September 17 - 19, 2004. The symposium will take place in the School of Mathematics. The topic chosen for this high-level conference is "Geometry and Physics". The list of confirmed speakers includes the eminent mathematicians Robert Bryant, Duke University; Kefeng Liu, U.C.L.A.; Duong Phong, Columbia University; Yongbin Ruan, University of Wisconsin; Isadore M. Singer, M.I.T.; and Shing-Tung Yau, Harvard University.
Organizing Committee: R. Gulliver (Chair), N. C. Leung, T.-J. Li, J. Wang
Robert Gulliver, Professor and Chair of the Yamabe Symposium Committee
Yamabe Memorial Symposium, in honor of the distinguished mathematician Hidehiko Yamabe (1923-1960), replaces, and continues in expanded form, the Yamabe Memorial Lecture which has been held annually since 1989, in alternating years, at the University of Minnesota and at Northwestern University. Lectures in this series have been given by Professors Neil Trudinger, Eugenio Calabi, Rick Schoen, Shizuo Kakutani, Craig Evans, Walter Rudin, Robert Hardt, Katsumi Nomizu, Fred Gehring, Richard Hamilton, Peter Sarnak, Jeff Cheeger and S.-T. Yau. The Yamabe Memorial Symposium is an enhancement of this tradition.
Mathematicians will gather every two years at the University of Minnesota for a long weekend to hear talks in an area related to geometry, to discuss the latest research and to interact with younger mathematicians.
Professor Hidehiko Yamabe (1923--1960) was an active and highly collaborative mathematician in the School of Mathematics at the University of Minnesota from 1954 until 1960, the year of his untimely death. His work on topological groups, geometry and analysis were outstanding contributions to modern mathematics.
Speaking Invitations & Other Notable Activities
Professor Douglas Arnold was recently elected to a three-year term on the Council of the Society for Industrial and Applied Mathematics (SIAM), SIAM's main policy-making body. He is also a member of a number of scientific advisory boards. As many of our readers are aware, since September 2001, he is serving as the Director of the Institute for Mathematics and its Applications which is associated with our department.
In October 2003, Professor Arnold was a ncm2 Distinguished Lecturer (ncm2 is the Network for Computing and Mathematical Modeling, a Canadian initiative based in Montreal). The title of his lecture was "From Exact Sequences to Colliding Black Holes: Differential Complexes in Numerical Analysis". In January 2004 he spoke at the Oxford University Colloquium on "Stable and Unstable Discretization of Partial Differential Equations".
His other recent invited talks include a keynote address at the opening of the Applied Mathematics Program at University of Illinois in Urbana-Champaign (UIUC), titled "Mathematics in a Dangerous Time", as well as a commencement address for the mathematics and statistics graduation at UIUC, titled "Doing the Math and Making an Impact". Both of these talks were given in May 2003.
The first of these talks deals with applications of mathematics to problems connected with homeland security and antiterrorism. Some of the topics addressed include cryptography, mathematical epidemiology with emphasis on special problems posed by bio-terrorism, data mining for counter-terrorism, and face and voice detection and recognition. Both history as well as current efforts are discussed. Slides can be found online at http://www.ima.umn.edu/~arnold/talks/danger.pdf
The second address covers topics that may be of wide interest, so we include some of the highlights below in the Newsletter in a note titled "Why is mathematics important".
Professor Maury Bramson gave an invited one-hour address at a Conference on Interacting Particle Systems held in Santiago, Chile in January 2004.
Professor Paul Garrett's book "Making and Breaking Codes: an Introduction to Cryptology" (Prentice-Hall, 2001), has been translated into Chinese. He wrote this book as a text for the popular course Cryptology (Math 5248) since no existing text met the needs of that course. His text "Mathematics of Coding Theory: Information, Compression, Error Correction" for the companion course Coding Theory (Math 5251) was published in 2003, also by Prentice-Hall.
During January 2004, Professor Dihua Jiang delivered invited lectures at Fudan University and East China Normal University in Shanghai, and at the Center of Mathematical Sciences, Zhejiang University in Hangzhou. He will give an invited 90 minute lecture on his work, with David Ginzburg (Tel Aviv University) and Stephen Rallis (Ohio State), on the Gross-Prasad conjecture, at the Joint Columbia-CUNY-NYU Number Theory Seminar, March 24, 2004. During the coming June, he will be an invited speaker at a conference celebrating the 10th anniversary of the founding of the Mathematics Institute at East China Normal University.
Professor Dennis Hejhal gave an invited series of lectures on "Maass Waveforms and Computational Spectral Theory" at the International Summer School on "Mathematical Aspects of Quantum Chaos", October 4-11, 2003, sponsored by the E.U. (i.e. European Union). The meeting was held at Schloss Reisensburg, a castle located near Ulm, Germany. Professor Hejhal will give a similar series of lectures this coming May at the Centre de Recherches Mathematiques in Montreal, Canada.
Professor Mark Keel was an invited speaker at the conference "Frontiers of PDE and Dynamical Systems" at Rutgers University in May 2003 and at the conference "Partial Differential Equations and Applications" at the University of Notre Dame in August 2003. Also, at the invitation of the Instituto Superior Tecnico in Lisbon, Portugal, he delivered a series of lectures to the mathematics department there in December 2003.
In October 2003, Professor Tian-Jun Li was an invited speaker at the Peking University Symposium commemorating the 90-th anniversary of the opening of the Faculty of Mathematics. During the current academic year, he is teaching a new, year long graduate level course on symplectic topology. The topic of the course is classification of symplectic structures on smooth manifolds. Professor Li received an invitation from the World Scientific Publishing Company to write a book on the subject and the lecture notes of his course will be the basis for the book, titled "Moduli space of symplectic structures".
Professor Mitchell Luskin currently serves on the Scientific Advisory Committee for the Centre de Recherches Mathematiques (CRM), Universite de Montreal. Professor Luskin served on the Organizing Committee for the Fall 2002 program of the UCLA Institute for Pure and Applied Mathematics (IPAM) on Mathematics in Nanoscale Science and Engineering, and was the chair of the Organizing Committee for the IPAM workshop on Modeling and Simulation for Materials held November 19-22, 2002. He also served on the Organizing Committee for the Caltech-IPAM Workshop on Molecular Modelling and Computation: Perspectives and Challenges held November 15-16, 2002 and the US/EU Meeting on Phase Transitions in Crystals at the University of Minnesota held April 11-12, 2003.
In April 2003, Professor Luskin delivered the Distinguished Lecture Series at the University of Iowa. He was an Invited Lecturer for a Spitalfield Day of the London Mathematical Society at the Newton Institute, University of Cambridge, May 13, 2003, as well as an Invited Lecturer at the following conferences: The 20th Biennial Conference on Numerical Analysis, University of Dundee, June 24, 2003; the Conference on Nonlinear Analysis and Numerics, Bonn, October 28, 2003; the Workshop on Hierarchical Modeling and Multiscale Simulation of Materials Interfaces, University of Maryland, October 30, 2003.
A note on Professor Luskin's reseach and teaching program entitled "Infinitesimal Machines Designed by the Mathematics of Shape" appears below in the Newsletter.
Professor Gennady Lyubeznik was a co-organizer, together with Luis Narvaez-Macarro from Universidad de Sevilla, of a special session on Differential Structures and Homological Methods in Commutative Algebra and Algebraic Geometry at the joint meeting of the AMS and the Spanish Mathematical Society. The meeting took place June 18 - 21, 2003 in Seville, Spain.
Professors Ezra Miller will be a principal speaker at the "Third Duke Mathematical Journal Conference", to be held on April 23--25, 2004 at Duke University. He is also a co-organizer, with Professor Victor Reiner and with Bernd Sturmfels from the University of California at Berkeley, for the Graduate Summer School and Research Program components of the upcoming Park City Math Institute (PCMI) on Geometric Combinatorics. This annual event, which this year will take place from July 11 through July 31, is planned, funded, and coordinated through the Institute for Advanced Study (IAS). The Summer School Lecturers will be Alexander Barvinok, University of Michigan; Sergey Fomin, University of Michigan; Robin Forman, Rice University; Mark Haiman, University of California at Berkeley; Robert MacPherson, Institute for Advanced Study; Richard Stanley, Massachusetts Institute of Technology; Michelle Wachs, University of Miami; and Guenter Ziegler, Technical University-Berlin. More information and further links can be found at http://www.admin.ias.edu/ma/program/index.html
Professor Duane Nykamp will be an invited speaker at the AIMS Fifth International Conference on Dynamical Systems and Differential Equations, session on "Computational Neuroscience: From Physiology to Mathematical Modelling". The conference will be held this coming June in Pomona.
Professor Peter Olver will be an invited plenary speaker at the following conferences: 6th International Workshop on Mathematics Mechanization, Shanghai, China, May, 2004; Joint Canadian Math Society and Canadian Applied and Industrial Mathematics Society, Halifax, Canada, June 2004; Ninth Meeting on Computer Algebra and Applications, Santander, Spain, July 2004. 13th School of Differential Geometry, Sao Paulo, Brazil, July, 2004. Red Raider Symposium, Texas Tech University, Lubbock, TX, November, 2004. He was, or is, a member of organizing committees of the following conferences and workshops: Differential Invariants and Invariant Differential Equations, Banff Institute, Canada, 2003; IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, Nice, France, 2003; Geometry, Integrable Systems and Quantization, Varna, Bulgaria, 2004; Symmetry and Perturbation Theory, Cala Gonone, Sardinia, 2004; Integrable and Near-integrable Hamiltonian PDE, Fields Institute, Toronto, Canada, 2004; and Foundations of Computational Mathematics, Santander, Spain, 2005.
Professor Peter Polacik was a plenary speaker at Equadiff 2003, Hasselt, Belgium, July 22-26, 2003. This conference was a part of a series of conferences on differential equations organized every four years in Western Europe. Professor Polacik also was an invited speaker at the conference Singularities in PDEs, Bratislava, Slovakia, May 25-28, 2003, and at the Canadian Mathematical Society Summer Meeting, June 14-16, 2003.
Professor Emerita Marian Pour-El was a member of the Scientific Program Committee of CCA 2003 International Conference on Computability and Complexity in Analysis held in Cincinnati, August 28-30, 2003. She also gave an invited talk at the conference on her joint work with Ning Zhong on "Boundary Regularity and Computability".
Professor George Sell was a co-organizer, together with Russell Johnson, Rafael Obaya, and Yingfei Yi, of a Mini-Symposium on Non-autonomous Dynamics, which was held at the Equadiff 2003 International Conference in Belgium in July 2003. He is also a member of the Scientific Organizing Committees both for the International Conference on Difference Equations (ICEDA), which is scheduled for the University of Southern California Los Angeles in August 2004, as well as the ICEDA conference to be held in Munich Germany in July 2005. A special issue of the Journal of Difference Equations and Applications was dedicated in honor of Professor Sell's 65th birthday in 2003.
Regent's Professor Emeritus James Serrin has recently published an extensive review article in the Journal of Differential Equations, vol 196, pp 1-66, with title "The Strong Maximum Principle Revisited" (with P. Pucci, University of Perugia). He is also organizing a workshop at the University of Minnesota, June 23 -June 25, on the subject "New Developments in Nonlinear Elliptic Equations", with speakers from Italy, Germany, the Netherlands and the United States. Serrin will also be a principal speaker at a conference in Gaeta this summer in honor of the 60th birthday of Haim Brezis, and will be the principal speaker at a meeting of the Mathematical Association of America at Ball State University in April. He is on the scientific committee for the Gaeta conference, and also on the scientific committee for a second conference in honor of Brezis to be held in Paris this summer.
Professor Alexander Voronov was a plenary speaker at the 3rd International Symposium on Quantum Theory and Symmetries held at the University of Cincinnati, September 10-14, 2003. Then, September 16-20, he delivered a mini-course on "String Topology and Beyond" at the Summer School on String Topology and Hochschild Homology, University of Almeria, Spain. During the Spring 2004 semester he is serving as a Stone Professor at Northeastern University, Boston, Massachusetts, where he is teaching a graduate course on Operad Theory. He is organizing a special session on Homotopical Physics at the American Mathematical Society meeting in Lawrenceville, NJ, April 17-18, 2004. And he is serving on the Advisory Committee for the XXIII workshop on Geometric Methods in Physics, Bialowieza, Poland, June-July, 2004.
Professor Peter Webb was an invited lecturer at a workshop on Group Representations and Cohomology at Australian National University, Canberra, June 30 - July 4, 2003.
Professor Ofer Zeitouni was a co-organizer and a speaker at the 29-th Conference on Stochastic Processes and their Applications, held August 3-9, 2003, at Rio de Janeiro.
How do we rank?
Did you think we were performing well in mathematics at Minnesota? Well, others agree. Thomson ISI publishes a list of 'highly cited researchers' in mathematics available at the internet site ISIHighlyCited.com. Worldwide, out of the top 234 mathematicians listed, 5 of them are currently in our department. They are Professors Douglas Arnold, Wei-Ming Ni, Peter Olver, George Sell and James Serrin. This surely puts us in a strong position compared to other departments.
Thomson ISI also has a number of different categories into which they break down the research output of federally funded universities. One of these categories is 'most prolific' - which measures the total number of papers produced by mathematics departments in the years 1998 - 2002. The top five in this 'most prolific' category, along with the number of papers contributed by each department to a certain group of journals is:
1. University of California, Berkeley 664
2. University of Michigan 576
3. Rutgers University 559
4. University of Wisconsin, Madison 546
5. University of Minnesota 506
(info available from http://www.in-cites.com/research/2003/december_22_2003-1.html).
It was comforting to read the more general ranking of 'Best Places to Work in Academia' compiled by 'The Scientist'. Their top 5 American institutions are:
1. Fox Chase Cancer Center
4. University of California at San Francisco
5. University of Minnesota - Twin Cities
In a similar vein the Massachusetts consulting firm Collegia Inc. produces a College Destination Index. They evaluate large, mid-size and small cities on various 'lifestyle' aspects. In the 'Large City' category the top 5 are:
1. Boston-Cambridge Mass.
3. San Francisco Bay Area
4. Minneapolis - St. Paul
5. New York - Long Island - Northern New Jersey
Exciting Math-Physics Interfaces
In recent years, there has been much interaction between mathematics and physics in the area of string theory and M-theory. These are theories that unify all forces in the universe. The development of these theories uses many different branches of modern mathematics, including algebraic geometry, differential geometry, symplectic geometry, combinatorics, representation theory and so on. On the other hand, these physical theories give mathematicians new insights, which lead to many exciting and surprising conjectures and problems in mathematics. Among them are the structure of Gromov-Witten invariants, the mirror symmetry conjecture for Calabi-Yau manifolds and the geometry of G2 manifolds.
Our School of Mathematics has a very strong group of mathematicians working on the interface between string theory and mathematics. This includes Ionut Ciocan-Fontanine on Gromov-Witten theory, Naichung Conan Leung on Differential Geometry, Tian-Jun Li on Symplectic Geometry and Alexander Voronov on Representation Theory. Dunham Jackson Assistant Professor Junho Lee and several graduate students also work on such topics. There are many fruitful interactions among people in our group. There are also many seminar talks on this interface in our department. Furthermore, the theme of the next Yamabe Symposium in the Fall of 2004 is 'Geometry and Physics'. Speakers for the symposium include I.M. Singer, C. Vafa, S.T. Yau and other mathematicians and physicists.
Naichung Leung, Professor of Mathematics
INFINITESIMAL MACHINES DESIGNED BY THE MATHEMATICS OF SHAPE
Can the "infinitesimal machines" envisioned by Feynman be constructed from transformations between cubic and tetragonal lattice structures by the magnetostrictive crystal Ni2MnGa? What kind of shape change can we construct if we coherently mix cubic and tetragonal cells, or cubic and orthorhombic cells? Professor Mitchell Luskin in the School of Mathematics is working with Professors Richard James (Department of Aerospace Engineering and Mechanics) and Chris Palmstrøm (Department of Chemical Engineering and Materials Science) to develop theory, computational methods, and experimental techniques to design and grow single crystal films as thin as 90 nanometers to build infinitesimal machines that utilize lattice transformations. The mathematics of shape change guides the search for the most effective atomic composition and crystallographic orientation of the film.
Mathematical and computational challenges are presented by the disparate space and time scales, from atomistic to continuum, needed to model small materials. Luskin, James, and Palmstrøm are utilizing ideas based on weak convergence and geometry to develop multiscale mathematical and computational methods. More details can be found at http://www.math.umn.edu/~luskin/.
Major contributions to this research program on the mathematics of shape change and related computational methods have been made by graduate students and postdocs in Luskin’s group, and a new program is being developed to provide an interdisciplinary experience in mathematics, science, and engineering for high school students in the University of Minnesota Talented Youth Math Program.
(a)Theory, (b) design, (c)computation, and (d)experiment for a small scale actuator. (a) The idealized two-dimensional crystal has gray square cells at high temperature and symmetry-related yellow and red rectangular cells at low temperature. (b) The film is flat and in the gray phase at high temperature. At low temperature, the film is tent-shaped as the upper and lower triangular regions of the film reversibly transform to red rectangular cells, and the left and right triangular regions reversibly transform to yellow rectangular cells (Bhattacharya & James). (c) Numerical model and simulation of a “melting” tent (Belik & Luskin). (d) Experiment with a single crystal CuAlNi film (Cui & James).
Mitchell Luskin, Professor of Mathematics
Hans Othmer on Mathematical Biology: In Interview with Peter Webb, Professor Othmer Expresses Some Thoughts
Peter Webb: Hans, first of all let me thank you very much for agreeing to be interviewed for the Departmental Newsletter. Before I ask you any questions I would like to congratulate you, because we have heard that you have received an award from the Alexander von Humboldt Foundation, which is a notable distinction and evidently is in response to your work and your various activities. Congratulations! I wonder if you could just tell me a little bit about it? It comes with some money, which I suppose will support work that you do with people in Germany. Do you have to do the work in Germany? Will you do it in certain places?
Hans Othmer: No, not strictly. As the director of the Max Planck Institute where I am staying emphasized, this is a prize, so there are no fixed requirements, but the purpose of it is to stimulate in part research between people in Germany and the rest of the world, and so I've made a commitment to stay there for about 6 months, and they also gave me generous travel funds to go back and forth and I can invite visitors and so forth. It's just perfect. It's out of the blue. It's very nice!
PW: Let me ask my first question about mathematical biology, which is a big question. It is really if you could give some sort of overall snapshot of how you see mathematical biology at the moment, where you see the current activity. We would have to have been blind and deaf not to appreciate in recent years that mathematical biology is receiving a lot of attention and that there is a lot of funding coming into mathematical biology. How do you see the overall picture at the moment?
HO: Well, given that I've been in the area for 30 years, I consider that it has changed very dramatically. When I started at Rutgers, 30 years ago last year, there were real, real hard questions. Is this a legitimate intellectual exercise? a), and b) does it belong in a mathematics department? Some of those questions people still ask, and that's perfectly legitimate. But I see it as coming into a golden age, because what has really changed fundamentally is that biologists have begun to realize that they need mathematics to understand these complex biological systems. Thirty years ago when a lot of the new molecular biology techniques started in, the attitude was: I will take the watch and I will dissect it, put its pieces on the table, and I will then understand how a watch works. Of course anybody could say that isn't true. You will understand how the pieces work, but you won't understand how the watch works. That realization has really sunk in full-force, because the more people understand about biology the more they realize how complex it is. Mathematics is the natural language that deals with extracting essential pieces and discarding what isn't so essential, and analyzing those essential pieces.
I think there are enormous possibilities for mathematicians in mathematical biology, just as there were 150 years ago in physics. Much of analysis came out of people trying to understand heat conduction, fluid flow, gas dynamics. Everything evolved into the field of PDEs, functional analysis and all these things. They all came out of very concrete problems long ago. It's interesting to ask, what would have happened to mathematics had people really started understanding biology first, rather than physics. How would mathematics have developed?
PW: Could you be specific about what parts of mathematics in technical terms have particular application in biology. I am aware of some things. So I think there is quite a lot of mathematical modeling using differential equations, there's that kind of thing. I understand also there's a certain amount of combinatorics, trying to understand DNA structure perhaps. What areas might a mathematician who is interested in moving in to mathematical biology focus on?
HO: Well, I think there are areas of biology in which almost any area of mathematics that I can think of has been used. Certainly differential equations and dynamical systems, ordinary differential equations, partial differential equations, those are the bread and butter of modeling in much of biology. We also need to know about stochastic processes. We are discovering that if we talk about gene control networks we have to worry about individual molecules. We can't treat things as continua the way we think of when we do a differential equation model. And so stochastic processes are going to be much more important in the future. In understanding languages one uses a lot of algebraic structures. Maybe DNA strings are a kind of a formal language.
PW: I have the impression that there is more emphasis on continuous phenomena than discrete. For instance, I do representations of groups, often-finite groups, and I am not aware that that particularly has application in mathematical biology.
HO: Well it actually has had some, in the form of symmetry groups. So there are huge issues about pattern formation. If you look at any issue of Nature you see people are trying to understand how the spatial structure of things evolves. To summarize it, how do you read out the information of the genome at the correct point in space at the correct time, so as to build an organism like me? And so, finite groups and group theory and group representations and so forth have been used in analyzing symmetry and symmetry breaking, pattern formation and so forth. In the area of bifurcation theory, one subarea is symmetric bifurcations. The point is that one should never say that a particular area of mathematics is never going to be useful. Wait! Somebody will find a use.
PW: How do you view the mathematics department here, at the University of Minnesota, in terms of mathematical biology, the people who are here at the moment, what courses we have, and the gap that probably exists between what there currently is and what you might hope for in the future?
HO: Yes, OK. Let me start answering that by backing up one step and emphasizing that mathematical biology is still a very interdisciplinary subject, and that's because we're not at the stage people are in fluid mechanics, for example, where the Navier-Stokes equation is very well-established. You don't have to justify working on Navier-Stokes to people doing fluids. There are well-established questions everybody agrees are very important, so you go off and look at them. In biology it's different, so people really have to learn some of the biology as well as the mathematics. You don't just go to someone and say, 'Give me an equation of a type I am very familiar with and let me work on it.' because that will frequently lead to nonsense. So it's an extremely interdisciplinary subject. As to how that plays out, it means for the students that they have to learn things in addition to various mathematical techniques. My students will take courses on differential equations, dynamical systems, PDE's numerical analysis, stochastic process, and then perhaps a biology course or two so that they have some grounding at least in the biological aspects of the problems that they are trying to understand.
As you know last year we hired someone in neuroscience, so now I would say roughly speaking the two areas which are represented here are pattern formation, developmental biology, physiology type of problems including gene control, all the complex networks issues; and then Duane Nykamp does theoretical neuroscience, which is a huge area in itself, and which I would hope more mathematicians would get interested in thinking about, because it is the canonical example of what mathematicians do very well, i.e. thinking about abstract ways to understand things. That's needed there, but it has to be grounded in some understanding of what the basic physiology of the brain is. You can't just think of it as an abstract machine, although the abstraction could help enormously.
PW: Do you think the courses that are available currently are well set-up to allow somebody who is a mathematician to obtain a knowledge of the biology that he or she needs?
HO: Well I give some courses the intent of which is to accomplish that in part, but let me also emphasize that it's an awful lot easier learning the biology as a mathematician, than it is learning the mathematics as a biologist. So we have an enormous advantage. I've never taken a biology course, I've learned it all by reading. I send my students to some courses so that they get a more formal introduction to it, but if one is sufficiently dedicated, you can read it and learn it, and by talking to people in the area understand it. So it's an asymmetric situation, and I would emphasize that people learn the mathematics first, and well, because they can learn the biology later.
One thing I find interesting here, and which surprised me when I came here is the latent need that exists on campus for people to have someone with more mathematical training to talk to. I could collaborate with 15 people at any given time, simply because there is so much interest in having mathematicians who know enough of the background to be able to converse, but can also do the mathematics. That's why people from other departments come here. And so, you know, many of our colleagues could probably do similar things.
PW: Do you think you need more people in your area in the department?
HO: I think so. I think in a department of this size, given the demand in terms of training Ph.D.s, given the possibilities for enhancing mathematics through interactions with other departments, I think it's an easy thing to justify.
PW: It's a difficult thing to run a program when you have one or two people and you are trying to do everything yourself.
HO: Well, believe me, the first four years here were very tough. I was doing a new graduate course every year, and now we're beginning to have a program, so people can see an intellectual path that will take them through courses and into the research, and that's good. I would also say that people have to realize that mathematics is by and large a service organization within the university. That's the reality. If we were only teaching our own progeny, there would be far fewer of us. That is the reality. And so, having people who understand some of the issues that people outside of the department are facing when they want to use mathematics, I think, is again healthy for mathematics. We can serve as a kind of bridge to people outside, and they can say, 'Yes, there's somebody who has some inkling of what we do when we struggle in trying to apply mathematics, and why our students struggle with the way mathematics is taught.' It all comes together. I think what we have to do is build on this and see that biology does as much for mathematics as mathematics can do for biology, because then both sides win, and that's the most interesting outcome.
School of Mathematics Involvement in the New K-12
This past year saw a major shift in the Minnesota public schools (K-12) standards, and members of the School had a significant impact in the process of producing and adopting these changes. This is an excellent example of the service to the larger community by our faculty. The process by which these changes were made was very complicated, requiring great deal of interaction with the legislators and the state government. The School faculty members participating in this important endeavor were Professors Bert Fristedt, Larry Gray and Chester Miracle. Professor Gray was, at the time, Director of Undergraduate Studies, and became the Head of the School in September 2003. Professor Fristedt has given us the following account of the process that led to the new standard.
In February 2003, the new state of Minnesota Commissioner of Education, Cheri Pierson Yecke, formed an Academic Standards Committee, consisting of approximately 80 people to write new math and language arts state standards for K-12 (that is, Kindergarten through grade 12). The standards that were developed will be important for the children of our state in the years to come. The following paragraphs give some insight into the process of developing these standards.
For the math subcommittee of 40, three School of Mathematics faculty where chosen: Bert Fristedt, Lawrence Gray, and Chester Miracle. The Mathematics Department at the Morris campus of the University of Minnesota was represented by Peh Ng. Another important contributor to the work of this subcommittee was Lesa Covington Clarkson, who is on the faculty in the Department of Curriculum and Instruction here on the Twin Cities campus. William Beck and Jerald TerEick of the School of Mathematics were not on the Academic Standards Committee, but made extremely important contributions in an 8-hour session arranged by Fristedt and Miracle with them and some members of the math subcommittee. Beck and TerEick are retired high school mathematics teachers who have for several years been on our staff as teaching specialists.
Within the math subcommittee there were further subcommittees: Fristedt served first on the 9-12 subcommittee and later on the 6-8 subcommittee, whereas Gray did the reverse. Miracle and Ng were on the 9-12 subcommittee throughout and Covington Clarkson was on the 6-8 subcommittee. Gray and Covington Clarkson were also on a composition subcommittee of six, chosen by the Commissioner to compose a well-written document integrating the ideas from the K-2, 3-5, 6-8, and 9-12 math subcommittees. This subcommittee did a superb job, especially considering the severe time-constraint that was imposed by virtue of the Federal `No Child Left Behind' legislation.
This document accommodates the mathematics relevant for a mathematics-rich college major while emphasizing the mathematics that all should learn in order to have constructive roles as citizens, as well as skills that are relevant for a wide variety of occupations.
With reference to the preceding paragraph, one might ask: What is so novel about that? Is that not what has always been done? With these two questions in mind, the following paragraph gives a bit of relevant background.
In the somewhat distant past, the state of Minnesota had very minimal high school mathematics requirements. A long period followed in which there was an attempt to entice all students to take more mathematics and to really learn the mathematics that they took. Roughly speaking this attempt had four strands, not all occurring at the same time and often occurring in reaction to other strands, but also not fully disjoint from each other either: (a) practice in being skillful in mathematical procedures; (b) develop an understanding of mathematics concepts; (c) learn about mathematics in real-world contexts; (d) learn mathematics by a variety of techniques that some might view as non-traditional, such as group discussions or discovery learning. A further complicating feature is that item (b), in particular, is subject to vastly different interpretations. In 2000-2002, Gray, in his then role as Director of Undergraduate Studies in the School of Mathematics, had been contacted by several scores of parents in the state complaining about the mathematics content in the schools. Gray, and occasionally Fristedt, visited many schools and parents groups at the invitation of parents or school administrators, and Fristedt started to make contacts with legislators on this issue. What had happened is that strands (c) and (d) above had become dominant, partly because of the way that the Minnesota 'Profiles of Learning' law had been written. In particular, the emphasis on (d) had pushed calculational skill and the accompanying understanding in arithmetic and algebra to the sidelines.
Therefore, when a chance developed to create new state standards, Fristedt and Gray were ready to volunteer in order that doing arithmetic and algebra be restored to its rightful place in K-12 and basic geometry to 9-12. [The K-8 `Profile of Learning' standards in geometry were generally fine and in some cases "better than fine", but the 9-12 geometry standards were vague and unnecessarily weak, especially given the fine K-8 preparation.] Fristedt contacted Ng and Gray contacted Miracle, and both Ng and Miracle responded by also volunteering.
Besides the official subcommittee meetings, Fristedt, Miracle and Ng joined the Commissioner at several meetings throughout Minnesota where the Commissioner sought public input on an early draft. At most of these, committee members were quiet listeners and observers, since many non-committee members wished to speak. An exception was the meeting in Onamia where it developed that Miracle was the main contributor. He was able to make two important points about the proposed standards: (i) that they represent a consensus, bringing together a variety of views of K-12 teachers, post-secondary faculty, parents, and business people; (ii) that they are outcome-focused while accommodating a variety of teaching styles.
There was no attempt to include calculus standards for those who have accelerated through the K-12 system in mathematics, but an accelerated student would typically take calculus in high school. A non-accelerated student who masters the material in the standards is well-prepared to succeed in post-secondary calculus. Of course, it is not expected that all students would be tested in high school on all of the standards---the standards focusing on the to-calculus path beyond what would be expected of all were primarily the work of Miracle with input from several others on the 9-12 subcommittee, most notably Steven Jones, the chair of mathematics at Mankato West High School.
All on the mathematics subcommittee took their tasks very seriously, but besides those described above, the author of this article noticed that several deserve special mention. These include all six members of the composition subcommittee who gave so freely of their time. Besides Gray and Covington Clarkson, there were two who had won Minnesota teacher-of-the-year awards (in different years, of course) ---Ellen
Delaney, a high school teacher from North St. Paul and Barbara Stoflet, an elementary school teacher from the Hopkins school district---and Nancy Nutting, the chair of Sci-Math Minnesota and Ellen Hoerle, a chemical engineer from Eden Prairie, who at present is a stay-at-home mother.
There are also others whose contributions were very special. John Kappler, a computer scientist from Shoreview, made a wide variety of specific nicely focused contributions to the 9-10-11 standards on which the grade 11 state mathematics test should be based; he did this both in the official committee meeting and in the informal session with Beck and TerEick mentioned above. Dale Akkerman, a physician from Burnsville, made several important contributions in the 6-8 math subcommittee, especially in adding richness to the standards without making the standards for grades 7 and 8 into mini-algebra standards. David Klitzke, a sixth grade teacher from Lester Prairie was a major player in creating the sixth-grade standards, especially in connection with the items related to prime numbers and factoring. The input of Kim Ross, a former mathematics teacher who is now superintendent of the Houston, Minnesota School District, guided the committee to solid but realistic 6-8 standards. Fristedt called on two other non-committee members for what turned out to be valuable input into the 9-10-11 standards: Julie Guelich, the Dean of Natural Sciences and Mathematics at Normandale Community College and long-time member of the Mathematics Department there, and Len Mrachek, who taught for more than a quarter century in Minnesota technical colleges, and as a "retired person" currently teaches mathematics in General College here on the Twin Cities campus.
Once the standards were written, there were hearings by the relevant committees in the House, the Senate, and by the joint-house-senate conference committee. Besides the general testimony of the Commissioner, most of the subject-specific testimony was given by Delaney, Fristedt, and Gray.
As the process goes forward with state tests aligned to the new standards and school districts possibly asking for suggestions or clarifications, Fristedt, Gray, and Miracle, as well as the Institute of Technology Center of Education Programs directed by our own faculty member Harvey Keynes, are resources on which the State can call to provide substantive input.
Bert Fristedt, Professor of Mathematics
Why Is Mathematics Important?
In this note we excerpt some of the highlights of Professor Arnold's May 2003 commencement address, titled "Doing the Math and Making an Impact", and given by him for the mathematics and statistics graduation at the University of Illinois in Urbana-Champaign. Professor Arnold is the Director of the Institute for Mathematics and its Applications which is associated with our department. The full text of this interesting and inspiring talk is online at http://www.ima.umn.edu/newsltrs/updates/summer03
Asking "What makes the math sciences so central?", he answers by quoting Galileo: "The great book of nature can be read only by those who know the language in which it was written. And that language is mathematics.", adding "Math is the way to understand all sorts of things in the world around us." To elaborate on this point he gives some well-chosen examples, beginning with some insightful comments on the Swiss victory in the 2003 America's Cup. "...you know that Switzerland is a small, mountainous, land-locked country. So how did the Swiss pull this upset off?" While acknowledging that a number of diverse factors had to come together, he makes his point: " Well Switzerland may not have a great sailing tradition (at least until now!) but it does have a very strong tradition in mathematics--Euler's picture appeared on a Swiss 10 franc note--and the Swiss team wisely brought this strength in math to bear on the America's Cup challenge. They enlisted a group of mathematicians specializing in mathematical modeling and numerical computation led by Professor Alfio Quarteroni at the national polytechnical university in Lausanne. The mathematicians used partial differential equations to model the flow of the sea around the hull, the dynamics of the air and the sails, and the turbulent interaction of the ocean, wind, and boat. They then applied advanced numerical algorithms to solve these equations on high performance computers. This allowed them to optimize such things as hull and keel design, sail geometry and placement, and so forth. Their work was essential to the design of the Alinghi, and so to the Swiss victory. They did the math and made a big impact." ("Alinghi" was the name of the Swiss boat.)
On the increasing role of mathematics in biological sciences he comments as follows: "Increasingly math is making an impact in the life sciences as well, prompting biologist Rita Colwell, director of the National Science Foundation, to observe that "mathematics is biology's next microscope--only better." In their recent bio textbook Keener and Sneyd wrote that "teaching physiology without a mathematical description of the underlying dynamical processes is like teaching planetary motion to physicists without mentioning...Kepler's laws;" He then mentions still other areas of applications: "And math increasingly reaches outside the sciences, to economics, sociology, and business for example. ...Illinois's new Applied Mathematics Program ...involves no less than 22 departments from bioengineering to linguistics. ...Problems which need mathematics for their solution also arise throughout industry."
To underline how seriously this is taken worldwide, he cites a strategic plan published by the British government in 2003, seeking to exploit mathematical research to improve the competitiveness of industry in the UK: ""Mathematics is the most versatile of all the sciences. It is uniquely well placed to respond to the demands of a rapidly changing economic landscape...Mathematics now has the opportunity more than ever before to under-pin quantitative understanding of industrial strategy and processes across all sectors of business. Companies that take best advantage of this opportunity will gain a significant competitive advantage: mathematics truly gives industry the edge." He also notes that British government policy in dealing with the hoof-and-mouth disease outbreak a few years ago relied heavily on studies based on mathematical epidemiology.
He states that a major current challenge we face is how to get the most out of all the data that has been accumulated thanks to the modern technology: "For example, how can we exploit the world-wide network of seismic sensors to predict earthquakes? How can we mine the vast genomic databanks to advance biology and medicine? How can we sift through the massive amounts of text, video, web, and satellite data to detect terrorist events before they happen? Well, data means big collections of numbers--remember that text and images are digitized and stored as numbers--and data mining means discovering the patterns and structures hidden in those collections. That's practically a definition of mathematics: the study of structures and patterns in large numerical sets. So you can be sure that in the 21st century--the century of data--math will again have a huge impact."
In conclusion he exhorts the graduates to cultivate and apply logical, mathematical and quantitative thinking even if they do not become research mathematicians. The full text of this interesting and inspiring talk is online at http://www.ima.umn.edu/newsltrs/updates/summer03
How to Teach
by Chester Miracle
Editors’ note: Professor Miracle has earned recognition as one of the best teachers in the department. He has administered for many years our very successful extension program and participated in numerous departmental teaching initiatives as well as being a long-term member of the Curriculum Committee. Recently he played a major role in the development of the K-12 standards, as described in Bert Fristedt’s contribution in this issue. As Director of the extension program, Professor Miracle has supervised and guided many instructors in mathematics. He kindly agreed to share with us
some of his thoughts on the methodology of teaching:
In my view, the most important single thing that a person should do in order to be a good teacher is to prepare the lecture before class. When preparing a lecture, take a realistic view of what the students will be able to understand. Years ago, almost no teacher came to calculus class with written notes. Now, I would guess, at least half of the lecturers come to a calculus class with written notes in hand. Teaching assistants should also always have something prepared.
Lecture to the students you have, not to some ideal student. The University of Minnesota may not be as selective as we might like. But we take the money from these students and so we have a moral obligation to teach a class they understand. Be sure that someone other than yourself is able to follow what you are saying. It is easy for an instructor to find an ‘advanced topic’ to discuss. Mostly, the students do not find this interesting. What they actually think is ‘this lecturer is a jerk and the worst part of it is he is wasting my time.’
Do not spend half a class period going over some ‘interesting idea’ that is not part of the course. Mostly, the students do not pay attention since they feel the instructor is talking about something not in the course. The job of a teacher is not to get up in front of class and just talk, it is to teach students something they feel they want to learn or at least must learn.
Very few students know everything we think they should know. If they need a little review on a topic, give a little review. If you are teaching polar coordinates and you know your students do not remember much trigonometry, then go over the ideas of trigonometry as you teach polar
coordinates. Try to start every lecture at a point where you are sure that the students understand what you are doing.
Spend some time getting to know your students and what they know. One very good way to get to know students is to grade their exams. I have
been teaching IT calculus for 5 years. I always help grade the hour exams and the final exam. This gives me a clearer picture of what the students can and can not do.
I consider attempts to motivate students using jokes or history of mathematics a waste of time. Math is not fun for students. Many students get satisfaction from success in mathematics, but it is not fun. The things like short biographies we once saw in calculus books do nothing to motivate students to want to study math.
Working with students in IT calculus has made me certain that people learn mathematics by doing mathematics. The most important thing about a mathematics course, at any level, is how much mathematics are the students
doing. I have talked with many students who were in lecture, were paying attention and took really great notes. My conclusion is: lecturers are not really as effective as we would like to think they are. Students learn very little during actual lecture. Students learn more by doing other things. These things can make the lecture much more meaningful. With this in mind it is important for the instructor to control what the students are doing with their ‘study time’ outside of class.
I always try to test students on what I teach them. Many times, I have asked a student that I know who is taking another class: “How was the test?” All too often they reply that the test was unfair or a bad test because the instructor asked a bunch of questions that were never discussed in class.
As teachers we often think that our primary job is to give great lectures. However, our primary job is to make students work problems correctly.
Retirements and Resignations
RETIREMENT OF MORTY HARRIS
This past year saw the retirement of Professor Morton (Morty) Harris. Morty joined our faculty in 1974 as an Associate Professor, and was promoted to Full Professor in 1976. He received his Ph.D. from Harvard University in 1960 under the direction of the eminent algebraist Richard Brauer. Before coming to the University of Minnesota he held positions at Clark University, Tufts University, and the University of Illinois at Chicago Circle where he reached the rank of Associate Professor. Morty’s chosen field of mathematics was finite group theory. This is one of the core areas of mathematics and has been a focus of intense study. Morty pursued a vigorous research program throughout his academic career and collaborated fruitfully with scholars both in the U.S. as well as in Europe, especially in France. He enjoys traveling and he has held numerous short term visiting positions in the U.S., Canada, Europe, and Israel. His zest for mathematics and his cheerful humor will be missed in our department.
Following retirement Morty has moved with his wife Ilene to Chicago, where he has many personal and mathematical connections. He intends to stay active in mathematics. We wish him the best in this new stage of his distinguished career.
Regents’ Professor Avner Friedman resigned from his position at the University of Minnesota in order to continue as Director of the Mathematical Biosciences Institute at the Ohio State University. A member of the National Academy of Sciences and recipient of many other major honors, Professor Friedman is one of the world’s leading mathematicians. Although his departure is a great loss to the School of Mathematics, the new Biosciences initiative in which he has had a pivotal role for the past two years is of major importance nationally.
Avner joined our faculty in 1987, serving as Director of the Institute for Mathematics and its Applications (IMA) for ten years. He subsequently founded, and directed, our highly successful Minnesota Center for Industrial Mathematics (MCIM). While the IMA is an NSF funded research institute affiliated with the department, the MCIM is a part of the department which deals with the issues of the industrial mathematics component of our graduate studies program, such as development of special courses and arranging industrial internships for the students. Both of these institutions remain vibrant under the guidance of his successors.
A Conference on Current Trends in Mathematics and its Applications, in honor of Avner’s 70th Birthday, was held at the University November 8 - 10, 2002. The Conference, sponsored by the School of Mathematics and by the Institute for Mathematics and its Applications, was attended by many leading mathematicians.
At the dinner event, Professor Fernando Reitich who chaired the organizing committee read a message from the then department Head Professor Naresh Jain who was unable to attend. In his message Naresh thanked Avner for his great contributions to both the IMA and the School of Mathematics and expressed admiration for his achievements. He went on to say, “I, together with my colleagues, have always marveled at the amount of energy that you possessed to bring so many great ideas to a successful conclusion. You always liked new challenges and embarked on the creation of the math-biology center at Ohio State. You have our best wishes for the success of this new venture, and we know you will succeed.”
One of our outstanding applied mathematicians, Professor John Lowengrub, has accepted a position at the University of California, Irvine.
John became a member of our faculty in 1992 as an Assistant Professor. He received his Ph.D. in 1988 from the Courant Institute and held prestigious postdoctoral appointments including a Szego Assistant Professorship at Stanford University as well as a Visiting Membership at the Institute for Advanced Study before joining our faculty. He was promoted to Associate Professor in 1995 and to Full Professor in 1999. His major recognitions include the McKnight Foundation Professorship (1994-1996), the Sloan Foundation Fellowship (1995-1997), and the 1998 Francois Frenkiel Award of the American Physical Society.
John’s research is in numerical analysis and applications to materials science and fluid flow. He collaborated extensively with researchers in
chemical engineering and aerospace engineering departments, including joint supervision of Ph.D. students. He also served as a mentor of postdoctoral researchers.
As a dynamic researcher and collaborator John was a notable member of the School of Mathematics. We wish him the best in his new position.
Dinner in Honor of Naresh Jain
After eight successful years at the helm of the School of Mathematics, Professor Naresh Jain decided to step down from the Headship. During his tenure as Head, Naresh fostered the research and teaching missions of the department in many ways, hiring outstanding new faculty, supporting educational initiatives such as the IT calculus program and REU’s (research experiences for undergrads), helping to develop the MCIM, and working closely with the IMA during its renewal and transition to a new Director. Naresh worked very hard and consistently to promote the School and ensure that our faculty received the recognitions that they deserved.
To thank Naresh for his exemplary service, and acknowledge his achievements, a dinner in his, and his wife Kusum’s honor, was held on Thursday May 8, 2003 in the Mississippi Room of the recently remodeled Coffman Memorial Union—
a great venue for this festive occasion.
The speakers included the IT Dean Ted Davis as well as several colleagues who worked closely with Naresh during his years as Head: the incoming department Head Larry Gray, who served for past several years as the Director of Undergraduate Studies, Professor Willard Miller, who served over the past several years first as an Associate Dean of IT, and then as the Director of the Institute for Mathematics and its Applications, as well as Professor Bert Fristedt and Professor Mitch Luskin. The Master of Ceremonies was (of course) Professor Walter Littman, who read greetings and good wishes to Naresh from Ordway Professor Nick Krylov, who was away, as well as the distinguished mathematicians Don Burkholder (University of Illinois) and Srinivasa Varadhan (Courant Institute).
Although Naresh is very happy to return to his research and teaching, he remains deeply involved in ongoing departmental initiatives, and we are sure that he will continue to contribute in a major way.
AN UPDATE ON OUR HONORS PROGRAM
We are very proud and excited about the advances we have made in our Honors Program over the last few years. When Professor Jay Goldman started the program about fifteen years ago, his initial function was to be an advisor and mentor for students capable of honors work, oversee the development of the IT Honors Calculus sequence, a hard problem solving oriented course, and recruit teachers for it.
Every fall Professor Goldman runs an information meeting for students planning to apply to graduate school. However, over the last few years, he and the department have adopted a much more activist role which includes designing new honors courses, coordinating programs of different students so they could get to know and motivate each other, and finding study and research opportunities for undergraduates.
Our department has funded undergraduate summer research programs for several years (see the following note). Professor Claudia Neuhauser's Grant currently sponsors undergraduate research in mathematical biology. Our students have also participated in NSF funded programs around the country. Two students have spent a semester in the well-known Budapest Seminar Program in Mathematics, which included Paul Erdos among its founders.
The department recently initiated a Math Club under the direction of Professor Carme Calderer and a Junior Colloquium organized by Professor Richard McGehee and advanced graduate students John Hall and James Swenson.
The new three semester theoretical honors sequence, which was inaugurated in the fall of 2002, has just turned out its first graduates. The subject of the first two semesters is primarily linear algebra and multivariable calculus.
Professor Steve Sperber, who taught the course during the academic year 2002-03, characterized it in the last year's newsletter as follows. The "...course...is designed to help develop the mathematical potential and ability of promising undergraduates.... The sequence has a much higher requirement of mathematical rigor explicitly including proofs in the treatment of topics than in the analogous IT sequence."
The course textbook is the superb "Vector Calculus, Linear Algebra, and Differential Forms" by John H. Hubbard and Barbara Burke Hubbard, which was developed for the honors course at Cornell University. A recent review in the American Mathematical Monthly said "It has a breadth and depth that is rarely seen in undergraduate texts, and it teaches real mathematics from a researcher's point of view instead of the standard off-the-shelf recipes that have little use outside the classroom. Its definitions and theorems are carefully formulated so that the essential content of the results is clearly manifested."
Professor Peter Webb is teaching this course during the current academic year. Professor Goldman says that several of the students in the course told him that it was their most challenging course, requiring a big time commitment, but it was a really fun course.
The third semester of the sequence is a topics course. In the fall of 2003 the subject was differential equations and dynamical systems, with Professor Rick Moeckel as the teacher. In addition to students from the first year of the sequence, the class included some of our more advanced honors mathematics majors. He used the classic text Differential Equations, Dynamical Systems, and Introduction to Chaos, by M. Hirsch and S. Smale, with R. Devaney co-authoring the 2nd edition. For most of the students, this was a first course in differential equations, whereas the book is really intended for a more advanced second course. But with such talented, hard working and highly motivated students, it was possible to get everyone up to speed quickly and to cover a lot of material, with emphasis on proofs.
Professor's Sperber and Webb have made similar comments about the high quality of the students.
THE MATH CLUB
The Math Club has entered its third year of meetings and activities. In addition to being a welcoming center for undergraduate students majoring in mathematics, it continues ongoing themes of mathematics and careers explorations.
The Math Club sponsors guest speakers and visitors who meet with students in an informal setting, over pizza, to discuss and answer questions about specific areas of research and career issues. During the past year, guests included faculty members from the School of Mathematics of the University of Minnesota as well as visitors. The 2002-03 list of visitors included Professors Jay Goldman, Markus Keel, Fadil Santosa, Peter Olver, Hans Othmer and Arnd Scheel, as well as Claudia Neuhauser from the Ecology Department.
Participants of the IMA (Institute for Mathematics and Its Applications) thematic year also visited the Math Club. Students got acquainted with research activities in Mathematical Optimization and its applications to problems in industry, such as design of airplane wings and transportation scheduling. Speakers from the IMA included Professors Collette Coullard (Northwestern University), John Dennis (Rice University), Lisa Miller (University of Minnesota), William Cooper (University of Minnesota) and Michael Powell (University of Cambridge).
During the spring semester of 2003, the Math Club sponsored two lunch gatherings in the School Lounge open to faculty, graduate and undergraduate students of mathematics. The lunch meetings provided undergraduate students with the opportunity to meet with faculty members and graduate students. The meetings also provided feedback to the organizers of the Math Club on activities of interest to math majors.
Currently the Math Club sponsors weekly meetings in the computer laboratory for students to become acquainted with MatLab, by working on special projects. The meetings take place every Tuesday at 2:30 pm in 314 Vincent; students are very much encouraged to join the MatLab group. If you are interested, please, come to the Undergraduate Lounge on Tuesday before 2:30 pm.
Participants in the current IMA special year on "Probability and Statistics in Complex Systems: Genomics, Networks, and Financial Engineering" are also scheduled to visit the Math Club.
A day of career and graduate school exploration in Mathematics is scheduled for Saturday, April 15.
The Math Club wants to reach out to all undergraduate math majors. Please contact the organizers with suggestions. Also, volunteers are very much needed and sought among faculty members, graduate and undergraduate students of Mathematics.
Carme Calderer, Professor of Mathematics
RESEARCH EXPERIENCES FOR UNDERGRADUATES
The department has offered REU's for three consecutive summers: 2000, 2001 and 2002. Due to the recent severe budgetary constraints there was no departmental REU program the past summer 2003, but Professors Ionut Ciocane-Fontanine and Victor Reiner supported REU's for several students from their NSF Grants: Reiner supported four students, one of whom was a high school student, and Ciocane-Fontanine supported two. By contrast, there were 16 undergraduate participants in 2000, and 18 in each of 2001 and 2002. There were seven faculty mentors in 2000 (S. Adams, A. Friedman, P. Garrett, L. Gray, R. Kuske, V.Reiner, J. Roberts), four faculty mentors in 2001 (S. Adams, P. Garrett, R. Kuske, V. Reiner), and five in 2002 (C. Calderer, P. Garrett, R. Kuske, V. Reiner, A. Voronov). Professor Avner Friedman coordinated the program in the year 2000, and Professor Paul Garrett did so the following two summers. Under their able leadership it has achieved national recognition as witnessed by the large roster of top universities that have sent participants. We should not fail to mention the former department Head, Professor Naresh Jain, without whose vision and faith in the validity of such a large scale endeavor the program could not have become a reality.
The Summer REU program is intended to introduce undergraduates to genuine research environments and to put them in close contact with research mathematicians. Working in teams or individually, students carry out their own projects, write reports on their findings, and make presentations, both within their own groups as well as to all participants. Some students have participated for more than one summer and many go on to pursue graduate study in mathematics, including in our department.
Typically, the students were in residence here for about 8 weeks and came from all around the U.S., both from top research universities as well as from small colleges. About a third of the participants were from Minnesota, both from the University as well as from local colleges.
The students mentored the past summer by Professor Reiner were U of M undergraduates Andrew Berget, Ramon Calderer and Jesse Plautz, as well a high school student, Adil Ali. After some preliminary study of graph theory and algebra, the group set to work on two projects in algebraic graph theory. Calderer and Plautz studied G-parking functions and their relation to the spanning tree number of a graph. They also gave a simple proof of a known relation between G-parking functions and the Tutte polynomial.
In the spirit of some of Reiner's previous REU's, Berget studied the critical group of a graph, which is an isomorphism invariant of the graph that comes in the form of a finite abelian group. In particular, he investigated the structure of the critical group of regular line graphs. This work was motivated by a result relating the spanning tree number of a regular graph and its line graph. His work is suggestive of a larger result, currently under investigation. A summary of the work of Professor Reiner's group is available online at http://www.math.umn.edu/~reiner/REU/REU.html.
Professor Ciocan-Fontanine mentored two students: Brian Jacobson and Derek Lee, both from U of M (in fact Brian had graduated in June and is now a graduate student at the U. of Michigan). They both studied the same problem: the "quantum Littlewood-Richardson Rule". This is a hard open problem with a rather elementary formulation, and lies at the intersection of Algebraic Geometry and Combinatorics, although the original motivation comes from string theory in Physics. It involves finding a positive combinatorial description of the number of rational curves on a Grassmannian. Brian and Derek explored the connections between two different ways of calculating these numbers (which involve signs and cancellations) and a recent conjectural rule involving counting of "puzzles". Although (as expected) they didn't solve the problem in general, one of them came up with a new proof of a known case - the quantum Pieri Rule - and he also wrote a nice (and fast!) computer program that generates the puzzles mentioned above. The program provided a lot of data, which will be a basis for future work on this problem.
We are grateful to Professors Ciocan-Fontanine and Reiner for continuing for another year what has almost become a tradition in our department, of providing deserving undergraduates with an experience that lets them feel what being a research mathematician is like, and we hope that in the near future our Summer REU program will be fully restored.
THE ACTUARIAL PROGRAM AT 21
The actuarial program was founded in 1983, and this is a good time to look back over the role it has played in the department. The total number of participant/graduates now stands at 440, so we are looking at a graduation average of just about 20 per year, or a participation average of about 40 at any moment of time. The actual number of graduations has been a fairly low-variance random variable, measuring 22,21,19,18,17,27 since 1998 , after starting slowly and peaking at 36 in 1993 . 56 % (247 of the 440) have been IT Math majors, and to put this in perspective, we have graduated 892 IT Math majors over the same 21-year period. This puts the proportion of actuarial students at 28% of our majors.
We have placed the "source" of each of our 440 into five categories: IT math majors, CLA math majors, Carlson School of Management (CSOM) majors, math graduate students, and "other". Historically, at 56% the IT math majors are the backbone, with CLA coming in at 19%, and CSOM at 11%. The source vector for 2003 was however (12,2,7,3,3), representative of the clear trends that CLA is slipping while CSOM is on the rise. As those who have followed my occasional reports in past newsletters will recall, in 1997 the CSOM introduced a so-called "Actuarial Science" major which has cost us (and IT) a certain number of students, while we continue to teach the actuarial courses taken by all program participants regardless of college.
We also track our students by success on Society of Actuaries (SoA) Examinations and with respect to employment, and have observed historical performances of 73% exam success and 58% employment. I always consider the conditional percentage "employed, given success on an exam" (79% = 58/73) not only more favorable, but genuinely more meaningful than the 58% ratio cited. There are at most a half dozen of the 440 who are in the classification of "working actuaries who have never passed an exam". It is safe to say that the IT students do better in exam success, but rather scary is the current employment count on the class of 2003: of 9 employed, 6 were from CSOM. Of course, there have always been cycles in both participation and employment, unfortunately rarely in phase. At the moment jobs are tight (note the blip in participation), and even the conditional employment rates are down (64% for 2002, 53% for 2003).
Recent stars of the program include: Matt Gray on the threshold of full Fellowship in the SoA after graduating from IT in 2001; Paul Tschida (full Fellow after graduating IT in 1999); Brandon Welte (graduated IT 2002 , Associate of the SoA) ; and Caixia Ge (MS 2001, Associate of the SoA). Paul is a distant relative of a famous American League umpire, and Matt is the son of a certain department member who bears the same last name.
Reporting: Steve Agard, Program Coordinator
PROFESSOR FRANK'S COURSE WEBSITE EARNS PRAISE
In the January 2002 issue of the Newsletter we surveyed the department's substantial effort in the area of teaching communication skills. We suggested at the time that, compared to the rest of the university, we would rank well in that respect. But we would not have imagined that our faculty would be complimented on their work by our colleagues at the University of Minnesota Center for Writing.
In fact, a recent letter from the Center to Professor David Frank states: "you have developed (and posted online) exemplary instructional materials that we have included in the Teaching with Writing section of our Web site.... Your materials are currently serving as valuable models to instructors on our campus.... Our goal is to choose models that enhance the role of writing activities in student learning and, at the same time, allow instructors and students to recognize ways in which writing tasks and expectations differ from discipline to discipline." The material referred to is the course website for Math 2374, IT Multivariable Calculus.
"I take credit for recognizing that my TA's had talent, for pointing them in the right direction, and then for getting out of their way," says Prof. Frank, who was course supervisor of Math 2374 from Fall 2001 through Fall 2003. "But the real credit goes to my TA's, especially Jonathan Rogness, James Swenson, Dan Drake, and Ryan Gantner. I maintained careful oversight of their work, making sure that what they did was consistent with the goals of the course. Naturally I was responsible for producing the syllabus and exams, and I always participate with my TA's in grading the exams, but they deserve the credit for developing the materials which are praised by the Center for Writing. It's gratifying to know that these TA's have already make significant contributions to undergraduate education and will continue to do so throughout their professional careers."
In the summer of 2003, Prof. Frank became Director of Undergraduate Studies. Although he was nominally the course supervisor of Math 2374 last Fall, in fact he turned over control of the course to Prof. Duane Nykamp (a new faculty member) and Jonathan Rogness. "Now the website is even better," Frank said. "They are continually improving the labs and Nykamp has added WebCT to the course. It's amazing how something supposedly under my control gets better when I put talented people in charge."
Writing a Senior Project paper is one of the ways for math majors to satisfy the writing requirement. All CLA math majors are required to do a Senior Project. A faculty member guides the student in the writing of the paper, which must be at least ten pages long. It is also required that the project demonstrate acquisition of new mathematical material. The goal is to provide a capstone experience in which the student combines mathematics that he or she already understands with some new mathematics or applications at a similar level. Extra one-on-one student-faculty contact is an added benefit of the senior projects.
Several faculty members have recently supervised a number of these projects. They are listed below with the project titles. Their dedication to guiding students through this intensive learning experience is very much appreciated.
Steve Agard: "Limiting Distributions of Finite Markov Chains", "Demystifying Calculus", "The Interpolation of Reserves Using Pseudopremiums", "Renewal Theory", "Topology: History and Principles", "Error-correcting Codes". John Baxter: "Self-Energy of Charges", "Bayesian analysis in game theory", "Mathematical Structure of Music", "The Central Limit Theorem". Carme Calderer:"Numerical simulations of ordering transitions in liquid crystals", "Differential equations and population models", "Multivariable optimization: sensitivity analysis". Max Jodeit: "The properties of the exponential function", "Mathematics and music". Karel Prikry: "On the completeness theorem". Joel Roberts: "Archimedes and pi (and some discussion of later results)", "Mathematics and perspective drawing", "Comparisons between Math 5335 and a recent high school geometry text", "High school math instruction: curriculum, expectations, and outcomes", "Alan Turing: code breaking and computable numbers", "Blaise Pascal: his mathematical work and later developments".
News About the Graduate Program
This year there were 22 new students: eleven from the U.S., five from P.R.C., two from India, one from Saint Lucia, one from Germany, one from France, and one from Russia.
In addition to the traditional orientation, the Director of Graduate Studies, Professor Paul Garrett, administered a six-hour "assessment/placement" exams to incoming students. These exams asked about basic abstract analysis, algebra, and topology, in addition to more concrete linear algebra and advanced calculus. The purpose of these exams was both to provide advice to new students and their advisors about the right level for their course work, as well as to gain insights into the relation between GRE (and other similar exams) scores and the actual knowledge that students have when they arrive here.
The Eugene Fabes Memorial Thesis Prizes
This year (February 2004) the recipients are:
Anton Leykin (Gennady Lyubeznik, advisor), "Algorithms in computational algebraic analysis". Anton is now a Research Assistant Professor in Mathematics at University of Illinois at Chicago.
Seick Kim (Mikhail Safonov, advisor), "On the regularity of solutions to second-order equations and systems". Seick is presently a Postdoctoral Fellow in Mathematics at University of Missouri.
They have both received a cash prize of five hundred dollars.
The thesis prize committee consisted of Professors Paul Garrett, Peter Webb, and Ofer Zeitouni.
Other students who earned their Ph.D.'s in 2003 were:
Feryal Alayont (Paul Garrett, advisor), "Meromorphic Continuation of Eisenstein Series", currently at the University of Arizona;
Ryan Berndt (Max Jodeit), "Singular Integrals with New Singularities", currently at Ohio State;
Grant Erdmann (Fadil Santosa, advisor), "A New Minimax Algorithm and
its Application to Optics Problems". currently research staff at Brooks
Air Force Base.
Alejandro Lopez (Gennady Lyubeznik, advisor), "Homological Algebra for Graded-commutative Rings", returned to Chile;
Gerardo Ortigoza (Fernando Reitich, advisor), "The Runge-Kutta Discontinuous Galerkin Method for Maxwell Equations";
Seung-Suk Seo (Vladimir Sverak, advisor), "Regularity theory for Landau-Lifschitz equations", returned to Korea;
Gabe Soto (Hans Othmer, advisor), "An integrated model for calcium dynamics during synaptic transmission", currently at the Center for BioDynamics, Boston University.
The following students have earned Master's Degrees in 2003:
Lin Fan (Steve Agard, advisor)
Jiseon Lee (Steve Agard, advisor)
Paul Macklin (John Lowengrub, advisor)
Junhyuck Park (Steve Agard, advisor)
Michael Weimerskirch (Harvey Keynes, advisor)
Departmental TA Awards for Teaching Excellence, June 2003
The department and our undergraduates are blessed with many dedicated and talented Teaching Assistants. This makes it always a difficult task for the departmental teaching evaluation committee to choose the small group for special distinction. In June 2003, the recipients of the departmental awards for Teaching Excellence were the following graduate students: Steven Firchow, Ryan Gantner, Min Gao, Nicolae Tarfulea, Nicoleta Tarfulea, Muge Taskin, Michael Weimerskirch, Todd Wittman, and Jinjun Xiao. We congratulate them all.
The Institute of Technology Student Board Best TA Awards, June 2003
Three of the department's Teaching Assistants have earned this recognition: Saleh Abudayeh, Todd Wittman, and Javier Zuniga. Our congratulations to all of them for this achievement.
John Bowers Excellence in Teaching Assistance Award, June 2003.
The recipient of this IT-wide Award was Todd Wittman.
The department Head at the time, Professor Naresh Jain, wrote to Todd as follows: "We in the School of Mathematics are very proud of you for this recognition. In fact, such individual honors for members of the School bring credit to the School as well."
In light of Todd's recognition for his excellent teaching we asked him about his approach to instruction. As a fifth year graduate student, Todd has had a lot of experience in combining the hard work of teaching math with the intense concentration of graduate study. For him, a key goal in teaching is motivation, giving students a reason to learn beyond just getting a good grade. He decided to follow his instincts in the classroom. Todd tells us, "Rather than doing homework-like problems in class to reinforce the material, I would work out more interesting problems and applications related to the material. I relied more on analogy than concrete math to prove theorems and illustrate ideas. Instead of giving quizzes, I would have quiz shows, like Jeopardy with calculus questions. Weather permitting, we would have class on the lawn outside." "Sometimes while doing a problem on the blackboard, I would intentionally make a mistake just to see how far into the problem I could go before one of the students would catch it. Whenever my wrist was sore from writing on the chalk board, I would force the students to put problems on the board. As the year went on, my recitation sections got progressively goofier. While preparing the students for an upcoming exam, one student suggested that I bring them cupcakes if the class mean was above a certain score. I said OK and set the bar higher than I thought they could attain. [They] actually did it. This became an ongoing bet through the year and I found myself constantly running to the grocery store to buy cookies and milk for 60 students." Todd concludes, "It seems strange, but putting in extra effort to make your workload fun will actually make the workload easier. Two of the greatest philosophers and social commentators of our time, Ben Cohen and Jerry Greenfield, once postulated: "If it's not fun, why do it?" It's tough to argue with them when they make such a fine Chocolate Chip Cookie Dough ice cream."
We congratulate Todd on his outstanding work with the students!
From undergraduates to full professors, the mathematics community is coming together in the Junior Colloquium. This is the second full year of existence for the Junior Colloquium, inaugurated in April 2002 with a talk by Ordway Visitor Mikhail Kapranov of the University of Toronto, entitled "Amoebas, power series, and hypergeometric functions." This seminar continues the work of the former ATaC seminar, offering a forum for graduate students, postdocs, faculty, and visitors to address the entire department on topics of general interest.
Attendees have enjoyed more excellent talks than it is possible to mention here. Memorably, Prof. Markus Keel studied the shape of a breaking wave and gave an intriguing introduction to nonlinear partial differential equations. Graduate student Leonard Blackburn (now of Knox College) familiarized his audience with transfinite ordinal numbers on the way to a spectacular number-theoretic result called Goodstein's Theorem. And IMA Visitor John Dennis, of Rice University, entertained his audience with stories and problems from his industrial experience in nonlinear optimization.
The initial faculty advisor for the Junior Colloquium, Prof. Victor Reiner, was instrumental in making the Junior Colloquium a valuable counterpart to the traditional Colloquium. Jon Rogness and James Swenson, who had served as organizers for the ATaC seminar, served as the initial student organizers. In fall 2003, John Hall replaced Jon Rogness as an organizer, and Prof. Richard McGehee took over Prof. Reiner's role as faculty advisor. As of spring 2004, James Swenson was replaced by Vasfiye Hande Tuzel.
This spring, the Junior Colloquium meets at 3:35 P.M. each Tuesday in Vincent 16, and is preceded by a tea in Vincent 120. The schedule is available online at a new location: http://www.math.umn.edu/jrcoll/ We invite you to join us at an upcoming talk!
James Swenson, Graduate Student
"The Mathematics of Change Ringing" was featured in an exhibit in the Mathematics Library during Fall 2003. A Junior Colloquium on the subject was given by Prof. Joan Hutchinson (Macalaster College), including demonstrations of this art of ringing permutations on bells. The text and links to more information are available at http://math.lib.umn.edu/changeringing.html ; web pages from selected previous exhibits are also available, such as "Mathematical Nonsense." In April 2003, the Mathematics Library and the School of Mathematics co-sponsored a colloquium on issues in mathematical scholarly communication; the featured speaker was Prof. Martin Groetschel (Technical University of Berlin), a member of the Committee on Electronic Information and Communication of the International Mathematical Union. The publishing landscape continues to transform itself, and the speakers encouraged their fellow mathematicians to support those publications whose practices benefit the mathematics community. This year the library again had to consider canceling journals--fortunately very few, as it turned out--since prices overall continue to increase faster than the budget. Nevertheless the library continues to expand access to electronic resources, such as the online Encyclopaedia of Mathematics (M. Hazewinkel, ed.) and recent volumes of Lecture Notes in Mathematics, which also became available electronically to those on campus. The library's print collection continues to grow as well: now more than 44,000 volumes. The books are newly reorganized under a single call number scheme (Library of Congress, completely replacing the Dewey Decimal call numbers). While this means people may have to go to an unfamiliar spot for their favorite text, the benefit is that books on a given topic are now gathered in one area.
Kristine Fowler, Mathematics Librarian
Mathematics Librarian e-mail:
University of Minnesota phone: (612)624-9395
310 Vincent Hall fax: (612)624-4302
206 Church St. S.E.
Minneapolis MN 55455
Early in the Fall semester, Fernando Reitich, Associate Director, and Fadil Santosa, Director, took stock of the center in order to evaluate its impacts and identify areas where it could improve. We were pleased to discover that MCIM continues to play an important role in the graduate education of the students in our department. We estimate that nearly one quarter of our graduate students have taken advantage of the Center's internship program. Over 30 MS thesis which are closely linked to the students' internship project have been completed. Indeed, several of the recent PhD thesis topics have their origin in industrial internships.
It can be said that not only our students benefit from the internship and industrial collaborations, our industry partners also attest to the value they have gotten in their interaction with the Center. Indeed, many of the companies we have worked continue to take our students for internships year after year.
The impact of the center can be measured also by the broadening of the mathematical experience our students are exposed to. Beyond the internships the Center and the IMA jointly sponsors the Industrial Problems Seminar. In this series, a speaker from industry makes a presentation about his or her research and explains how mathematics are used to answer important questions that arise. Many of these issues are in product development, while others arise in the service sector. Nearly all our speakers spend time discussing with students in an informal setting about job opportunities and careers in industry.
Research in the department has also been enriched by the Center's contacts with industry. The accompanying article by Bob Gulliver, Fadil Santosa, and Jing Wang, gives an account of a research project that was started during an internship, and eventually lead to the filing of a patent.
A report on the Center, which goes deeper into the activities and accomplishments of the Center, and includes candid testimonials from our former students and industry contacts, is available upon request. Please send email to firstname.lastname@example.org to ask for a copy.
OPHTHALMIC LENS DESIGN: SEEING BETTER THROUGH MATHEMATICS
By Robert Gulliver, Fadil Santosa and Jing Wang.
In the summer of 1999, two representatives from a company that makes ophthalmic lenses, made a cold-call to Fadil Santosa, and arrange to talk to him. Fadil was puzzled about why a local lens company that he has never heard of would want to talk to him. It turned out that the company was looking for help in their lens development program, and wisely realized that sophisticated mathematics was the key to their quest. Fadil subsequently found out that they had talked to engineering professors on campus who told them that they should talk to the mathematicians.
Nevertheless, the result of this initial conversation was to set up an internship for Jing Wang, then third year graduate student in Mathematics, for the following summer. At the end of summer of 2000, Jing came back and told Fadil about the project he worked on, and his interests in further developing his research experience into a thesis topic. After many hours of discussion, it was clear that the problem was basically that of surface design, and involves a lot of geometry. It was also clear that we needed to recruit a geometer, so they convinced Bob Gulliver to be coadvisor to Jing.
The design of progressive ophthalmic lenses, which are worn by many adults over 40 years old, call for creation of an optical element whose power vary smoothly over different portions of the lens. More negative correction is usually needed in the far distance-viewing zone, and less is required in the near distance-viewing zone. Geometric optics is an accurate theory for describing the light bending phenomena. But upon further simplification, the problem can be reduced to that of prescribing mean curvature, which is proportional to power. While there are many ways to achieve the desired power distribution, for the purpose of minimizing aberration, it is desirable to have small principal curvature difference. In a nutshell, we want to create a surface over the xy-plane such that
where P(x,y) is the prescribed progressive power distribution over the lens. The curvature difference is referred to as astigmatism, and is undesirable. If P is not constant, it is impossible to make zero everywhere. Thus, a compromise is necessary. The game is to balance how well the prescribed power is met with how small one can make the astigmatism in critical viewing areas. This "game" can be played by devising a cost function and optimizing it.
While this idea is not new, what is new in our approach is the idea to linearize the problem around a base surface and look for a perturbation. The resulting problem is a fourth order elliptic partial differential equation. We also devised an accurate and efficient numerical method to solve the problem. Jing defended his thesis in August 2001, and is now a postdoc at the IMA. The work we did resulted in two papers published in international applied mathematics journals.
|A screen shot from a lens design tool. Displayed on the left is the designed surface. Parameters of the lens are entered into the form on the right panel. A lens is produced almost instantaneously when the "Design the Lens" button is pushed.|
When we showed our results to our contacts in the lens industry, we were encouraged to market the method. We then got in touch with Jim Hildebrand at the University of Minnesota’s Patents and Technology Management Office about our method. Jim hired a lawyer and we started working with him in writing a patent application. This in itself was a very interesting and educational process for us.
Jim is now busy marketing the technology to several companies. We are hopeful that it will start paying rolayties. By the way, the income distribution is as follows. A third goes to the University, a third goes to the patent authors, and the remaining third is divided between the department and the IT Dean’s office. While it’s too early to know if we’ll ever make money off this patent, the experience has been truly exhilarating.
We have learned a lot through our interactions with companies in the effort to market our technology. More questions and problems arise that need further research. These are challenging and interesting problems on which we hope to continue to work. Who knows, the next pair of glasses you buy, may be designed by us!
The Institute for Mathematics and its Applications (IMA) is funded by the National Science Foundation and the University of Minnesota, and is closely associated with our department. Professors Douglas Arnold, Fadil Santosa, and Scot Adams serve as the institute's administrators: Arnold as Director, Santosa as Deputy Director, and Adams as Associate Director.
The 2003 - 04 annual program at the IMA is on "Probability and Statistics in Complex Systems: Genomics, Networks, and Financial Engineering." The program has three components: Mathematical & Statistical Problems in Genome Sciences (September-December 2003), Communication Networks (January - March 2004), and Quantitative Modeling in Finance and Econometrics (April-June 2004). For details about the annual program please consult the IMA website http://www.ima.umn.edu/
Every year several department faculty members, in addition to the IMA administrators, participate in the annual program. Currently these include Professors Greg Anderson, Maury Bramson, Naresh Jain, Richard McGehee, Arnd Scheel and Ofer Zeitouni. Several of these faculty members also serve as mentors of the IMA's postdoctoral researchers. Other current mentors include Professors Nicolai Krylov, Andrew Odlyzko and Victor Reiner as well as Professors Emeriti Don Aronson and Hans Weinberger. Professor Thomas G. Kurtz (University of Wisconsin, Madison) who is a Distinguished Ordway Visitor at the department, chairs the Organizing Committee of the 2003 - 04 annual program. Another member of the Organizing Committee, Professor Marco Avellaneda (Courant Institute, NYU) who is one of the world's leading experts in the area of financial mathematics, is a 1985 Ph.D. graduate of our department.
Summer 2003 saw the 20th anniversary of the founding of the IMA. The occasion was celebrated by a conference "The IMA at 20: Mathematics and its Impact", held June 6-7, 2003. The speakers at the conference included the following leading mathematicians who work in fields of mathematics and applications where the IMA has played a major role: Bjorn Engquist, Princeton U., Nancy Kopell, Boston U., Graeme Milton, U. of Utah, Andrew Odlyzko, U. of Minnesota, George Papanicolaou, Stanford U., Takis Souganidis, U. of Texas, Wim Sweldens, Bell Labs, Margaret Wright, Courant Institute, and Lai-Sang Young, Courant Institute. The talks were aimed at a broad mathematical audience. In addition, Charles Peskin, Courant Institute, delivered a lecture for the general public entitled "Secrets of the Heart Revealed--by Mathematics and Computer Simulation".
The IMA Public Lectures, co-sponsored with the IT Alumni Society, are an important part of the IMA outreach. During the 2003-04 academic year the Lectures include: Leroy Hood, After the Human Genome Project: Systems Biology and Predictive, Preventive and Personalized Medicine (September 15, 2003); Richard A. Tapia, Math at Top Speed: Breaking Myths in the Drag Racing Folklore (November 20, 2003); Steven H. Strogatz, Sync: The Emerging Science of Spontaneous Order (January 7, 2004); and Stephen Ross, Behavioral Finance - The Closed End Fund Puzzle (March 30, 2004).
The speakers at the IMA Public Lectures Series are world's leading experts in their areas and the lectures are always very informative as well as great entertainment, often including attractive videos, and engendering lively discussion. Large audiences at these presentations are drawn not just from the University community, but typically include a strong component of intellectually curious public, many of whom clearly consider these events high points of their intellectual and entertainment calendars. Tapia's lecture, for example, attracted a substantial audience of drag racing enthusiasts. Strogatz's engaging presentation, with its beautiful video of thousands of fireflies flashing in synchrony along a Malaysian river, as well as other interesting videos, likewise found a very receptive audience packing a large lecture hall, the semester break notwithstanding.
ITCEP's flagship program, known as UMTYMP (University of Minnesota Talented Youth Mathematics Program), now in its twenty-third year, has an enrollment of 512 students in grades 6-12 in the Twin Cities and Outreach (St. Cloud and Rochester) combined. Of these, 187 are calculus students, including 47 students taking Calculus III in the Twin Cities. In addition several others are taking Advanced Topics or doing IT honors course work. In the Twin Cities, the teachers include ITCEP Assistant Professors Peter Berman, Simon Morgan and Jennifer Wagner as well as ITCEP's director Professor Harvey Keynes. Assistant Professor Robert Hesse, a School of Mathematics Ph.D. graduate, continues teaching UMTYMP calculus at St. John's University, St. Cloud, and Adjunct Professor Tom Schwartzbauer is likewise continuing at the Rochester site.
Professor Harvey Keynes, continues to be the advisor for the six-year-old Master's Degree Program in Mathematics, emphasis in Mathematics Education. John Hall, one of its thirteen graduates, is currently completing his thesis as a mathematics PhD student. Michael Weimerskirch who graduated in 2003 is now also in the math PhD program. Leah Prom anticipates graduating from the masters program this spring, and Sara Van Asten and Eric Sinkula are enrolled as first-year students. Melissa Morgan, Justin Jacobs, and Carraig Hegi, Master's Program alumni, were instructional team members for ITCEP's 2003 Summer Enrichment Programs for pre-collegiate students.
Carraig Hegi and Simon Morgan are also on the instructional team for the 2003-04 Improving Teacher Quality (ITQ) project, which is funded by the MN Higher Education Services Office and implemented by ITCEP. The ITQ project is the second year of ITCEP's Mathematics Within initiative. This professional development initiative for grade 3-6 teachers aims to deepen teacher mathematics knowledge, to increase understanding of the connections among math topics, to explore how best practices in teaching literacy enhance student performance in math, and to build leadership capacity. To date, 57 elementary school teachers have benefited from participation in the initiative. In 2003, 31 practicing teachers, 7 teacher leaders and 24 classroom teachers participated, and in 2002, 26 classroom teachers were actively engaged.
In the third year of the Mathematics Within initiative, we intend to continue strengthening teachers' mathematics knowledge and leadership capacity as a means of effecting high quality math instruction for all students. The Anoka-Hennepin, St. Paul, White Bear Lake, and Forest Lake public school districts have again agreed to be partners in 2004-05. A new partner, the Higher Ground Academy, is an urban charter school where 90% of 437 students are low income and 99% are of African American heritage. With this partner we expect to gain new insights about effective approaches to math instruction for high-need students.
For second consecutive year, a former UMTYMP student was named a Rhodes Scholar. The new Rhodes Scholar is Allison Gilmore, who is now a math major at Washington University in St. Louis.
Note: We are grateful to ITCEP's Director Professor Harvey Keynes and Associate Director Dr. Andrea Olson for providing the information on which the preceding note is based.
The following interesting History Note was given to the editors by Professor James Thompson.
The 7th International Congress of Mathematicians was held at the University of Toronto on Aug. 11-16, 1924. This was the first time the meeting was held outside of Europe. The famous Belgian analyst Charles Jean de la Vallee Poussin was president of the International Mathematical Union at that time. This was his first visit to this continent, and he was awarded an honorary degree by the University of Toronto.
He remained in the USA after the meeting to lecture at many of the large universities, under the auspices of the Educational Foundation for Belgian Relief. He spoke at Chicago, Berkeley, UCLA, Caltech, Wisconsin, Minnesota, Michigan, Cornell, Columbia, MIT, Brown, Yale, and Princeton.
By studying the October 1924 issues of the Minnesota Daily, the following announcement was found.
Professor C. J. de la Vallee Poussin, of the University of Louvain, will lecture at the University of Minnesota on Tuesday, October 14, and Wednesday October 15, at 4:30 p. m., in Folwell 101. The titles of the lectures, which will be delivered in French, are "L'approximation des fonctions de variables reelles" and "Les fonctions d'ensemble et les fonctionnelles." Professor de la Vallee Poussin is the most distinguished of Belgian mathematicians, and one of the most distinguished mathematicians of Europe. All members of the University are invited. Guy Stanton Ford, Dean
The speaker was introduced by Professor Dunham Jackson (1888-1946), who was well-known in the field of approximation theory. Jackson was a professor at Minnesota from 1919 to 1946. Translations were given by Professor Anthony L. Underhill, member of the Minnesota math department for many years. Professor Underhill had translated Hadamard's book on Partial Differential Equations from French to English.
Undoubtedly, the reputation of Dunham Jackson was the reason for scheduling the talk at Minnesota. Jackson was a member of the National Academy of Sciences, and was the advisor of 18 Ph.D. students at Minnesota. For more information, see the interesting memorial article about Professor Jackson in the AMS Bulletin of September 1946 (p.847-860).
The Math Newsletter is published annually for the members, alumni and friends of the School of Mathematics.
Editorial Board: Rhonda Dragan, Karel Prikry, Jackie Shen, Peter Webb
School of Mathematics
|Institute for Mathematics and its Applications (IMA)
Douglas Arnold, Director
Fadil Santosa, Deputy Director
Scot Adams, Associate Director
400 Lind Hall, 207 Church Street S.E.
Minneapolis, MN 55455-0463
telephone: (612) 624-6066
fax: (612) 626-7370
Minnesota Center for Industrial Mathematics (MCIM)
IT Center for Educational Programs (ITCEP)