00-XX 
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General
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01-XX
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History and biography
[See also the classification number -03 in the other sections]
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03-XX
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Mathematical logic and foundations
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05-XX
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Combinatorics
{For finite fields, see
11Txx }
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06-XX
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Order, lattices, ordered algebraic structures
[See also
18B35 ]
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08-XX
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General algebraic systems
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11-XX
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Number theory
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12-XX
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Field theory and polynomials
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13-XX
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Commutative rings and algebras
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14-XX
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Algebraic geometry
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15-XX
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Linear and multilinear algebra; matrix theory
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16-XX
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Associative rings and algebras
{For the commutative case, see
13-XX }
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17-XX
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Nonassociative rings and algebras
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18-XX
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Category theory; abstract homological algebra
{See
13Dxx
for commutative rings,
16Exx
for associative rings,
20Jxx
for groups,
57Txx
for topological groups and related structures; see also
55Nxx
and
55Uxx
for algebraic topology}
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19-XX
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$K$-theory
[See also
16E20 ,
18F25 ]
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20-XX
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Group theory and generalizations
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22-XX
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Topological groups, Lie groups
{For transformation groups, see
54H15 ,
57Sxx ,
58-XX .
For abstract harmonic analysis, see
43-XX }
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26-XX
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Real functions
[See also
54C30 ]
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28-XX
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Measure and integration
{For analysis on manifolds, see
58-XX }
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30-XX
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Functions of a complex variable
{For analysis on manifolds, see
58-XX }
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31-XX
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Potential theory
{For probabilistic potential theory, see
60J45 }
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32-XX
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Several complex variables and analytic spaces
{For infinite-dimensional holomorphy, see also
46G20 ,
58B12 }
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33-XX
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Special functions {!
33-XX
deals with the properties of functions as functions}
{For orthogonal functions, see also
42Cxx ;
for aspects of combinatorics, see
05Axx ;
for number-theoretic aspects, see
11-XX ;
for representation theory, see
22Exx }
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34-XX
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Ordinary differential equations
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35-XX
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Partial differential equations
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37-XX
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Dynamical systems and ergodic theory
[See also
26A18 ,
34Cxx ,
34Dxx ,
35Bxx ,
46Lxx ,
58Jxx ,
70-XX ]
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39-XX
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Difference and functional equations
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40-XX
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Sequences, series, summability
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41-XX
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Approximations and expansions
{For all approximation theory in the complex domain, see
30Exx ,
30E05
and
30E10 ;
for all trigonometric approximation and interpolation, see
42Axx ,
42A10
and
42A15 ;
for numerical approximation, see
65Dxx }
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42-XX
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Fourier analysis
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43-XX
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Abstract harmonic analysis
{For other analysis on topological and Lie groups, see
22Exx }
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44-XX
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Integral transforms, operational calculus
{For fractional derivatives and integrals, see
26A33 .
For Fourier transforms, see
42A38 ,
42B10 .
For integral transforms in distribution spaces, see
46F12 .
For numerical methods, see
65R10 }
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45-XX
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Integral equations
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46-XX
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Functional analysis
{For manifolds modeled on topological linear spaces, see
57N20 ,
58Bxx }
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47-XX
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Operator theory
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49-XX
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Calculus of variations and optimal control; optimization
[See also
34H05 ,
34K35 ,
65Kxx ,
90Cxx ,
93-XX ]
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51-XX
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Geometry
{For algebraic geometry, see
14-XX }
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52-XX
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Convex and discrete geometry
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53-XX
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Differential geometry
{For differential topology, see
57Rxx .
For foundational questions of differentiable manifolds, see
58Axx }
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54-XX
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General topology
{For the topology of manifolds of all dimensions, see
57Nxx }
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55-XX
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Algebraic topology
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57-XX
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Manifolds and cell complexes
{For complex manifolds, see
32Qxx }
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58-XX
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Global analysis, analysis on manifolds
[See also
32Cxx ,
32Fxx ,
46-XX ,
47Hxx ,
53Cxx ]
{For geometric integration theory, see
49Q15 }
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60-XX
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Probability theory and stochastic processes
{For additional applications, see
11Kxx ,
62-XX ,
90-XX ,
92-XX ,
93-XX ,
94-XX }
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62-XX
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Statistics
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65-XX
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Numerical analysis
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68-XX
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Computer science
{For papers involving machine computations and programs in a specific mathematical area, see section -04 in that area}
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70-XX
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Mechanics of particles and systems
{For relativistic mechanics, see
83A05
and
83C10 ;
for statistical mechanics, see
82-XX }
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74-XX
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Mechanics of deformable solids
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76-XX
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Fluid mechanics
{For general continuum mechanics, see
74Axx
or other parts of
74-XX }
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78-XX
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Optics, electromagnetic theory
{For quantum optics, see
81V80 }
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80-XX
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Classical thermodynamics, heat transfer
{For thermodynamics of solids, see
74A15 }
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81-XX
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Quantum theory
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82-XX
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Statistical mechanics, structure of matter
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83-XX
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Relativity and gravitational theory
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85-XX
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Astronomy and astrophysics
{For celestial mechanics, see
70F15 }
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86-XX
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Geophysics
[See also
76U05 ,
76V05 ]
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90-XX
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Operations research, mathematical programming
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91-XX
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Game theory, economic, social and behavioral sciences
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92-XX
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Biology and other natural sciences
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93-XX
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Systems theory; control
{For optimal control, see
49-XX }
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94-XX
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Information and communication, circuits
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97-XX
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Mathematics education
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