BIOGRAPHICAL SKETCH

### Personal Data

 Department of Mathematics Tel. 205-934-2154 University of Alabama at Birmingham Fax: 205-934-9025 Birmingham AL 35294 Email: mayer@math.uab.edu

### Professional Preparation

 Randolph-Macon College, Ashland, VA Philosophy/Physics BA, 1967 University of Florida, Gainesville, FL Philosophy MA, 1978 University of Florida, Gainesville, FL Philosophy (Logic) PhD, 1980 University of Florida, Gainesville, FL Mathematics PhD, 1982 University of Saskatchewan, Saskatoon, SK, Canada Mathematics 1982-84

### Appointments

 Associate Chair, UAB 1997 – present Undergraduate Program Director, UAB 1996 – present Professor of Mathematics, UAB 1999 – present Graduate Program Director, UAB 1990 – 1996 Associate Professor, UAB 1990 – 1999 Assistant Professor, UAB 1984 – 1990. Visiting Positions: Florida Spring, 1989 Virginia Tech Winter, 1988 Lecturer in Mathematics, Saskatchewan 1982 – 84 Adjunct Assistant in Mathematics, Florida Summers, 1982, 1985 Teacher, Academic Dean, and Principal, Brandon Hall, Atlanta, GA 1968 – 77

### Selected Publications

1.      B. L. Brechner and J. C. Mayer, Antoine's necklace, or how to keep a necklace from falling apart, The College Mathematics Journal 19 (1988), 306 – 320. (George Polya Award, MAA, 1989.)

2.      J. C. Mayer, An explosion point for the set of endpoints of the Julia set of $\lambda\exp(z)$, Ergodic Theory and Dynamical Systems 10 (1990), 177 – 183.

3.      J. C. Mayer and L. G. Oversteegen, A topological characterization of R-trees, AMS Transactions 320 (1990), 395 – 415.

4.      J. C. Mayer, Complex dynamics and continuum theory, in the book Continua: with the Houston Problem Book, ed. H. Cook, et al., Lecture Notes in Pure and Applied Mathematics 170 (Marcel Dekker, NY, 1995), 133 – 158.

5.      A. M. Blokh, J. C. Mayer, and L. G. Oversteegen, Recurrent critical points and typical limit sets for rational maps, Proc. Amer. Math. Soc., 127 (1999), 1215 – 1220.

6.      J. Grispolakis, J. C. Mayer, and L. G. Oversteegen, Building  blocks for quadratic Julia sets, Trans. Amer. Math. Soc. 351 (1999), 1171 – 1201.

7.      J. M. Malaugh, J. C. Mayer, and D. K. Parris, Distribution of centers of triangles, Preprint 1999, (undergraduate research paper presented at national MAA conference).

8.      J. C. Mayer and J. T. Rogers, Jr., Indecomposable continua and the Julia sets of polynomials, AMS Proceedings 117 (1993), 795 – 802.

9.      J. C. Mayer and J. T. Rogers, Jr., Indecomposable continua and the Julia sets of polynomials, II, in preparation, 2003.

10.   D. K. Childers, J. C. Mayer, H. M. Tuncali, and E. D. Tymchatyn, Indecomposable continua and the Julia sets of rational maps, in preparation, 2003.

### Synergistic Activities

1. Started and currently direct an accelerated program for undergraduate mathematics majors at UAB, called the Fast-Track Program.  Lex Oversteegen and I have been co-directors of the Fast-Track Program since its inception in 1993.  The program received NSF support 1996-2001 during its major growth period.  The program aims to attract, support, and maintain the interest in mathematics of talented students coming right out of high school.  Students in the program are expected to complete both a BS and MS degree in mathematics.  Many go on to higher degrees in mathematics, the sciences, and the professions (http://www.math.uab.edu/alumni/ftalumni.html).   Students typically finish the program in 4-5 years, during which time they have been mentored in mathematics steadily, with a research project ongoing at all times.  They attend special seminars, have shared office space in the department, and many receive attractive scholarships.  For the past few years, we have typically had 15-20 students concurrently enrolled in the program at various levels.  It is an integral part of the life of our department.  The activity is ongoing (http://www.math.uab.edu/programs/fasttrack.html).
2. Mentoring GK-12 Teaching Fellows in an NSF-sponsored fellowship program bringing graduate students in mathematics and the sciences into K-12 classrooms working with K-12 students and teachers. Ongoing (http://www.ed.uab.edu/GK12/).
3. Developing courses in mathematical modeling for mathematics majors and minors and pre-service and in-service mathematics and science teachers.  One course (MA 261, Introduction to Mathematical Modeling)  has been developed and is now institutionalized as a mathematics major requirement at UAB, also taken by pre- and in-service teachers.  A second course aimed at middle school teachers is being developed.  Some of this development work is joint with colleagues in the School of Education at UAB and with my current PhD students.  Ongoing.

## Recent Collaborators

 Alexander Blokh (UAB) Andrew Maner (Boeing) Harold Bell (Cincinnati) Lex G. Oversteegen (UAB) Douglas Childers (UAB, PhD student) James T. Rogers, Jr. (Tulane) Robbert Fokkink (Delft) Murat Tuncali (Nipissing) James Malaugh (UAB, PhD student) E. D. Tymchatyn (Saskatchewan)

Philosophy PhD Advisor: Jay J. Zeman (Florida)

Mathematics PhD Advisor: Beverly L. Brechner (Florida)