The Fourier transform and its extensions have historically been the prime vehi-
cle for signal analysis and representation. Since the early 1970s, block transforms
with real basis functions, particularly the discrete cosine transform (DCT), have
been studied extensively for transform coding applications. The availability of
simple fast transform algorithms and good signal coding performance made the
DCT the standard signal decomposition technique, particularly for image and
video. The international standard image-video coding algorithms, i.e., CCITT...
This is a book I wished I had found when, many years ago, I first learned
the subject of ring theory. All those years have flown by, but I still did not
find that book. So finally I decided to write it myself.
All the books I have written so far were developed from my lectures;
this one is no exception. After writing A First Course in Noncommutative
Rings (Springer-Verlag GTM 131, hereafter referred to as “FC ”), I taught
ring theory in Berkeley again in the fall of 1993, using FC as text. Since the
main theory is already fully developed in FC, I asked my...
Combinatorics is generally concerned with counting arrangements
within a finite set. One of the basic problems is to determine the
number of possible configurations of a given kind. Even when the
rules specifying the configuration are relatively simple, the questions
of existence and enumeration often present great difficulties. Besides
counting, combinatorics is also concerned with questions involving
symmetries, regularity properties, and morphisms of these
arrangements. The theory of block designs is an important area where
these facts are very apparent.