Computational and Information Sciences
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By design of the Mathematics Subject Classification, literature
concerning specific computations and algorithms is classified with the
area of mathematics to which the computations are applied. But
mathematics can return the favor and study the process by which
machines carry out their information handling.
68: Computer science, today more accurately a separate
discipline, considers a number of rather mathematical topics. In addition
to computability questions arising from many problems in discrete mathematics,
and logic questions related to recursion theory, one must consider scheduling
questions, stochastic models, and so on.
94: Information and communication includes questions
of particular interest to algebraists, especially coding theory (related
to linear algebra and finite groups) and encryption (related to number theory
and combinatorics). Many topics appropriate to this area
can be expressed in graph-theoretic terms, such as network flows and
circuit design. Data compression and visualization overlap with statistics.
93: Systems theory; control study the evolution
over time of complex systems such as those in engineering. In particular, one
may try to identify the system -- to determine the equations or parameters
which govern its development -- or to control the system -- to select the
parameters (e.g. via feedback loops) to achieve a desired state. Of particular
interest are issues in stability (steady-state configurations) and the
effects of random changes and noise (stochastic systems). While popularly
the domain of "cybernetics" or "robotics", perhaps, this is in practice a
field of application of differential (or difference) equations, functional
analysis, numerical analysis, and global analysis (or differential geometry).
For more fields concerned with the theory and development of numerical
algorithms and their applications, take the Numerical
methods part of the tour. Principal among these is Numerical Analysis proper, the study of methods of computing numerical data.
Fields which have contributed to the development of Computer Science
in particular include 03: Logic (e.g. Turing
machines and so on) and 05: Combinatorics (e.g.
complexity analysis, the traveling salesman problem). Of particular interest
in Information and Communication are tools from abstract algebra, particularly linear algebra and group theory, for the
analysis of coding theory.
You might want to continue the tour with a trip through applications to the sciences.
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Last modified 2000/01/25 by Dave Rusin. Mail: