My dissertation was in the area of finite groups. Most of my research has been in finite groups and the related area of combinatorics. I did some work in coding and cryptology. I worked in artificial intelligence/expert systems in the 1980’s and retain an interest in the area, especially as it relates to mathematics.
2013 - Applications of the Matrix of Forbidden Pairs, Congressus Numerantium (with A. Mihnea)
2015 - Distributions for Transformations of Derangements, Journal of Combinatorial
Combinatorial Computing (with A. Mihnea)
1998 - Introduction and History, in Mathematical Aspects of Artificial Intelligence.
1998 - Mathematical Aspects of Artificial Intelligence (editor), American Mathematical Society, Providence.
1976 - Orbits under Actions of Affine Groups over GF(2). Linear Algebra and Its Applications
1971- Products of Two Involutions in the General Linear Group,
(with E.C. Paige).
1964 - N ilpotent Height of Finite Groups Admitting Fixed-point-free Automorphisms, Math . Zeitschr.
I directed the doctoral dissertations of Randy Garrett and Amy Mihnea. I was one of the founding faculty of the FAU Computer Science Department. I was a Founding Fellow of The Institute of Combinatorics and its Applications, and I serve on its Council. I have directed thirty-five of the Southeastern International Conferences on Combinatorics, Graph Theory and Computing, and served as conference chair for fourteen of the International Symposia on Artificial Intelligence and Mathematics. I was local arrangements chair for the twenty-fifth IEEE Symposium on the Foundations of Computer Science. I served as President and Governor of the Florida Section of the Mathematical Association of America, and chaired the national MAA committee on mini-courses. I was one of the two organizers of the AMS short course at the Joint Mathematics Meetings in 1996. On May 22, 2017, I received the Douglas D. Dankel II Award for service to the Florida AI Research Society.
Frederick Hoffman, Bal Khadka, Maria Provost and Parshuram Budhathoki at JMM, 2017, Atlanta, Georgia.
Gus Simmins, Ron Mullin, Jan Mullin, Frederick Hoffman, Doug Stinson, Frederick Hoffman, Ebrahim Salehi, Arthur Finbow and his wife at Morikami Museum and Japanese Gardens, Boca Raton, Florida, during the excursion of the Southeastern International Conference on Combinatorics, Graph Theory and Computing, March, 2015.
Frederick Hoffman received the 2017 Douglas D. Dankel II for many years of service to the Florida Artificial Intelligence Research Society on May 22, 2017, Marco Island, Florida.