 [Search][Subject Index][MathMap][Tour][Help!] # Computational and Information Sciences

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 computers 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 include in particular 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.