Joseph Kirtland received his Ph.D. from the University of New Hampshire and his B.S. from Syracuse University. His professional interests are finite and infinite group theory, linear algebra, mathematics education, and mathematical computing. He also enjoys poetry, hiking, and scuba diving.
Due to Joe's interest in group theory, he collaborated on research projects with faculty from SUNY Binghamton. Joe is also interested in innovative ways to teach mathematics. In particular, he is working with Dr. Haruta of English Department on developing collaborative techniques for teaching freshman mathematics and college composition. Additionally, Joe studies the application of group theory to the creation and use of check digit schemes. Based on his efforts, he has written a book, entitled Identification Numbers and Check Digit Schemes, published by the Mathematical Association of America (MAA). This book won the MAAs Beckenback Book Prize, awarded to an author of a distinguished, innovative book published by the MAA.
Dr. Kirtland has published numerous articles in the area of both finite and infinite group theory. They are listed below.
The Geometry of Finite Groups Through the Use of Splitting Systems, Communications in Algebra 22(3), 735-764, 1994.
Direct Products of Inseparable Finite Groups, Archiv der Mathematik 62, 289-291, 1994.
Finite Solvable Multiprimitive Groups, Communications in Algebra 23(1), 335-356, 1995.
Direct Products of Inseparable Finite Groups, II, Communications in Algebra 25(1), 243-246,1997.
Finite Groups with a Minimal Frattini Subgroup Property, Glasgow Mathematical Journal 45, 41-44, 2003.
Kappe, L.-C. and Kirtland, J., Some Analogues of the Frattini Subgroup, Algebra Colloquium 4(4), 419-426, 1997.
Kappe, L.-C. and Kirtland, J., Supplementation in Groups, Glasgow Mathematical Journal 42, 37-50, 2000.
Kappe, L.-C. and Kirtland, J., Finite Groups with Trivial Frattini Subgroups, Archiv der Mathematik 80, 225-234, 2003.
Dr. Haruta and Dr. Kirtland have published two articles concerning their efforts to teach mathematics and composition to freshmen students. They are listed below.
Haruta, P.S., and Kirtland, J., Integrating Mathematics and Composition Instruction, PRIMUS XII(1), 11-26, 2002.
Haruta, P.S. and Kirtland, J., Emergentist Framework for Evaluating Writing in Mathematics, ERIC ED 453552, 453-552, 2001.
Dr. Kirtland has written a book, entitled "Identification Numbers and Check Digit Schemes", which was published by the Mathematical Association of America in their Classroom Resource Materials series. This book was awarded the MAA Beckenbach Book Prize.
Dr. Kirtland has two research interests.
A) Group Theory: Studying structure and classification issues. He is particularly interested in complementation and supplementation issues, as well as permutability (subgroups and elements), decomposition, and group actions.
B) Interdisciplinary Teaching of Mathematics and English: He is currently investigating the ways in which writing, done inside and outside of class, can positively influence a student's learning of mathematics. In addition, Dr. Kirtland is also interested in how mathematics can be used to positively influence a students learning of composition and basic writing skills.