[Search][Subject Index][MathMap][Tour][Help!]

	Index using Library Of Congress System

Here are the top-level areas of mathematics and related fields classified according to the Library of Congress classification system, used in many research libraries in North America and elsewhere. For further information about the LOC system, visit the Library itself; you may prefer to search for a subject classification or browse the LOC's classification system [Note: the browse feature offers subfields in response to the 'See other search suggestions for:' directive, but these do not appear to be offered in a systematic way, e.g. "multilinear algebra" is offered but not "linear algebra"] Further information also available from sites which use the system.

At the level of generality shown below, the LOC serves only as a coarse guide to the subject areas of mathematics. The system used more commonly among mathematicians is the Mathematics Subject Classification (MSC) scheme, which is the basis for the organization of materials at this site. A more refined list of subject headings (they are published but not easily accessible here) received from any librarian would be most welcome. Here we link some of the major headings of the LOC code with nearly corresponding index pages at this site.

QA 1-939 --- Mathematics

• 1-43 General
  • 1-7 Periodicals, collections, dictionaries, etc.
  • 9-10.3 Mathematical Logic
  • 11-14 Study and Teaching, Research
  • 16-20 Special Teaching Methods and Aids
  • 21-35 History
  • 36-39 General Works (encyclopedias, textbooks)
  • 40-43 Handbooks, Manuals, Problem books, etc.
• 47-59 Tables
• 71-90 Instruments and Machines
  • 73 Slide Rules
  • 75-76.95 Calculating Machines
  • 75.5-76.95 Electronic Computers, Computer Science
• 93-95 Popular works, Mathematical recreations
• 99 Miscellany and Curiosa
• 101-145 Elementary Mathematics, Arithmetic
  • 135-139 Study and Teaching
• 150-272.5 Algebra
  • 152-159 Textbooks, Treatises, Problems and exercises, Study and teaching
  • 161-165 Elementary topics. Permutations, Combinations, Partitions, Distributions
  • 171 Group Theory
  • 172-172.4 Ordered algebraic structures
  • 184-205 Linear and Multilinear Algebra, Matrices
  • 211-218 Theory of Equations
  • 241-247 Theory of Numbers
  • 248 Foundations of arithmetic
  • 251-263 Universal algebra
  • 251.4 Noncommutative algebras
  • 266 Abstract algebra
• 273-274.76 Probabilities
• 275-280 Mathematical Statistics
• 281 Interpolation
• 295 Series, infinite products and other infinite processes
• 297-299.4 Numerical Analysis
• 299.6-433 Analysis
  • 300-302 Comprehensive works, historical works
  • 303-312 Calculus
  • 315-316 Calculus of variations
  • 319-329 Functional Analysis
  • 331-355 Theory of Functions
    • 331 General, including functions of a complex variable
    • 331.5 Functions of a real variable
    • 332 Uniform functions
    • 333 Multiform functions, Riemann surfaces
    • 341 Algebraic functions
    • 342 Logarithmic, circular, and exponential functions
    • 343 Elliptic functions, elliptic integrals, modular functions
    • 345 Abelian functions (including hyperelliptic). Theta functions
    • 351 Miscellaneous special functions
    • 355 Miscellaneous special topics
    • 360 Geometric principles of Analysis. Mapping of Regions. Conformal representation
  • 370-387 Differential Equations
  • 401-433 Analytical methods connected with physical sciences
• 440-699 Geometry, Trigonometry, Topology
  • 451-469 Elementary Geometry
  • 501-521 Descriptive Geometry
  • 531-538 Trigonometry
  • 551-563 Analytic Geometry
  • 564-581 Algebraic Geometry
  • 601-608 Transformations, Correspondences, and General Methods for Algebraic Configurations
  • 611-614 Topology
  • 615-640 Infinitesimal Geometry
  • 641-660 Projective Differential Geometry
• 801-939 Analytic Mechanics

The Library of Congress system treats the following as separate from Mathematics but there are some areas of substantial overlap with portions of the MSC. Note that the MSC, and the materials at this site, consider only the mathematical aspects of these sciences.

• Q General Science.
  • Q300-390 Cybernetics
  • Q350-390 Information theory
• QB Astronomy.
  • QB275-343: Geodesy
  • QB349-421: Celestial Mechanics
  • QB460-466: Astrophysics
• QC Physics.
  • 1-168.85 General, Weights and measures, Descriptive and experimental mechanics
  • 170-197 Atomic physics, Constitution and properties of matter, including molecular physics, relativity, quantum theory, and solid state physics
  • 221-246 Acoustics. Sound
  • 251-338.5 Heat, Thermodynamics
  • 350-467 Optics. Light
  • 474-496.9 Radiation physics (General)
  • 501-766 Electricity and magnetism
  • 770-798 Nuclear and particle physics
  • 801-849 Geophysics. Cosmic physics. Geomagnetism
  • 851-999 Meteorology. Climatology
• QD Chemistry.
• QE Geology. (esp QE500-639.5 Dynamic and structural geology)
• QH Natural History, Biology.
  • QH426-470 Genetics
  • QH540-549.5 Ecology
• QM Anatomy
• QP Physiology

[See also Engineering applications, Sociology, Psychology, Financial math, etc.]

The LOC subject browser offers this list of "Narrower Topics" within Mathematics; many are not within the purview of this site. (Indeed, many are scarcely part of mathematics at all, and many subfields of mathematics are not listed, so it is not clear how this list was generated.)

• Algebra
• Arithmetic
• Associative law (Mathematics)
• Ausdehnungslehre
• Australian aborigines--Mathematics
• Axioms
• Binary system (Mathematics)
• Biomathematics
• Business mathematics
• Combinations
• Commutative law (Mathematics)
• Congruences (Geometry)
• Congruences and residues
• Conic sections
• Coordinates
• Curves
• Decomposition (Mathematics)
• Determinants
• Distributive law (Mathematics)
• Dynamics
• Economics, Mathematical
• Equations
• Ethnomathematics
• Factorization (Mathematics)
• Fiberings (Mathematics)
• Filters (Mathematics)
• Forms (Mathematics)
• Fourth dimension
• Fractions
• Functions
• Fuzzy mathematics
• Game theory
• Geodesics (Mathematics)
• Geometry
• Graphic methods
• Harmonic analysis
• Hyperspace
• Index theory (Mathematics)
• Indians of North America--Mathematics
• Induction (Mathematics)
• Information theory in mathematics
• Interval analysis (Mathematics)
• Intuitionistic mathematics
• Kinematics
• Least squares
• Logic, Symbolic and mathematical
• Mathematical constants
• Maxima and minima
• Mensuration
• Metric system
• Minorities in mathematics
• Normal forms (Mathematics)
• Numeracy
• Numerals
• Permutations
• Probabilities
• Projection
• Reciprocity theorems
• Sequences (Mathematics)
• Series
• Set theory
• Shop mathematics
• Statics
• Tiling (Mathematics)
• Trigonometry
• Variables (Mathematics)
• Vector analysis
• Women in mathematics
• Word problems (Mathematics)