LEHIGH MATH NEWS NOTE FROM THE CHAIRMAN Welcome to the first issue of the newsletter of the Mathematics Department of Lehigh University. Its main purpose is to let our alumni know what is going on in the department, and to provide a forum for you to keep in touch with us and each other. This first issue is being mailed to all alumni, but I would ask that if you wish to receive subsequent issues, please let me know by mail or e-mail. We would also appreciate news of what you have been doing, which we will incorporate into future newsletters. I am in my second year as chairman, succeeding Drew Snyder, who served for six years. Some of the major thrusts of my chairmanship have been to improve our relationship with our client disciplines, and to promote interaction between our students and our alumni, as evidenced by this newsletter and the Career Night described below. Essential to my transition into the chairmanship has been the department coordinator, Judy Arroyo. Judy, who has been in the math department since 1967, knows all the Lehigh people and procedures, and her insights are invariably on target. The Math Department has a home page on the World Wide Web at http://www.lehigh.edu/~incmd/incmd.html. You can read updated accounts of our activities there. Please feel free to contact me at dmd1@lehigh.edu, (610) 758-3756, or by mail at the Math Department, Bethlehem, PA 18015. Don Davis CAREER NIGHT Our first Career Night for math majors and alumni will be held Thursday, February 29, 1996, from 5:30 to 8:30. We promise that future career events will be held more frequently than reoccurrences of the date, February 29. We have chosen a panel of seven alumni to talk about their careers and offer advice. If you would like to serve on such a panel in a future career event, please let me know. The alumni who have agreed to participate in this first career night are Diane Duda, '80, CIGNA Insurance; Matt Fante, '93, MS '95; John Francisco, '82, AT\&T; Richard Gibbs, '68, TIAA-CREF; Gerry Grube, '67, AT\&T; Bruce Knoll, '73, Fuller Co.; Bill Mirth, '77, WorldPartners Co. FACULTY CHANGES During the past five years we have lost three faculty and gained two replacements. This is in line with the downsizing of the university, which offered an early retirement package in 1993, and did not fill many of the vacated positions. The three retirements were Tommy Wilansky, Dominic Edelen, and Ed Assmus. Ed still maintains an active presence in the department, as he is an editor of two journals and still active in research. Tommy still lives in Bethlehem and drops by the department occasionally. Dominic has moved to Galveston, Texas, and is Adjunct Professor at Texas A&M. We have two Assistant Professors. Terry Napier is in his fourth year here. His degrees are from Notre Dame and Chicago, and he works in complex analysis and geometry. Garth Isaak is in his third year here. His degrees are from Bethel College (same as Samir Khabbaz) and Rutgers, and he works in combinatorics and graph theory. OTHER RETIRED FACULTY Three faculty who have been retired for many years are still very active in the department. Everett Pitcher is still intent on proving the Poincare Conjecture, probably the most famous open question in topology. Some days it seems that he has proved it, while other days it doesn't seem quite so clear. C.C. Hsiung is still a principal editor of the Journal of Differential Geometry, which is still published at Lehigh. This journal is one of the most prestigious journals in the world, having published many of the revolutionary papers in 4-dimensional topology during the past 14 years. World Publishing recently published C.C.'s book "Almost complex and complex structures." In this book, C.C. provides a detailed argument which seems to establish that there are no complex structures on the 6-sphere, which has been a famous unsolved question in geometry. Because of the delicate techniques involved, C.C.'s proof has not yet received universal acceptance. Ted Hailperin has been heading the mathematics effort in the Learning Center since his retirement in 1980. This is his last year in that position, and we thank him for his efforts. Ted's book "Boole's Logic and Probability" is in its second edition, while a new book, "Sequential Probability Logic," will be published by Lehigh University Press this year. Last summer Ted gave a major invited address in Ireland on "Boole and Probability." C.C. HSIUNG FUND Monies accrued by the Journal of Differential Geometry have formed a fund from which the Math Department has benefited. This fund is known as the C.C. Hsiung Fund for the Advancement of Mathematics. The fund has sponsored an annual conference in geometry and topology since 1986, which brings about 80 visitors, including six distinguished invited speakers, to the campus almost every spring. Every third year the conference is held at Harvard, home of C.C.'s co- editor S.-T. Yau. On May 3 to 5, 1996, the conference will be held at Harvard, and will honor C.C. Hsiung's 80th birthday. The Hsiung Fund has also supported visiting faculty. During this academic year, Jim Coykendall is the C.C. Hsiung Visiting Assistant Professor. Jim just received his PhD from Cornell. He is working with Cliff Queen in number theory. UNDERGRADUATE AWARDS In 1995, cash awards were given to two graduating seniors. Mary Ann Olenick was named the first winner of the C.C. Hsiung Undergraduate Award for outstanding scholarship by a senior mathematics major. Mary is now working as an actuary at Guardian Insurance in Bethlehem. Alison Shields won the Thornburg Award for outstanding performance in advanced mathematics courses. Alison is now employed at Merrill Lynch in New York City, where she is learning about derivatives (not the ones she studied in calculus). COMPUTERS In 1992, a computer laboratory consisting of 21 IBM RISC 6000 work stations was installed in Christmas-Saucon room B1. These machines are used by our graduate students and undergraduates. We incorporate assignments involving the computer algebra system Maple in our Math 21-23 Calculus courses. Students working on these assignments keep Room B1 very busy in the evening. Regular meetings of our Applied Statistics course are held in the lab. We are in the process of installing a Local Area Network in Christmas-Saucon to link many of the faculty offices to a file server and printer located in the department office. This will also allow faculty to access the World Wide Web from their offices. The university has upgraded the 1984 vintage computers in most, but not all, of our offices. Professor Bruce Dodson and Matt Fante (BS '93, MS '95) have been actively involved in widely publicized work in factoring large numbers. The difficulty of factoring large numbers forms the underpinning of the RSA system of cryptography. The RSA Corporation offers cash awards to people who are able to factor certain challenge numbers, which usually have more than 100 digits. These are group efforts involving many computers and sophisticated mathematics. Dodson and Fante won significant cash awards for their work, and Dodson donated his award to the department for purchase of a computer. PhD STUDENTS Our department continues to grant 3 or 4 PhD's per year, on average. Despite a tight job market for academic mathematicians, our recent PhD's have all found college or university teaching positions. The six PhD recipients in 1994 and 1995 are listed with their positions and advisors: * Matt Haines, Spring Hill College (Alabama), Dodson; * Bob Stolz, Lafayette, Dobric; * Cathy Liebars, Trenton State University, Dobric; * Margaret Dodson, Kutztown University, Stengle; * Huajian Yang, McMaster University (Ontario), Davis; * Maureen Carroll, University of Scranton, Snyder. Jeannette Janssen, a 1993 PhD student of Ed Assmus, wrote a celebrated thesis on Latin squares. Her work was featured in several major periodicals such as "Science." She had many job offers, and chose to go to Concordia University in Montreal. For those of you who are members of the Math Association of America, be on the lookout for an article by Professor Bennett Eisenberg and his PhD student Rosemary Sullivan in the April American Math Monthly. It is titled "Random Triangles in n dimensions" and deals with the old question "What is the probability that a random triangle is obtuse." It should be of general interest. We are doing two new things to help our PhD students in the job market. One is to give them an opportunity to teach a lecture section of a calculus course for a semester, once they have established that they are excellent teachers. The other is to institute a new course called "Professional Seminar," which deals with teaching methods and other aspects of being a professor. EVERETT PITCHER LECTURE SERIES Each year since 1982, the department has held a series of three expository lectures by a mathematician of international repute. For example, Michael Atiyah, Jean Pierre Serre, and John Milnor have been speakers in this series. The money to establish the lecture series initially was a gift of Terry Pitcher. The talks, which attract visitors from a broad area, are accompanied by several social events. The next Pitcher Lectures will be given by Carl Pomerance on April 30, May 1, and May 2, 1996, on the topic "Primes: a Computational Perspective." Pomerance, from the University of Georgia, has done some of the most important research on the number theory related to factoring large numbers. Tentative titles and descriptions of his talks are as follows. (1) Witnesses for Composite Numbers. This describes some "easy" ways to tell primes and composites apart. (2) Factoring: a Tale of Two Sieves. This describes and compares two factoring algorithms, the quadratic sieve and the number field sieve. (3) Thresholds for Random Integers. This describes some theoretical probability problems suggested by the algorithms in the second lecture. HIGH SCHOOL CONTEST Each March since 1981, our department has conducted a high school math contest, attracting over 200 students from about 25 high schools within a 60 mile radius of Bethlehem. 1996 will be the fourth year that prize money has been provided by AT&T, with $250, $175, $100, $50, and $25 for the top five finishers. 1996 will also be the fourth year that Don Davis has selected a team of 15 top finishers in the Lehigh contest to participate as the Lehigh Valley team in the American Regions Math League, a national math contest. In 1995 the Davis- coached team finished 14th out of 90 teams, and was named Most Improved Team. Johanna Miller, now a scholarship freshman at Duke after graduating from Southern Lehigh High School, was the mainstay of the team all three years, and also the all-time top performer in the Lehigh contest, winning the contest twice and finishing second the other two years. This year the contest will be held on Saturday, March 2. If you know of someone who might be interested in participating, contact Don Davis. ALUMNI NEWS Letters were sent in September 1995 to people who have received a Bachelor's degree from Lehigh's math department, asking for information about what they have been doing and how their Lehigh mathematics education has affected their career. We received 37 responses. We include 25 of those responses here, in abbreviated form. The other responses, together with the many more which we hope to receive in the coming months, will be included in the next issue of this newsletter. Francis Carner, BA '38, MA '39 "I did get a BA in 1938 and an MA in 1939 in what I would designate as being a major in math and a minor in physical sciences. In 1939 I got a job in the Mutual Life Insurance of NYC. In 1941, I moved on to the Airplane Division of Curtiss Wright Co. in Buffalo, NY, who trained me and employed me until 1945 as a structures engineer specializing in flutter and vibration analysis. "Until my retirement in 1982 I had jobs with about 6 other corporations (mostly large) based mostly on my war-time employment but as far as possible from 'defense efforts' but still based on math and physical science training. Often I was the traveling expert on special machines over most of the western world. I liked it very much." Henry Seebald, BA '46, MS '49 Immediately upon graduation, "I reported for active duty as a second lieutenant in the US Army. I spent the next 46 months as an Infantry Officer in the States and the Southwest Pacific." After the war and a few months as a Claims Investigator for the Travelers Insurance Co., he "accepted a job offer from Professor Reynolds of the Math Dept of Lehigh University to teach Freshman and Sophomore math courses." He later held the following positions: 1951 Programmer analyst with the Univac Division of Sperry Rand. 1959 Programmer with the Systems Development Corp. 1963 Manager of the Computer Dept of Isotopes, Inc. 1970 Programmer Analyst with the Beneficial Corp. 1983 Retired Ken Coghlan, '48 Owner and principal: Corson Associates. Extensive experience in research and development of communication, navigation and electronics systems for marine and aviation applications. For example, submarine navigation, antisubmarine defensive systems, sonar, radio navigation, marine sensors. "A major advantage derived from my math education has been the ability to analyze and solve difficult technical problems in the areas of navigation and communication systems." Brian Bauknight, '61 This is one graduate from the department of mathematics at Lehigh University who has gone off in a totally unrelated vocation. I am currently the senior minister of a 3000 member congregation in the South Hills of Pittsburgh--- recently beginning my 16th year here. "In actual truth, the only mathematical image that I have used in my ministry is one that I have used for over 25 years. I have found that the image of the ellipse gives a nearly perfect conveyance of my understanding of the church in the United Methodist tradition. More people have been educated in the theology of an ellipse than you can possibly imagine!" Clif Lando, '62 "I went on to Rutgers immediately following graduation in 1962, receiving my MS in 1964 and PhD (both in mathematics) in 1969. My wife and I then came to the University of Alaska Fairbanks, flagship campus of the University of Alaska system, and the home of the only mathematics graduate programs in the state. We came up here in 1969, thinking it would be fun to try out Alaska for a year or two and then maybe go to Australia. We haven't made it to Australia yet. "Currently I'm head of the Department of Mathematical Sciences here --- a department of 23 full-time faculty which includes Computer Science and Statistics as well as Mathematics. "I have fond memories of Lehigh in the days of Wilansky and Pitcher." Charles Katholi, '63 "After I finished Lehigh in 1963, I entered graduate school at Adelphi University in Garden City, NY. I completed a MS in mathematics in 1965 and the PhD in 1971. I did my dissertation in 'classical mechanics', specifically in Elasticity Theory. After completing my degree, I was offered a position at the University of Alabama at Birmingham in the applied mathematics field of Biomathematics. I have been at UAB ever since. "Professionally, I have expanded my interests significantly over the years. I enrolled in statistics courses as a regular graduate student and completed 30 hours of training in probability and statistics. I have been a practicing statistician as well as mathematician ever since. More recently, I expanded my knowledge in computer science, particularly in the area of Computer Architecture and currently hold academic appointments in the Departments of Biostatistics, Mathematics and Computer and Information Sciences. My current teaching efforts are in the areas of Numerical Analysis, Computational Linear Algebra, Elementary Statistics and Computer Architecture. I am also actively involved in collaborative medical research as well as in my own research area of Computationally Intensive Statistical Methods. "The effects of my Lehigh mathematics education on my career can be summarized simply by saying that it made it all possible. When I entered graduate school, I was far ahead of my fellow students academically. My senior year at Lehigh was comparable to my first year of graduate study. For mathematics majors today, I can strongly recommend the consideration of a career in Statistics." Rob Gibby, '64 "For 3 years I taught math at Episcopal Academy in Philadelphia until my first child was born. Since that time I have been in the specialty steel business. For the past 23 years I have been associated with Lindquist Steels." Joe Alber, '65 "I am a professor of Business Computer Systems at Bradley University. After graduating from Lehigh, I went to the University of Pittsburgh for an MBA, and after spending six years in the Air Force, NASA, and two civilian jobs, I attended Penn State where I got a PhD in Operations Management (1977). "While at Bradley I have had a couple of jobs in administration in addition to my teaching assignments. My research interests lie in emerging technologies and I have three books and some articles on that and other subjects." Dale Landis, BS '66, PhD '73 "I have been employed at Draper Laboratory (Mass.) for 15 years, and am now a Principal Member of Technical Staff. Before that I was with The Analytic Sciences Corporation. The field I am in is navigation systems... Much of my work has been analytical; this analysis involves mathematical modeling of errors (in instruments, geophysical disturbances, algorithms, etc.), and a prediction of their effect on system accuracy. On other projects I have contributed to the algorithm design and real time software which is used in navigation systems ... All this relies very heavily on mathematics that I learned at Lehigh, particularly on studies in stochastic processes and linear systems. "What I think should be stressed is the way in which a mathematical education-- even with a 'pure' mathematical emphasis--has given me some advantage over many engineers in the same role. This is seen mainly in the cases where the 'recipe' solutions need to be reexamined for their assumptions, and one has to go back to first principles for correct solutions. Mathematicians are somewhat quicker to do this, and it may make the difference between a correct or incorrect result. "In my undergraduate years, Lehigh education had a strong emphasis on English and distributions. My writing and speaking skills have been one of the most important assets in my work. Further, I believe that people with balanced educations (a balance between science and humanities) have a real advantage in work. I hope that Lehigh can keep this kind of liberal education perspective in the face of economic pressure of the times." Steve Simpson, BA '66, MS '66 "After Lehigh, I went on to get a PhD in math at MIT in 1971. I'm now a math professor at Penn State. I've been at Penn State since 1975. My research field is mathematical logic and foundations of mathematics. My research is supported by the NSF. My first mentor in mathematics was Tommy Wilansky and others at Lehigh were Everett Pitcher, Gerry Rayna, Sam Gulden, Bhaskar Ghosh, Jerry King, and Bill Fleischmann. I've been back to Xmas-Saucon a couple of times to visit old friends and give talks." Gerry Grube, '67 "Following my BA at Lehigh, I received an MS from Purdue and a PhD from Courant Institute of NYU (both in Applied Mathematics). My work at AT&T has progressed from algorithmic development to analysis, system engineering, processing system architectures, strategic planning, and business development." Richard Gibbs, '68 is the Executive Vice President for the Finance and Planning area of TIAA-CREF. He is responsible for corporate financial reporting and rating agency relationships, accounting, corporate actuarial, treasury, corporate tax, and the financial planning and budgeting functions. He writes "I wanted to get into the business world and use my mathematical knowledge to solve practical business problems. As it turned out, pursuing a career as an actuary was a perfect fit. I took all of the actuarial exams, and actually passed the first two exams while I was at Lehigh. I then went on to the University of Michigan and received an MA in mathematics in their actuarial program. I passed all of the actuarial exams and became a Fellow of the Society of Actuaries in 1973. "A mathematics major combined with a solid foundation in business and finance courses is an excellent springboard for a career as an actuary. The first actuary of the Social Security Administration, Robert Meyers, is a Lehigh graduate. You will find actuaries in many senior management positions in life insurance companies." Jim Mihalakis, '69 "I was a 1969 Lehigh graduate in Mathematics. Late in my Lehigh years I became interested in computer science and programming. Since a computer science program did not then exist at Lehigh, I graduated with a math degree. I then attended the University of Michigan for a Master's degree and again got a degree in Mathematics, but with heavy emphasis in Computer Science. I have pursued system analysis and computer programming in my career. I worked for Bell Labs and now for Bellcore." John Skvoretz, '69 He sends a program of his address "A Structural Theory of Commitment," which he delivered in February 1995 as the recipient of the 1994 Educational Foundation Award in the Humanities and Social Sciences at University of South Carolina, where he is Carolina Distinguished Professor of Sociology. He was a National Science Foundation Graduate Fellow at the University of Pittsburgh where he earned a PhD in Sociology in 1976. He joined the faculty of the Department of Sociology at the University of South Carolina in 1975. He chaired the department from 1984 to 1994. Professor Skvoretz has published nearly 50 research articles, book chapters and papers. He contributes to several areas in sociology: stratification and mobility, social network theory, group processes, power in exchange networks and the structure of social action systems. His contributions are characterized by the innovative use of mathematics to formulate theory and analyze data. He adds a note which says "As you can see, my training in mathematics has had an overwhelming impact on my career!" Robert Kendig, '71 "After leaving Lehigh, I went to graduate school at Penn State in the Department of Engineering Science and Mechanics. My PhD thesis focused on a solution of the wave equation. I found a closed-form solution to a problem describing acoustic diffraction by an impedance covered half-plane. I later was able to apply my research to a study of selected highway noise barrier parameters. Results of this noise barrier study helped the Federal Highway Administration plan and subsequently construct highway noise barriers next to some highways passing through environmentally sensitive residential communities. "I continue to pursue my interests in mathematics through my daily work as a senior engineer in acoustics and dynamics at the Westinghouse Science and Technology Center. I applied many aspects of Fourier Analysis to develop advanced signal processing algorithms for the purposes of machinery diagnostics. I have attempted to use mathematical tools to extract information from sound and vibration signals emitted by critical electromechanical machines and devices. An application of the Hilbert Transform has formed the basis for a patent to evaluate acoustic fatigue caused by random vibrations. "I am now examining superconducting energy storage systems. I must routinely apply multiple aspects of my mathematical training ranging from linear algebra, solid geometry, differential equations, complex variables, etc. Bruce Knoll, '73 "When I graduated from Lehigh in 73, I went to work for the Dept of Defense as a mathematician. I completed my masters in computer science in 1978 and after 5 years at the DoD, I returned to the Lehigh Valley to work for Fuller Co. I have been with Fuller for the last 17 years. My present position is manager, CAD/CAM." Gene Connell, '75 "I currently serve as the Chief Actuary for the Erie Insurance Group, responsible for the company's property/casualty products. I have been in the insurance industry since graduating from Lehigh in 1975. "As Chief Actuary, most of my responsibilities are managerial. I have a staff of 45. However, I am still called on for quantitative analysis of business decisions, usually in some crisis. I have been designated by the Board of Directors as their 'appointed actuary' and have to attest personally to the accuracy of the liabilities in our financial statements. At the present time, these liabilities amount to nearly $2 billion---a considerable responsibility. I assure you I still take a hands-on approach to the mathematics involved in these calculations." Sanjoy Banerjee, '76 "I received my BA in Mathematics and International Relations from Lehigh in 1976. Then I got a PhD from Yale in Political Science. I taught in Political Science at Baruch CUNY, and since 1987 I've been in the International Relations Department at San Francisco State University, where I am an Associate Professor. "My research has focused on artificial intelligence modelling in international relations. I have used logic programming to write programs simulating aspects of the Early Cold War. My articles using logic programming have been published in prestigious journals in International Relations. Obviously, I could do this because of my mathematics education. Another benefit has been that I can talk to people in a wide variety of disciplines and follow what they are saying. Let me say that when I got to Yale, I did not feel any less prepared than Ivy League graduates there." Tim Spellman, '77 "Since Lehigh I have had a wonderfully successful career in software engineering, progressing steadily from programmer to senior architect. By successful I mean that I am getting paid a lot of money to play with hot boxes all day long. "I spent my first few years in hospital information systems at Medical Information Technology in Cambridge, MA. I then joined National Computer Systems, also in Cambridge, working on several of their banking applications. I just joined IntraNet in Newton, MA, and will be working on their Automated Clearinghouse product. "By far the most relevant Mathematics courses were the ones in Algebra. Having the mathematical vocabulary to talk about relational algebra has given me a fundamental understanding of modern databases that not all programmers have.'' Bill Mirth, BA '77, MS '79 "I currently hold the title of Information Management Consultant within AT&T as an Officer of the WorldPartners Company. In this capacity I have had the opportunity to take a leading role in starting up a new global telecommunications partnership, including negotiating technical design and business policy agreements with our international partners as well as forming and staffing a new corporate work center with employees representing Asian, American, and European cultures. "I have always believed that my undergraduate and graduate level mathematics degrees, while not directly applicable to my career, have equipped me with the underlying discipline and analytical thought processes needed to develop coherent, structured business and technical arguments. This has proved particularly useful when analyzing and responding to the positions and arguments put forward in an international business negotiation." Diane Duda, '80 "I graduated from Lehigh in 1980 with a BA in Mathematics and a Fundamentals of Business minor. I was employed as an actuary right after graduation, after passing two actuarial exams while at Lehigh. I received my Fellowship in the Casualty Actuarial Society in 1985 and I remain employed in the insurance industry---I currently hold a position at CIGNA Property and Casualty Insurance Companies as the Division Financial Officer for the Specialty Insurance Services division of CIGNA P&C. "Typical of many women today, I am managing the responsibilities of both a successful and rewarding career and a young family---my children are ages three and one ... I must add that for any students interested in functioning in the business world, strong communications skills are also a must, which is often not a focus of students drawn to mathematics as an area of emphasis. I usually counsel students who are interested in applying their mathematics skills in a business arena to seek out a course in business communications while they are in college." John Francisco, '82, MS His resume shows an MS in Computer Science from Lehigh in 1986, and Member of Technical Staff at AT&T in Middletown, NJ, from 1986 to the present. One of many projects on which he has been involved there is a system-to-system interface for the Testing Operations Provisioning Administration System, allowing the migration of its user interface to graphical workstations. He desires a software development position where his experience with graphical user and system-to-system interfaces can be utilized using the object oriented paradigm. Charles Coronella, '86 "I graduated in 1986 from Lehigh with a BS in Chemical Engineering and a BA in Mathematics through the five-year Arts/Engineering program. Subsequently, I attended graduate school at the University of Utah where I earned a PhD in chemical engineering. Currently I am an assistant professor of chemical engineering at the University of Nevada, Reno. "Although my emphasis is engineering rather than mathematics, I am certain that my mathematics degree has given me some distinct advantages. First, in applying for tenure-track positions in chemical engineering, I believe that the BA in mathematics gave my application a degree of respect that would not have been accorded to an application with engineering degrees only. The classes that I believe were of greatest benefit were real and complex analysis, instead of applied classes. I picked up numerical techniques in graduate school, but the ability to 'analyze' a problem can be directly related to analysis." Paul Doody, '87 "After Lehigh, I returned to Switzerland and worked for an electronics firm called Kemet. I then decided to continue my studies and got an MBA from the Fuqua school at Duke University. Again, I returned to Switzerland and after a brief stint in banking I took my current job with Reuters as an account manager in Geneva. I sell financial information as well as systems." Mary Jo Lewis, '88 "For the last two years, I have been working at the National Board of Medical Examiners, the organization responsible for licensing US physicians, and certifying and recertifying various specialists in medicine and health-related fields. Specifically, I am a psychometric technician, involved in the certification and recertification of physician specialists and various other health care providers. Much of what I do during the course of a routine day involves the use of statistics. "I have also had the opportunity to participate in some research projects and present my findings at educational research conferences while here at NBME. Specifically, I am currently working on research regarding computer adaptive administration of certification examinations."