Polynomials furnish the most important and perhaps most neglected
concept in pure and applied mathematics. Yet they appear whenever we
have finite setting.
Indeed, we meet them in the construction of
extension fields, as annihilating polynomials in linear algera and
module theory, in Zarisky topology, in DSP and DIP, in interpolation and
numerical analysis, in coding and cryptography, in combinatorial
biology, etc etc
Their importance to applied math comes in large
part due to the tri-partheid relations between coefficients, roots and
power-sums.
This will be a talk about the connection between
polynomial multiplication and Toeplitz matrix multiplication. This
connection will link the binary world to the polynomial world.
A
block versions of this connection will be applied to the study of
convolutional codes. |