Tremain prefers math talks to movies or television (except watching the stock ticker on CNBS with no sound).  She prefers building mathematical models,examples, and counterexamples to any games.  Other countries are just new places to see and do math with different people.  Mathematics is an endlessly entertaining source of amusement that can be done anytime, anywhere, with anyone.  Absolutely everything can be related to mathematics.  She works while the world sleeps.  She thinks in pictures, and is willing to work on any problem for anyone … and give them the usually handwritten originals … most of the time for just a thank you.  She is supported by the National Science Foundation, the Defense Threat Reduction Agency and the National Geospatial Intelligence Agency and does not teach anymore.

Tremain is a Senior Researcher in the Frame Research Center.  To her the world is full of mathematical adventures just waiting to be explored.  She prefers pictures to mathematical notation which she calls “freak speak”.  She wrote an article for an MAA book entitled “Intelligence, Creativity, and Conformity.” 

Research Interests
Janet Tremain is interested in all areas, but especially in mathematics:  frame theory, applied math, and engineering.  She’s interested in (and has worked in) model logic and artificial intelligence…and is especially interested in “cognition and the brain” (which she has also worked in).  She can write source code in several programming languages.  She has worked in the stock market since she was a teenager and is also interested in financial math.

Education: 

• 1991  Mathematical Tripos - Part III, Certicate of Advanced Study in Mathematics Honors, Trinity College, University of Cambridge, England
• 1985   M.S. University of Missouri, Columbia, MO
• 1979   B.S. in Mathematics, Southwest Missouri State University, Springfield, MO. Graduated magna cum laude.

Select Publications: 

M. Fickus, D. Mixon and J.C. Tremain, Steiner equiangular tight frames, Linear Algebra and Applications 436 (2012) 1014-1027.

J.C. Tremain, Algorithmic constructions of unitary matrices and tight frames, Preprint.

M. Fickus, D.G. Mixon and J.C. Tremain, Constructing a large family of equiangular tight frames, Proceedings of SAMPTA (2011).

B.G. Bodmann, P.G. Casazza, J. Peterson, I. Smalyanau, and J.C. Tremain, Equi-isoclinic fusion frames and mutually unbiased basic sequences, to appear.

P.G. Casazza, M. Fickus, D. Mixon and J.C. Tremain, The Bourgain- Tzafriri Conjecture and concrete constructions of non-pavable projections, Operators and Matrices, 5 No. 2 (2011) 351-363.

J.C. Tremain and C. Vaidyanathan, An elementary representation of all real Hessenberg unitary matrices, preprint.

P.G. Casazza, R. Lynch, J.C. Tremain and L. Woodland, Integer Frames, preprint.