Rings are usually named after one or more of their investigators. But such a prac-
tice usually makes understanding the properties of the various associated rings diffi-
cult for anyone other than the mathematician working on the ring.What is linear algebra?
Linear algebra is the study of linear sets of equations. It encompasses their transfor-
mation properties and includes the analysis of rotations in space, least squares fitting,
and numerous other problems in mathe-
matics, physics, and engineering.What is Boolean algebra?
Boolean algebra is an abstract mathemat-
ical system used to express the relation-
ship between sets (groups of objects or
concepts). It is important in the study of
information theory, the theory of proba-
bility, and the geometry of sets. The use
of Boolean notation in electrical net-
works aided the development of switch-
ing theory and the eventual design of
computers.It was English mathematician George
Boole (1815–1864) who first developed
this type of logic by demonstrating the
algebraic manipulation of logical state-
ments, showing whether or not a state-
ment is true, and showing how a state-
162 ment can be made into a simpler, more
Why are mathematicians so interested in transcendental numbers?
T
ranscendental numbers are those that are not the root of any integer polyno-
mial, or that are not an algebraic number of any degree. Thus, all transcen-
dental numbers are irrational (rational numbers are algebraic numbers of
degree one). The importance of such numbers translates through more than two
millennia of history: For example, they provided the first proof that circle squar-
ing was insoluble, which is one of the geometric problems that has baffled math-
ematicians throughout antiquity.Though Charles Dodgson is more commonly known
as the author of Alice’s Adventures in Wonderland
under the pen name of Lewis Carroll, he was also a
brilliant mathematician. Among other accomplish-
ments, he devised ways to refine Boolean algebra
notations. Library of Congress.