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68: Computer science


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.

Computer Science is no more about computers than astronomy is about telescopes.
-- E. W. Dijkstra


There is a website devoted to the history of computing (only some of this, of course, is "computer science" in the mathematical sense).

Applications and related fields

For papers involving machine computations and programs in a specific mathematical area, See Section --04 in that area. This includes computational issues in group theory, number theory, statistics, and so on.

In particular, for numerical linear algebra see linear algebra, and for graph-theoretic questions such as the traveling salesman problem or scheduling algorithms, see Combinatorics.

Issues of numerical stability of algorithms, rates of convergence, and so on form the field of numerical analysis.

For cellular automata see Dynamical systems

The word programming in this context is essentially unrelated to the use of the word in e.g. Linear Programming. For that topic see 90: Optimization. [Schematic of subareas and related areas]

This image slightly hand-edited for clarity.


This is among the largest areas in the Math Reviews database. This is largely because subfield 68Q (computing theory) is among the largest of the three-digits subfields in the database; the extent to which that literature is part of mathematics is not clear. Apart from that area (which is nearly half the total), Computer Science would be nearer the average size of the disciplines. Also 68U05 (computational geometry) is one of the largest 5-digit areas.

Section 68 has been reorganized into subdisciplines several times, most recently in 1990. To increase clarity, this map was made using only data from 1991.

Browse all (old) classifications for this area at the AMS.

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

Surely Knuth, "The Art of Computer Programming":

Online Dictionary of computing.

Kallay, Michael: "Convex hull made easy", Inform. Process. Lett. 22 (1986), no. 3, 161. CMP833183

Van Hove, H.; Verschoren, A.: "What is `epistasis'?", Bull. Belg. Math. Soc. Simon Stevin 5 (1998), no. 1, 69--77. MR99c:68219

Schank, Roger C., "What is AI, anyway?" The foundations of artificial intelligence, 3--13; Cambridge Univ. Press, Cambridge, 1990. CMP1114137

Software and tables

For the major all-in-one software products for handling general mathematical problems (e.g. Ma***, Ma****, etc.), see 68Q40: Symbolic computation.

Software of more limited scope is usually mentioned on an appropriate page. See in particular the symbolic-computation resources for number theory and commutative algebra; many of the algorithms for those areas is incorporated in the more general-purpose software.

Other web sites with this focus

Selected topics at this site

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Last modified 1999/05/12 by Dave Rusin. Mail: feedback@math-atlas.org