In the 1985 revision of the Mathematics Subject Classification, the old
classification 10 was replaced by a new 11. The parts were somewhat
reorganized, and in addition the first three parts of section 12 were
incorporated into 11. Here is a review of the older classifications in
section 10, and a list of approximate correspondences between 10 and 11.
* 10-XX (1940-1984) Number theory [Excluding 10Axx and 10Mxx, this classification does not distinguish work in the rational number fields from that in other algebraic number fields.]
* 10-00 (1973-1979) Difficult to classify at the second level (must be assigned at least one other classification number in this section)
* 10-01 (1973-1984) Elementary exposition, textbooks
* 10-02 (1973-1984) Advanced exposition (research surveys, monographs, etc.)
* 10-03 (1973-1984) Historical (must also be assigned at least one classification number from Section 01)
* 10-04 (1973-1984) Explicit machine computation and programs (not the theory of computation or programming)
* 10-06 (1973-1984) Proceedings, conferences, etc.
* 10A (1973-1984) Elementary number theory [For analogues in number fields, see 12A05.]
* 10B (1973-1984) Diophantine equations [See also 14Gxx.]
* 10C (1973-1984) Forms (especially quadratic) [For quadratic forms in linear algebra, see 15A63.]
* 10D (1973-1984) Theory of automorphic and modular functions and forms [See also 12A67, 12B27, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx; for relations with quadratic forms, see 10C15.]
* 10E (1973-1984) Geometry of numbers
* 10F (1973-1984) Diophantine approximation [See also 10K15.]
* 10G (1980-1984) Trigonometric sums, exponential sums and character sums
* 10H (1973-1984) Multiplicative theory
* 10J (1973-1984) Additive theory
* 10K (1973-1984) Probabilistic theory; measure, dimension, etc.
* 10L (1973-1984) Sequences of integers
* 10M (1973-1984) Rational arithmetic of algebraic objects
* 10N (1973-1984) Connections with logic
* 10.0X (1940-1958) Number theory
* 10.00 (1959-1972) General
* 10.01 (1959-1972) General books
* 10.02 (1959-1972) Tables
* 10.03 (1959-1972) Computations
* 10.05 (1959-1972) Elementary number theory, general
* 10.06 (1959-1972) Congruences, residues
* 10.07 (1959-1972) Special functions and sequences
* 10.08 (1959-1972) Elementary prime number theory
* 10.09 (1959-1972) Expansions and algorithms
* 10.1X (1940-1958) Analytic number theory
* 10.10 (1959-1972) Diophantine equations, general
* 10.11 (1959-1972) Linear and quadratic equations
* 10.12 (1959-1972) Cubic and quartic equations
* 10.13 (1959-1972) Equations of higher degree
* 10.14 (1959-1972) Local ($p$-adic) theory
* 10.15 (1959-1972) Forms, general
* 10.16 (1959-1972) Quadratic, Hermitian forms
* 10.17 (1959-1972) Forms of degree $\geq 3$
* 10.18 (1959-1972) Multi-linear forms
* 10.2X (1940-1958) Algebraic number theory
* 10.20 (1959-1972) Modular functions and forms, automorphic functions [See also 20.65, 30.49, 32.65]
* 10.21 (1959-1972) Modular group, modular functions
* 10.22 (1959-1972) Automorphic forms, one variable
* 10.23 (1959-1972) Several variables
* 10.25 (1959-1972) Geometry of numbers
* 10.3X (1940-1958) Geometry of numbers, Diophantine approximation
* 10.30 (1959-1972) Diophantine approximation
* 10.31 (1959-1972) Linear approximation, continued fractions
* 10.32 (1959-1972) Algebraicity, irrationality and transcendence
* 10.33 (1959-1972) Distribution modulo 1, normal numbers
* 10.34 (1959-1972) Analytic and $p$-adic theory
* 10.4X (1940-1958) Continued fractions
* 10.40 (1959-1972) Analytic multiplicative theory, general
* 10.41 (1959-1972) Analytic tools (Zeta- and $L$-functions, exponential sums, etc.)
* 10.42 (1959-1972) Distribution of the integers with specified multiplicative structure (including primes)
* 10.43 (1959-1972) Number-theoretic functions
* 10.45 (1959-1972) Analytic additive theory, general
* 10.46 (1959-1972) Sums of powers, generalizations
* 10.47 (1959-1972) Additive questions concerning primes
* 10.48 (1959-1972) Partitions, generating functions
* 10.49 (1959-1972) Sequences
* 10.50 (1959-1972) Probabilistic number theory
* 10.55 (1959-1972) Combinatorial problems in number theory [See also 05.00]
* 10.60 (1959-1972) Sequences of integers, general
* 10.61 (1959-1972) Recursive and other special sequences
* 10.62 (1959-1972) Addition of sequences, basis, essential components, etc.
* 10.63 (1959-1972) Density of special sequences
* 10.64 (1959-1972) Sieves
* 10.65 (1959-1972) Algebraic number theory, general [See also 12.50]
* 10.66 (1959-1972) Individual algebraic number fields (quadratic, cubic, cyclotomic, Kummer, etc.)
* 10.67 (1959-1972) Local theory (valuations, finite extensions of $p$-adic fields)
* 10.68 (1959-1972) Class field theory, complex multiplication
* 10.69 (1959-1972) Arithmetic of general rings
* 10.75 (1959-1972) Arithmetic theory of algebraic objects
* 10.76 (1959-1972) Polynomials
* 10.77 (1959-1972) Finite fields, power series fields
* 10.78 (1959-1972) Valued fields, algebraic function fields
* 10.79 (1959-1972) Matrices
* 10.80 (1959-1972) Decidability, other logical questions
* 10.99 (1959-1972) None of the above, but in this section
© Copyright American Mathematical Society 1999
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Correspondences between 1973-1984 and 1985-1999 schemes
10A Elementary number theory [For analogues in number fields, see 12A05.]
11A: Elementary number theory, including continued fractions. For analogues in number fields, see 11R04
10B Diophantine equations [See also 14Gxx.]
11D: Diophantine equations.
10C Forms (especially quadratic) [For quadratic forms in linear algebra, see 15A63.]
11E: Forms and linear algebraic groups See also 19GXX. For quadratic forms in linear algebra, See 15A63
10D Theory of automorphic and modular functions and forms [See also 12A67, 12B27, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx; for relations with quadratic forms, see 10C15.]
11F: Discontinuous groups and automorphic forms See also 11R39,11S37, 14-XX, 22EXX, 14GXX, 14KXX, 22E50, 22E55, 30F35, 32NXX; for relations with quadratic forms, See 11E45
10E Geometry of numbers
11H: Geometry of numbers For applications in coding theory, see 94B75
10F Diophantine approximation [See also 10K15.]
11J: Diophantine approximation, transcendental number theory (including Pi). See also 11K60
10G Trigonometric sums, exponential sums and character sums
11L: Exponential sums and character sums (For finite fields, see 11T)
10H Multiplicative theory
11N: Multiplicative number theory
11M: Zeta and L-functions: analytic theory
10J Additive theory
11P: Additive number theory; partitions (inc. Waring's problem)
10K Probabilistic theory; measure, dimension, etc.
11K: Probabilistic theory: distribution modulo 1; metric theory of algorithms
10L Sequences of integers
11B: Sequences and sets (including Fibonacci,...)
10M Rational arithmetic of algebraic objects
11G: Arithmetic algebraic geometry (Diophantine geometry), see also 11DXX, 14-XX, 14GXX, 14KXX
10N Connections with logic
11U: Connections with logic
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These sections of 12 were moved to 11 in 1985:
12A
11R: Algebraic number theory: global fields. For complex multiplication, see 11G15. For Galois theory see also 12-XX.
12B
11S: Algebraic number theory: local and p-adic fields For Galois theory see also 12-XX.
12C
11T: Finite fields and commutative rings (number-theoretic aspects)
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These sections of 11 were added in 1985 and have no direct counterpart
in the pre-1985 MSC:
11C: Polynomials and matrices
11Y: Computational number theory, including factorization and primality testing. See also 11-04
11Z05: Miscellaneous applications of number theory
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