Galois
theory. An informal account of the main idea with copious examples.
Algorithms
for factorising large polynomials,
reviewing basic background including congruences and Fermat's little
theorem, and explaining with many examples how the Distinct Degree,
Berlekamp and CantorZassenhaus algorithms work, without going into
details about computing times.
Sums
of powers of integers and the EulerMaclaurin
summation formula
A revision
article on Fourier series and transforms.
In it I give an illustrated account of the representation of periodic
functions by Fourier series, and extend this to the Fourier transform
of a nonperiodic continuous function. Then I illustrate sampling
at discrete data points and the discrete Fourier transform. There
is a brief discussion of convolution and deconvolution with relevance
to recovering true signals from signals mixed with noise. An appendix
describes in some detail the fast Fourier Transform algorithm.
Continued
fractions
The shapes
of musical phrases.
