math education taxonomy
Math Taxonomy
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Subject Taxonomy
Core Subject Taxonomy for Mathematical Sciences Education
This taxonomy is based on the Math NSDL Taxonomy Committee Report, April 2, 2002, with draft changes proposed for Section 9 by CAUSE, May 16, 2004. Further changes to Section 9 were approved by the Math Gateway Partners Group, April 29, 2005
The first two levels of this taxonomy are used for classifying JOMA documents by subject matter. A fuller indication of the meanings of those levels may be obtained by scanning the deeper levels.
- 1.0 Numbers and Computation
- 1.1 Number Concepts
- 1.1.1 Natural
- 1.1.2 Integers
- 1.1.3 Rational
- 1.1.4 Irrational
- 1.1.5 Algebraic
- 1.1.6 Real
- 1.1.7 Complex
- 1.1.8 Famous Numbers
- 1.1.8.1 0
- 1.1.8.2 pi
- 1.1.8.3 e
- 1.1.8.4 i
- 1.1.8.5 Golden Mean
- 1.2 Arithmetic
- 1.2.1 Operations
- 1.2.1.1 Addition
- 1.2.1.2 Subtraction
- 1.2.1.3 Multiplication
- 1.2.1.4 Division
- 1.2.1.5 Roots
- 1.2.1.6 Factorials
- 1.2.1.7 Factoring
- 1.2.1.8 Properties of Operations
- 1.2.1.9 Estimation
- 1.2.2 Fractions
- 1.2.2.1 Addition
- 1.2.2.2 Subtraction
- 1.2.2.3 Multiplication
- 1.2.2.4 Division
- 1.2.2.5 Ratio and Proportion
- 1.2.2.6 Equivalent Fractions
- 1.2.3 Decimals
- 1.2.3.1 Addition
- 1.2.3.2 Subtraction
- 1.2.3.3 Multiplication
- 1.2.3.4 Division
- 1.2.3.5 Percents
- 1.2.4 Comparison of numbers
- 1.2.5 Exponents
- 1.2.5.1 Multiplication
- 1.2.5.2 Division
- 1.2.5.3 Powers
- 1.2.5.4 Integer Exponents
- 1.2.5.5 Rational Exponents
- 1.2.1 Operations
- 1.3 Patterns and Sequences
- 1.3.1 Number Patterns
- 1.3.2 Fibonacci Sequence
- 1.3.3 Arithmetic Sequence
- 1.3.4 Geometric Sequence
- 1.4 Measurement
- 1.4.1 Units of Measurement
- 1.4.1.1 Metric System
- 1.4.1.2 Standard Units
- 1.4.1.3 Nonstandard Units
- 1.4.2 Linear Measure
- 1.4.2.1 Distance
- 1.4.2.2 Circumference
- 1.4.2.3 Perimeter
- 1.4.3 Area
- 1.4.3.1 Area of Polygons
- 1.4.3.2 Area of Circles
- 1.4.3.3 Surface Area
- 1.4.3.4 Nonstandard Shapes
- 1.4.4 Volume
- 1.4.5 Weight and Mass
- 1.4.6 Temperature
- 1.4.7 Time
- 1.4.8 Speed
- 1.4.9 Money
- 1.4.10 Scale
- 1.4.1 Units of Measurement
- 1.1 Number Concepts
- 2.0 Logic and Foundations
- 2.1 Logic
- 2.1.1 Venn Diagrams
- 2.1.2 Propositional and Predicate Logic
- 2.1.3 Methods of Proof
- 2.2 Set Theory
- 2.2.1 Sets and Set Operations
- 2.2.2 Relations and Functions
- 2.2.3 Cardinality
- 2.2.4 Axiom of Choice
- 2.3 Computability and Decidability
- 2.4 Model Theory
- 2.1 Logic
- 3.0 Algebra and Number Theory
- 3.1 Algebra
- 3.1.1 Graphing Techniques
- 3.1.2 Algebraic Manipulation
- 3.1.3 Functions
- 3.1.3.1 Linear
- 3.1.3.2 Quadratic
- 3.1.3.3 Polynomial
- 3.1.3.4 Rational
- 3.1.3.5 Exponential
- 3.1.3.6 Logarithmic
- 3.1.3.7 Piece-wise
- 3.1.3.8 Step
- 3.1.4 Equations
- 3.1.4.1 Linear
- 3.1.4.2 Quadratic
- 3.1.4.3 Polynomial
- 3.1.4.4 Rational
- 3.1.4.5 Exponential
- 3.1.4.6 Logarithmic
- 3.1.4.7 Systems
- 3.1.5 Inequalities
- 3.1.6 Matrices
- 3.1.7 Sequences and Series
- 3.1.8 Algebraic Proof
- 3.2 Linear Algebra
- 3.2.1 Systems of Linear Equations
- 3.2.2 Matrix algebra
- 3.2.3 Vectors in R3
- 3.2.4 Vector Spaces
- 3.2.5 Linear Transformations
- 3.2.6 Eigenvalues and Eigenvectors
- 3.2.7 Inner Product Spaces
- 3.3 Abstract Algebra
- 3.3.1 Groups
- 3.3.2 Rings and Ideals
- 3.3.3 Fields
- 3.3.4 Galois Theory
- 3.3.5 Multilinear Algebra
- 3.4 Number Theory
- 3.4.1 Integers
- 3.4.2 Primes
- 3.4.2.1 Divisibility
- 3.4.2.2 Factorization
- 3.4.2.3 Distributions of Primes
- 3.4.3 Congruences
- 3.4.4 Diophantine Equations
- 3.4.5 Irrational Numbers
- 3.4.6 Famous Problems
- 3.4.7 Coding Theory
- 3.4.8 Cryptography
- 3.5 Category Theory
- 3.6 K-Theory
- 3.7 Homological Algebra
- 3.8 Modular Arithmetic
- 3.1 Algebra
- 4.0 Discrete Mathematics
- 4.1 Cellular Automata
- 4.2 Combinatorics
- 4.2.1 Combinations
- 4.2.2 Permutations
- 4.3 Game Theory
- 4.4 Algorithms
- 4.5 Recursion
- 4.6 Graph Theory
- 4.7 Linear Programming
- 4.8 Order and Lattices
- 4.9 Theory of Computation
- 4.10 Chaos
- 5.0 Geometry and Topology
- 5.1 Geometric Proof
- 5.2 Plane Geometry
- 5.2.1 Measurement
- 5.2.2 Lines and Planes
- 5.2.3 Angles
- 5.2.4 Triangles
- 5.2.4.1 Properties
- 5.2.4.2 Congruence
- 5.2.4.3 Similarity
- 5.2.4.4 Pythagorean Theorem
- 5.2.5 Polygons
- 5.2.5.1 Properties
- 5.2.5.2 Regular
- 5.2.5.3 Irregular
- 5.2.5.4 Congruence
- 5.2.5.5 Similarity
- 5.2.6 Circles
- 5.2.7 Patterns
- 5.2.7.1 Geometric Patterns
- 5.2.7.2 Tilings and Tessellations
- 5.2.7.3 Symmetry
- 5.2.7.4 Golden Ratio
- 5.2.8 Transformations
- 5.2.8.1 Translation
- 5.2.8.2 Rotation
- 5.2.8.3 Reflection
- 5.2.8.4 Scaling
- 5.3 Solid Geometry
- 5.3.1 Dihedral Angles
- 5.3.2 Spheres
- 5.3.3 Cones
- 5.3.4 Cylinders
- 5.3.5 Pyramids
- 5.3.6 Prisms
- 5.3.7 Polyhedra
- 5.4 Analytic Geometry
- 5.4.1 Cartesian Coordinates
- 5.4.2 Lines
- 5.4.3 Circles
- 5.4.4 Planes
- 5.4.5 Conics
- 5.4.6 Polar Coordinates
- 5.4.7 Parametric Curves
- 5.4.8 Surfaces
- 5.4.9 Distance Formula
- 5.5 Projective Geometry
- 5.6 Differential Geometry
- 5.7 Algebraic Geometry
- 5.8 Topology
- 5.8.1 Point Set Topology
- 5.8.2 General Topology
- 5.8.3 Differential Topology
- 5.8.4 Algebraic Topology
- 5.9 Trigonometry
- 5.9.1 Angles
- 5.9.2 Trigonometric Functions
- 5.9.3 Inverse Trigonometric Functions
- 5.9.4 Trigonometric Identities
- 5.9.5 Trigonometric Equations
- 5.9.6 Roots of Unity
- 5.9.7 Spherical Trigonometry
- 5.10 Fractal Geometry
- 6.0 Calculus
- 6.1 Single Variable
- 6.1.1 Functions
- 6.1.2 Limits
- 6.1.3 Continuity
- 6.1.4 Differentiation
- 6.1.5 Integration
- 6.1.6 Series
- 6.2 Several Variables
- 6.2.1 Functions of Several Variables
- 6.2.2 Limits
- 6.2.3 Continuity
- 6.2.4 Partial Derivatives
- 6.2.5 Multiple integrals
- 6.2.6 Taylor Series
- 6.3 Advanced Calculus
- 6.3.1 Vector Valued Functions
- 6.3.2 Line Integrals
- 6.3.3 Surface Integrals
- 6.3.4 Stokes Theorem
- 6.3.5 Curvilinear Coordinates
- 6.3.6 Linear spaces
- 6.3.7 Fourier Series
- 6.3.8 Orthogonal Functions
- 6.4 Tensor Calculus
- 6.5 Calculus of Variations
- 6.6 Operational Calculus
- 6.1 Single Variable
- 7.0 Analysis
- 7.1 Real Analysis
- 7.1.1 Metric Spaces
- 7.1.2 Convergence
- 7.1.3 Continuity
- 7.1.4 Differentiation
- 7.1.5 Integration
- 7.1.6 Measure Theory
- 7.2 Complex Analysis
- 7.2.1 Convergence
- 7.2.2 Infinite Series
- 7.2.3 Analytic Functions
- 7.2.4 Integration
- 7.2.5 Contour Integrals
- 7.2.6 Conformal Mappings
- 7.2.7 Several Complex Variables
- 7.3 Numerical Analysis
- 7.3.1 Computer Arithmetic
- 7.3.2 Solutions of Equations
- 7.3.3 Solutions of Systems
- 7.3.4 Interpolation
- 7.3.5 Numerical Differentiation
- 7.3.6 Numerical Integration
- 7.3.7 Numerical Solutions of ODEs
- 7.3.8 Numerical Solutions of PDEs
- 7.4 Integral Transforms
- 7.4.1 Fourier Transforms
- 7.4.2 Laplace Transforms
- 7.4.3 Hankel Transforms
- 7.4.4 Wavelets
- 7.4.5 Other Transforms
- 7.5 Signal Analysis
- 7.5.1 Sampling Theory
- 7.5.2 Filters
- 7.5.3 Noise
- 7.5.4 Data Compression
- 7.5.5 Image Processing
- 7.6 Functional Analysis
- 7.6.1 Hilbert Spaces
- 7.6.2 Banach Spaces
- 7.6.3 Topological Spaces
- 7.6.4 Locally Convex Spaces
- 7.6.5 Bounded Operators
- 7.6.6 Spectral Theorem
- 7.6.7 Unbounded Operators
- 7.7 Harmonic Analysis
- 7.8 Global Analysis
- 7.1 Real Analysis
- 8.0 Differential and Difference Equations
- 8.1 Ordinary Differential Equations
- 8.1.1 First Order
- 8.1.2 Second Order
- 8.1.3 Linear Oscillations
- 8.1.4 Nonlinear Oscillations
- 8.1.5 Systems of Differential Equations
- 8.1.6 Sturm Liouville Problems
- 8.1.7 Special Functions
- 8.1.8 Power Series Methods
- 8.1.9 Laplace Transforms
- 8.2 Partial Differential Equations
- 8.2.1 First Order
- 8.2.2 Elliptic
- 8.2.3 Parabolic
- 8.2.4 Hyperbolic
- 8.2.5 Integral Transforms
- 8.2.6 Integral Equations
- 8.2.7 Potential Theory
- 8.2.8 Nonlinear Equations
- 8.2.9 Symmetries and Integrability
- 8.3 Difference Equations
- 8.3.1 First Order
- 8.3.2 Second Order
- 8.3.3 Linear Systems
- 8.3.4 Z Transforms
- 8.3.5 Orthogonal Polynomials
- 8.4 Dynamical Systems
- 8.4.1 1D Maps
- 8.4.2 2D Maps
- 8.4.3 Lyapunov Exponents
- 8.4.4 Bifurcations
- 8.4.5 Fractals
- 8.4.6 Differentiable Dynamics
- 8.4.7 Conservative Dynamics
- 8.4.8 Chaos
- 8.4.9 Complex Dynamical Systems
- 8.1 Ordinary Differential Equations
- 9.0 Statistics and Probability
- 9.1 Data Collection
- 9.1.1 Experimental Design
- 9.1.2 Sampling and Surveys
- 9.1.3 Data and Measurement Issues
- 9.2 Data Summary and Presentation
- 9.2.1 Summary Statistics
- 9.2.1.1 Measures of Central Tendencies
- 9.2.1.2 Measures of Spread
- 9.2.2 Data Representation
- 9.2.2.1 Graphs and Plots
- 9.2.2.2 Tables
- 9.2.1 Summary Statistics
- 9.3 Statistical Inference and Techniques
- 9.3.1 Sampling Distributions
- 9.3.2 Regression and Correlation
- 9.3.3 Confidence Intervals
- 9.3.4 Hypothesis Tests
- 9.3.5 Statistical Quality Control
- 9.3.6 Non-parametric Techniques
- 9.3.7 Multivariate Techniques
- 9.3.8 Survival Analysis
- 9.3.9 Bayesian Statistics
- 9.4 Probability
- 9.4.1 Elementary Probability
- 9.4.1.1 Sample Space and Sets
- 9.4.1.2 General Rules
- 9.4.1.3 Combinations and Permutations
- 9.4.1.4 Random Variables
- 9.4.2 Univariate Distributions
- 9.4.2.1 Discrete Distributions
- 9.4.2.2 Continuous Distributions
- 9.4.2.3 Expected Value
- 9.4.3 Limit Theorems
- 9.4.3.1 Central Limit Theorem
- 9.4.3.2 Law of Large Numbers
- 9.4.4 Multivariate Distributions
- 9.4.4.1 Joint
- 9.4.4.2 Conditional
- 9.4.4.3 Expectations
- 9.4.5 Stochastic Processes
- 9.4.5.1 Brownian Motion
- 9.4.5.2 Markov Chains
- 9.4.5.3 Queuing Theory
- 9.4.6 Probability Measures
- 9.4.7 Simulation
- 9.4.1 Elementary Probability
- 9.1 Data Collection
- 10.0 Applied Mathematics
- 10.1 Mathematical Physics
- 10.2 Mathematical Economics
- 10.3 Mathematical Biology
- 10.4 Mathematics for Business
- 10.5 Engineering Mathematics
- 10.6 Mathematical Sociology
- 10.7 Mathematics for Social Sciences
- 10.8 Mathematics for Computer Science
- 10.9 Mathematics for Humanities
- 10.10 Consumer Mathematics
- 11.0 Mathematics History
- 11.1 General
- 11.2 Famous Problems
- 11.3 Biographies of Mathematicians
Inspirations
Quanta's Map
sourceDomain of Science Map

University of Michigan

Swarthmore

Binghamton

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