| 58-00 | General reference works (handbooks, dictionaries, bibliographies, etc.)
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| 58-01 | Instructional exposition (textbooks, tutorial papers, etc.)
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| 58-02 | Research exposition (monographs, survey articles)
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| 58-03 | Historical (must also be assigned at least one classification number from Section 01)
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| 58-04 | Explicit machine computation and programs (not the theory of computation or programming)
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| 58-06 | Proceedings, conferences, collections, etc.
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| 58Axx | General theory of differentiable manifolds [See also 32Cxx]
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| 58Bxx | Infinite-dimensional manifolds
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| 58Cxx | Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]
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| 58Dxx | Spaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]
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| 58Exx | Variational problems in infinite-dimensional spaces
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| 58Hxx | Pseudogroups, differentiable groupoids and general structures on manifolds
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| 58Jxx | Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]
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| 58Kxx | Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]
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| 58Z05 | Applications to physics
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