I received my Ph.D. in 1997 at the Johns Hopkins University Department of Mathematics, in Baltimore, Maryland. My dissertation topic involves work in homotopy theory, in the discipline of algebraic topology. I worked with a team of thesis advisors, Dr. J. Michael Boardman and Dr. W. Stephen Wilson . Prior to the completion of my dissertation, I received my M.A. in mathematics at Johns Hopkins in 1994. I completed my B.A. in 1991 at the State University of New York at Buffalo, at which my father, Dr. Michael Cowen, is a professor in the Mathematics Department. In August 1997, at the conclusion of my studies, I received the post of Visiting Assistant Professor of Mathematics at John Carroll University in Cleveland, Ohio. I am currently an Associate Professor of Mathematics at Xavier University in Cincinnati, Ohio.
Ongoing Research Projects
My area of research is in algebraic topology -- specifically homotopy theory. I have been working to compute the homology of various spectra using their added structure as Hopf rings. My joint paper with Neil Strickland, entitled The Hopf Rings for KO and KU, was published in the Journal of Pure and Applied Algebra number 166 (2002). Additionally, I have successfully completed the calculations of the Hopf rings for bo, bo<1>, bo<2>, and bo<4>, which is the topic of my next paper, which will shortly appear in the Journal of Pure and Applied Algebra . My Ph.D. dissertation is The Homology of the Spectrum bo and its Connective Covers. A brief summary of my research is also available. Additionally, you can check out the Hopf Topology Archive to get a feel for different research projects in topology.
I have been researching mathematical games and the combinatorics of words with Dr. Lowell Abrams since Fall 2002. Related to our research are some seriously cool and beautiful pictures:
In addition, I am writing a topology textbook with the man who was my first topology professor, Dr. Scott Williams at the University of Buffalo. In Fall 2005, I was on sabbatical in order to continue work on this project.
Talks and Presentations of Research
During my time at John Carroll, I was an active participant in the Cleveland
Geometry-Topology seminar. During the spring 1999 semester, I gave
a one-hour seminar about my research. Additionally, I attended the
1998, 1999, and 2000 joint AMS-MAA meetings, at which I presented my research.
I have since attended both the 2002 and the 2003 joint meetings and
enjoyed myself immensely.
Grants
I was a part of a group that received a $100,000 NSF grant to attract and
retain our math, computer science, and science majors. Additionally, I am involved
in CSEMS (Computer Science, Engineering, Mathematical Scholarships).
Academic Year 2008-2009
This (Falll 2008) semester, I am teaching two courses:
Other Coursework
Since Fall 1997, I have taught multiple sections of a 3-semester sequence of Calculus for science and math majors, a one-year sequence of Calculus for business majors, and a one-semester Calculus course. I have taught the first semester of statistics for non-mathematics majors, and a course devoted to mathematics and creativity. Since arriving at Xavier, I have taught multiple sections of Precalculus, Elements of Calculus I, Calculus I and II, Multivariable Calculus (Calculus III), Elementary Topology, and Discrete Mathematics (our first "proofs" course for all mathematics and computer science majors). Additionally, I developed and taught a new course for math majors on the subject of cryptography. Lastly, I introduced my own section of our MATH 125: Mathematical Perspectives, with the title of Mathematics and the Creative Imagination.
Technology
Technology used in my courses include DERIVE, TI-83 graphing calculators, Maple and Minitab. The numerous applications of mathematics to real-life problems lend themselves to the use of technology, allowing us to explore certain aspects of our courses more fully. Amongst the techniques I have employed and applications which we have discussed are:
In all courses, the additional information gleaned with the use of technology has been an invaluable learning and teaching tool, enhancing the classroom experience.
A few years ago, a group of my discrete math students (along with a mathematics and the creative imagination student) compiled the following list: Top 17 Prime Ways to tell that you are turning into Dr. Morton. This list cracks me up!
When I joined the faculty of the Mathematics and Computer Sciences department at John Carroll, I became increasingly interested in programming. I have now successfully completed three courses; C Programming, Data Structures/ Algorithms (using C), and C++. I had so much fun!!!
After receiving my Ph.D., I spent the summer working for IAAY -- the Institute for the Academic Advancement of Youth. This terrific program is a comprehensive, university-based initiative that promotes the academic ability of children and youth throughout the world. The program that I worked with was a subset of IAAY, the Center for Talented Youth (CTY). This program was essentially a math camp for kids, and everyone involved had a blast!
I am was an Ohio Project NExT fellow, which is offered in conjunction with the Ohio Section of the MAA.
Math in the movies. Yes, that’s right. We’re everywhere!
The American Mathematical Society. Devoted to mathematical research and teaching.
The Mathematical Association of America. Devoted to the interests of collegiate mathematics.
The Association for Women in Mathematics. Devoted to the interests of women in mathematics.
Monty Python. Yes, it is time for something completely different.
Contact Me!