UofL Math
March 2001

Department of Mathematics
College of Arts and Sciences
University of Louisville

  Table of Contents:
Chair's Corner
Puzzle Page
Bullitt Lecture Announcement
A Ph.D. program in Industrial and Applied Mathematics at UofL?
Women in Mathematics Club
The Biostatistics-Decision Science Program at UofL
Faculty Activities
MBTI Teaching And Learning Style Differences - Should We Consider Them?

Chair’s Corner
Dr. Inessa Levi

Excellence in professional activity and teaching are the prime institutional goals of the University of Louisville. Getting a Ph.D. program in Mathematics has been one of the goals of the Department and College for the last 25 years. This year we revised and submitted a Ph.D. proposal in Applied and Industrial Mathematics. In the course of conducting the Needs Assessment for the proposed doctoral program we visited and interviewed a number of local companies and found overwhelming interest and support for our proposed program. In the process of conducting the interviews, we also secured internship possibilities for our students. We interviewed program directors and department chairs at the University to build interest in our proposed program and possibilities of joint degrees offerings (e.g. Master’s degree in public health and a Ph.D. in mathematics). We secured support from the Medical School, Engineering School, Logistics and Distribution Institute, and other Departments in the College of Arts and Sciences. This proposal has already been approved by the Graduate Council of the University of Louisville. We are hopeful that the final approval from the Council on Post-Secondary Education will be given sometime during this academic year.

Very recently the Mathematics Department approved a new option in our MA degree, where the students may complete the degree requirements by taking course work and by completing and reporting on an industrial internship. This option is designed to accommodate the ever increasing need for highly educated individuals with graduate degrees in Mathematics who are prepared to work in industry.

As the Mathematics Department is concerned with excellence in teaching we organized a workshop on different learning styles as assessed by Myers-Briggs Test. We met frequently with teachers from local high schools, engaging in an on-going dialog about how to make the process of education work.

As always the Mathematics Department promotes professional excellence. A number of invited speakers gave presentations at the Department Colloquia. The Department and the University are helping to support a mini-conference in Real Analysis that will attract prominent researchers in this important area of mathematics. Our Bullitt Lecture is scheduled for April 5th 2001 at 7:00 p.m. The Department expresses its gratitude to the Bullitt family for their extremely generous donations over the years that allow the initiation and continuation of the Bullitt Lecture Series.

Our special thanks go to Mr. Lowry Watkins, Jr., for his extremely generous donation to establish the William Marshall Bullitt Mathematics Fellowship and Astronomy Scholarship Fund in the College of Arts and Sciences.

To support student retention and involvement, this year the Mathematics Department organized and secured financial support for a new student organization, Women in Mathematics Club. One goal for this club is to recruit middle and high school students into our program.

The Department supports and fosters excellence in student performance by recognizing student achievement by awarding the Robert J. Bickel and Petty Scholarships. We are very grateful for the generous donations that help us attract and reward good and hardworking students, striving for excellence in their education.


Editor’s Note - Dean Brennan appointed Dr. Inessa Levi acting Chair for AY 2000-01. The Department will have a new Chair starting Summer 2001.

Puzzle Page
Dr. Jeno Lehel

New Puzzle - Worm in the Apple

A worm eats itself into a spherical apple of radius 2.4 inches and gets out of it leaving a trace of 4.75 inches long. Assuming that the trace is widthless, can you always cut the apple into two hemispheres such that one of them is intact?

Old Puzzle: Batting Average

Batter A has a higher batting average than batter B for every single day of the season. Does it follow that batter A has a better batting average than B for the whole season?

First solution by Robert N. White (BA ’53)

The answer is that A’s batting average for the whole season could be more, the same or even less that B’s batting average. To see the last case, assume A’s batting average for the opening day was .400, and B played in the same game with a batting average of .350. In all other games A batted less well and ended with a season average of only .290. Batter B didn’t play in any more games and so ended with a season average of .350, which is higher than A’s season average.

Second solution by Jerry Claypool (BS ’93)

Consider the following artificial scenario. On the first and second game batter A goes 1 of 5 and 1 of 2, respectively, and batter B goes 0 of 1 and 2 of 5, respectively. If the same averages repeat for odd and even games during the whole season, then A has a higher batting average than batter B on each individual day (because 1/5> 0 and 1/2> 2/5). However, for the whole season A has an average of 2/7 lower than that of B which is equal to 2/6.

Also solved by Mike Markwell (Math 351 student in Dr. Williams’ Spring 2000 class), Dow Marvin (BA ’97), Jim Twohey (MA ’95), and John E. Ward (MA ’95).

Mail or e-mail your solution to: Dr. Jeno Lehel lehel@louisville.eduMath Dept, Louisville, KY 40292.


Bullitt Lecture – 2001

Professor Douglas Hofstadter
Indiana University

Thursday, April 5, 2001
7:00 P.M.
Comstock Auditorium
School of Music
University of Louisville

"Unexpected Puns Lurking in the
Heart of Mathematics"


A Ph.D. program in Industrial and Applied Mathematics at UofL?
By Robert McFadden

The Department’s long-sought goal of a doctoral program may be achieved this year. Since the decade of the eighties the faculty of the Department has had thoughts of such a program, but it was only in the early nineties that resources began to reach the necessary level. As the university’s General Education Program began to grow the role of the Department of Mathematics in that program grew too. General Education remains a major part of the Department’s mission, as does its undergraduate program in general. To strengthen its role in General Education, the Department added eight new faculty positions from 1990 to 1994. Like their colleagues, those faculty members all had and retain active scholarly programs as well as contributing to the teaching programs of the Department.

On June 27, 1994 the Board of Regents of the University of Louisville approved unanimously a proposal for the initiation of a new degree program, a Ph.D. in Mathematics. The faculty of the Department designed that program specifically to focus sharply on two modern branches of mathematics that apply directly to the needs of urban societies everywhere. Those branches are: Applied Analysis, with applications to pattern recognition, actuarial science and investment analysis, measures of information, risk analysis and decision making; and Discrete Mathematics with its applications to environmental biology, classification theory, scheduling and theoretical computer science. With this proposal UofL was poised to begin a modern, progressive and unconventional Ph.D. program in mathematics – one following national trends in teaching and research while directly addressing local needs.

It became clear from discussions with the staff of the Kentucky Council on Higher Education staff that the Council would not approve the program. If the Council had voted against the proposal, its action would have killed any realistic possibilities of a new Ph.D. program for the Department for many years. In order to avoid this outcome, then-President Swain decided in 1995 to withdraw the proposal so as to preserve a chance to put together a new approach at a later date. His action was prophetic! A completely re-written version of the program has been approved this year at almost all levels of the university. After posting on the Web for a 45-day review by the chief academic offices of Kentucky’s public institutions, and others, it has been approved by the faculty of the Department of Mathematics, by the College of Arts and Sciences and by the Graduate School. The Faculty Assembly of the University will consider the proposal in March 2001.

The title of the proposal now is "A Doctor of Philosophy Program in Industrial and Applied Mathematics". The program contains a new feature, an Industrial Internship. The program has been designed according to the recommendations of local industry and national recommendations based upon the research of the Institute of Industrial Mathematics, the Society for Industrial and Applied Mathematics, the American Statistical Association, The American Mathematical Society, and the National Science Foundation. Their reports recommend that programs be developed to emphasize industrial employment. The following are some points raised in these reports -- points that indicate the need for a doctoral program like the one proposed here for students intending industrial employment:

• Breadth of training for problem-solving in industry.

• Instruction in oral and written communication of technical material.

• Industrial experience.

In light of the recommendations of the national associations listed above, the proposed program incorporates the following four main components: The proposal is accompanied by a comprehensive Needs Analysis. The Analysis documents the need for a Ph.D. program in Applied and Industrial Mathematics at the University of Louisville. This year, the Carnegie Foundation has designated UofL for the Advancement of Teaching as one of the "doctoral/extensive research universities – extensive." Of the 3,856 colleges and universities classified, the University of Louisville is one of only 148 to make this elite roster. Implementation of this program will consolidate UofL’s position in that category, and lend support to the research programs already in place at the university.

Collaboration with Departments at UofL that have strong mathematics components such as Business, Education, and Psychology will be pursued. There are also programs at the University of Louisville not available elsewhere in Kentucky. Students who want to utilize the strengths of the Department in Discrete Mathematics can specialize in their application area in Logistics through the Logistics Institute (LoDi), a program developed in part in collaboration with mathematics faculty (the initial acting director was a faculty member from the Department of Mathematics). Students with strong interests in Applied Statistics can take courses in either Decision Sciences/Biostatistics or Epidemiology/ Clinical Investigations. Faculty from the Department of Mathematics helped to develop both programs, currently teach courses and will serve as dissertation advisors in the Public Health programs. The possibility of a joint degree of PhD in Mathematics/MSPH in Decision Sciences/ Biostatistics has been explored. Other options for joint degrees are currently under exploration. Present requirements are being explored through the Graduate School.

Read the next issue of this Newsletter for the continuation of the quest for "A Doctor of Philosophy Program in Industrial and Applied Mathematics" by UofL’s Department of Mathematics. Wouldn’t it be nice if we could answer the title of this article with a resounding Yes!?

Women in Mathematics Club
Mary E. Bradley and Inessa Levi

This year the Mathematics Department organized and secured financial support for a new student organization, Women in Mathematics Club. It is well-known that women respond well to being in community and typically do not perform at their best under a feeling of isolation. A central purpose of this group is to create a woman-friendly atmosphere in the Mathematics Department for our female students. Regular lunch gatherings directed toward our female students have been organized, giving the students an opportunity to meet each other in a setting other than the classroom.

Role models are an important aspect of a successful mentoring project. This year we had several prominent female speakers making presentations for the Women in Mathematics Club, including Dr. Suzanne Lenhart, the president-elect of the Association for Women in Mathematics, and Dr. Sharon Weissbach, Vice President of the National City Bank. The informal setting of a group meeting, which includes some social aspect such as food, allows the students to get close to the speaker and ask their questions and voice their concerns as well.

The Women in Mathematics Club will be an organization for service. The outgrowth of the work of the Women in Mathematics Club is intended to include the following acts of service.

The Biostatistics-Decision Science Program at UofL
By Troy Abel
Director of the Biostatistics –
Decision Science Program
Institute for Public Health Research

Last year the Council on Postsecondary Education (CPE) of the Commonwealth of Kentucky approved the University of Louisville to offer the MSPH and PhD in Biostatistics and Decision Science. These degree programs are a part of the offerings of the new Kentucky School of Public Health: the University of Kentucky is offering the professional degrees of MPH and DrPH and the University of Louisville is offering the research degrees of MSPH and PhD.

One of the goals of the Biostatistics-Decision Science Program is to be trans-disciplinary. There are faculty at UofL in Mathematics, Psychology and Brain Sciences, Electrical and Computer Engineering, Computer Science, Industrial Engineering, Anthropology, and Urban Policy – as well as in the Health Science Center departments of Pediatrics, Medicine, Surgery, Pharmacology and Toxicology, and Family and Community Medicine – who have research expertise in Biostatistics, formal decision analysis, or descriptive decision making. These faculty graciously are making their courses and expertise available to the graduate students in Biostatistics-Decision Science.

The students that have been accepted into the Biostatistics-Decision Science are outstanding, e.g. bachelors or masters degrees in mathematics, masters degree in biology, Ph.D. in nursing, MD hand surgeon, doctoral candidate in cognitive psychology. Each student is required to have two practicum experiences in a local health care agency. The formal decision research coming out of the practicum experiences is of very high quality. The students are learning to work with teams of administrators, policy makers, physicians, and researchers.

The collegial spirit of a number of departments at UofL is phenomenal. The Department of Mathematics especially has been open and creative in planning programs. Dr. Patricia Cerrito submitted a training grant that would fund underrepresented minority students to come and build their undergraduate-level mathematics skills for two years in the Department of Mathematics before embarking on an MSPH in Biostatistics or Decision Science.

The Mathematics Department and the Biostatistics-Decision Science Program are discussing a five-year BS/MSPH program, in which the undergraduate mathematics major would begin taking the MSPH courses in Biostatistics-Decision Science during the junior and senior year and complete the MSPH by the end of the fifth year. This program should attract high-quality students who desire the rigorous foundation of a BS in mathematics and the practical application afforded in public health.

An MS/MSPH joint degree program between Mathematics and Biostatistics-Decision Science is also being discussed. Again, the goal is for the graduate student to be well grounded in mathematics and gain a research specialization in public health.

In the early days of public health planning at UofL, Mathematics Chair Michael Jacobson and Dr. Greg Rempala were enthusiastic supporters of the proposed Biostatistics-Decision Science Program. As the proposed program became more specified over a two-year period, Chair Inessa Levi, Dr. George Barnes, and Dr. Pat Cerrito were strong supporters.

A primary recruitment goal of the Biostatistics-Decision Science Program is to build research ties with various researchers at UofL. As established research programs see the need for biostatisticians and decision scientists on their research teams, funds are made available to hire graduate students. These funds are being used to attract outstanding students into the Program.

The need for quantitative analysis in public health and clinical research is quite high at UofL, the regional, and nationally. Collaborative programs such as those being developed between the Department of Mathematics and the Biostatistics-Decision Science Program will help place rigorously trained graduate students in key research positions. These joint efforts are a good combination of theory and application, formal and scientific problem solving.

Faculty Activities:

Dr Larson and Dr Das will be hosting the 14th Annual Spring Mini-Conference in Real Analysis March 30-31. This is an international conference, funded by the National Science Foundation.

Dr Richard Davitt was awarded one of five "Red Apple" awards by the Alumni Association October 2000, for being a great and enduring influence on a former student, Dr. Wanda Weidemann, (who nominated him). Dr. Davitt also won his second Metroversity Instructional Development award for the design of an honors course he taught on the history of science in the Fall 2000 semester.

Professor Davitt gave a talk on four emigre´ mathematicians who taught at Indiana University, the University of Louisville, the University of Kentucky, and the University of Cincinnati before and during World War II at the biennial Midwest History of Mathematics Conference in October 2000. Much of the information was supplied by Professor W. Henry Spraegens.

Dr Grzegorz Rempala will be attending the International Conference on Stochastic Processes at Cambridge, England in July. His trip will be partially sponsored by NSF.

He will also present a paper jointly with former student and 99’ Mathematics Department graduate Rafal Komendarczyk at the VI National Conference of New Researchers. This conference is organized and sponsored by the NSF and hosted by Georgia Tech.

MBTIã Teaching And Learning Style Differences -
Should We Consider Them?

Gale Rhodes
Director, Academic Services
Robert McAlpine

How often in your class have you presented a concept only to find your students confused and lost? Here are some real life comments made by students who expressed frustration regarding how their professor taught and graded. One student was recently complaining about losing points because she did not show all of her work when answering a question. Her comments were, "I know I have the right answer, now you want me to back into the justification of it." Another student when discussing homework stated that he needed to be shown how to work a problem before having similar problems assigned as homework. The first student immediately jumped in stating that she found it a complete waste of time to have homework problems assigned after she had been shown how to work them. In light of these comments you might want to consider the style differences easily identified by the Myers-Briggs Type Indicator (MBTI) and depicted in the chart below. The comments demonstrate that students are very different, which translates to students’ need to be taught very differently in order to achieve success.

Without going into a lot of detail, the MBTI provides four methods for gathering and evaluating information. When two people prefer the same method of learning they seem to connect and information is transferred rather easily. However, when the methods are different it is almost as if they do not speak the same language. The chart below briefly describes the four methods. To use this chart you might identify your preferred method of learning and compare that to the other three methods and brainstorm ways to present your material differently. If you can stretch your teaching style to include approaches that connect with each of the learning styles, you should have better student success in the classroom.

Sensing and Thinking
Sensing and Feeling
Intuiting and Feeling
Intuiting and Thinking
Engage by probing for:
Specific facts

Focus is on:
Comparing and contrasting
Explaining why

Constructing timelines
Creating pictures or 
Recording similarities and differences

Engage by getting individual 
personal reactions

Focus is on:

Sharing feelings
Speculating about 
others feelings
Knowing the basis for 
the feelings
Knowing who was 
rewarded and how
Knowing the 

Engage by having them synthesize 

Focus is on:

Associating objects 
and thoughts
Exploring alternatives
Combining parts into

Engage by:
Seeking patterns
Developing consequences
Exploring future applications
Taking different perspectives

Focus is on:

Identifying differences
and commonalities
Breaking down concepts 
parts and describing the 
relationship between the parts

University of Louisville
Department of Mathematics
Louisville, Kentucky 40292