MathDL Taxonomy Proposal

1. Arithmetic / Basic Math
   1. About Numbers
      1. Imaginary / Complex / Real
      2. Negative / Positive
      3. Prime / Composite
      4. Rational / Irrational
      5. i
      6. e
      7. Pi
      8. Infinity
   2. Basic Operations
      1. Addition
      2. Subtraction
      3. Multiplication
      4. Division
   3. Estimation
   4. Exponents / Roots / Bases
   5. Factorials
   6. Fractions / Decimals / Percents
   7. Inequality
   8. Logarithms
   9. Patterns / Relationships
      1. Fibonacci
      2. Golden Ratio
      3. Ratio / Proportion
      4. Sequences
      5. Series
      6. Tiling
2. Number Theory / Logic / Foundations
   1. About Numbers
      1. Imaginary / Complex / Real
      2. Negative / Positive
      3. Prime / Composite
      4. Rational / Irrational
      5. i
      6. e
      7. Pi
      8. Infinity
   2. Algebraic Number Theory
   3. Analytic Number Theory
   4. Cryptography
   5. Logic
      1. Axiomatic Systems
      2. Induction
      3. Proof
   6. Set Theory
3. Algebra
   1. Basic Algebra
      1. Equations
      2. Graphing
      3. Inequality
      4. Polynomials
      5. Systems of Equations
   2. Linear Algebra
      1. Eigenvectors / Eigenvalues
      2. Linear Transformation
      3. Matrix / Matrices
      4. Systems of Linear Equations
      5. Vectors
   3. Modern Algebra
      1. Category Theory / Homologic Algebra
      2. Fields
      3. Group Theory
      4. K-Theory
      5. Multilinear Algebra
      6. Nonassociative Algebra
      7. Rings / Ideals
4. Trigonometry
   1. Angles
   2. Trigonometric Functions
   3. Inverse Trigonometric Functions
   4. Trigonometric Identities
   5. Trigonometric Equations
   6. Roots of Unity
5. Geometry & Topology
   1. Algebraic Topology
   2. Euclidean Geometry
   3. Computational Geometry
   4. Conic Sections
   5. Differential Geometry
   6. Non-Euclidean Geometry
   7. Transformational Geometry
   8. Knot Theory
   9. Lie Groups
6. Calculus
   1. Continuity
   2. Differentiation
      1. Multiple Variable
      2. Single Variable
   3. Integration
      1. Multiple Variable
      2. Numerical Integration
      3. Path / Surface Integrals
      4. Single Variable
   4. Limits
   5. Parametric Equations
   6. Sequences / Series
   7. Vector Analysis
7. Discrete Math
   1. Cellular Automata
   2. Combination / Permutation
   3. Game Theory
   4. Genetic Algorithms
   5. Graph Theory
   6. Linear Programming
   7. Order / Lattices
   8. Theory of Computation
8. Differential Equations
   1. Difference Equations
   2. Ordinary Differential Equations
      1. First Order
      2. Second Order
      3. Linear Oscillations
      4. Nonlinear Oscillations
      5. Systems of Differential Equations
      6. Sturm - Liouville Problems
      7. Special Functions
      8. Power Series Methods
      9. Laplace Transform Methods
   3. Partial Differential Equations
      1. First Order
      2. Elliptic
      3. Parabolic
      4. Hyperbolic
      5. Nonlinear Equations
      6. Symmetries and Integrability
9. Probability / Statistics / Measurement / Data
   1. Brownian Motion
   2. Data Analysis
      1. Graphing of Data
      2. Data Sets
      3. Probability
      4. Statistics
      5. Stochastic Processes
   3. Measurement
      1. Calendars / Dates / Time
      2. Temperature
      3. Units
   4. Probability
      1. Markov Chains
   5. Queuing Theory
   6. Statistics
      1. Bayesian Statistics
      2. Linear Regression
      3. Nonlinear Regression
10. Analysis
    1. Abstract Harmonic Analysis
    2. Approximation / Expansion
    3. Calculus of Variations
    4. Complex Analysis
    5. Fourier/Wavelets
    6. Functional Analysis
    7. Global Analysis
    8. Integral Equations
    9. Integral Transforms / Operational Calculus
    10. Manifolds / Cell Complexes
    11. Measure / Integration
    12. Potential Theory
    13. Real Analysis
    14. Several Complex Variables
11. Dynamic Systems & Modeling
    1. Chaos
    2. Complex Dynamics
    3. Difference Equations
    4. Fractal Geometry
    5. Real Variable Dynamics
    6. Symbolic Dynamics and Coding Theory
12. Numerical Analysis
    1. Approximation Theory
    2. Differential Equations
    3. Linear Algebra
    4. Partial Differential Equations
13. Applications / Connections / Math History
    1. Biology
       1. Animal Biology
       2. Genetics/Evolution
       3. Human Biology
       4. Paleontology / Paleobotany
       5. Plant Biology
       6. Population Growth
    2. Business
       1. Actuarial Science
       2. Economics
       3. Interest
       4. Investment / Finance
       5. Stock Market
    3. Chemistry
    4. Computer Science
       1. AI
       2. Computer Algebra
       3. Computer Systems
       4. Cryptography
       5. Data Structures
       6. Formal Language / Automata
    5. Earth Sciences
       1. Ecology
       2. Geography
       3. Geology
       4. Meteorology
    6. Engineering
       1. Acoustics
       2. Architecture
       3. Control Systems
       4. Electronics
       5. Fluid Mechanics
       6. Operations Research
       7. Signal Analysis
    7. History of Mathematics
    8. Humanities
       1. Art
       2. Literature
       3. Music
       4. Philosophy
       5. Religion
    9. Medicine/Health
    10. Physics / Astronomy
        1. Electromagnetic Theory
        2. Fluid Mechanics
        3. Mechanics of Particles
        4. Mechanics of Solids
        5. Optics
        6. Quantum Mechanics
        7. Relativity / Gravitational Theory
        8. Statistical Mechanics
        9. Thermodynamics
    11. Social Sciences
        1. Linguistics
        2. Political Science
        3. Population
        4. Psychology
        5. Sociology / Anthropology
    12. Sports

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