
Mathematics: Mapping iLumina to Math NSDL
These columns show the mapping of the iLumina taxonomy to the Mathematics NSDL taxonomy.
iLumina Mathematics Classification Scheme  Mathematics NSDL Classification Scheme  
6.1.0  Numbers and Computation  1.0.0  Numbers and Computation  
Number Concepts  1.1.0  Number Concepts  
Arithmetic  1.2.0  Arithmetic  
Patterns and Sequences  1.3.0  Patterns and Sequences  
Measurement  1.4.0  Measurement  
6.2.0  Algebra  3.1.0  Algebra  
Graphing Techniques  3.1.1  Graphing Techniques  
Algebraic Manipulation  3.1.2  Algebraic Manipulation  
Functions  3.1.3  Functions  
Equations  3.1.4  Equations  
Inequalities  3.1.5  Inequalities  
Matrices  3.1.6  Matrices  
Sequences and Series  3.1.7  Sequences and Series  
Algebraic Proof  3.1.8  Algebraic Proof  
6.3.0  Trigonometry  5.9.0  Trigonometry  
Angles  5.9.1  Angles  
Trigonometric Functions  5.9.2  Trigonometric Functions  
Inverse Trigonometric Functions  5.9.3  Inverse Trigonometric Functions  
Trigonometric Identities  5.9.4  Trigonometric Identities  
Trigonometric Equations  5.9.5  Trigonometric Equations  
Roots of Unity  5.9.6  Roots of Unity  
Spherical Trigonometry  5.9.7  Spherical Trigonometry  
Fractal Geometry  5.10.0  Fractal Geometry  
6.4.0  Plane Geometry  5.2.0  Plane Geometry  
Geometric Proof  5.1.0  Geometric Proof  
Measurement  5.2.1  Measurement  
Lines and Planes  5.2.2  Lines and Planes  
Angles  5.2.3  Angles  
Triangles  5.2.4  Triangles  
Polygons  5.2.5  Polygons  
Circles  5.2.6  Circles  
Patterns  5.2.7  Patterns  
Transformations  5.2.8  Transformations  
6.5.0  Solid Geometry  5.3.0  Solid Geometry  
Dihedral Angles  5.3.1  Dihedral Angles  
Spheres  5.3.2  Spheres  
Cones  5.3.3  Cones  
Cylinders  5.3.4  Cylinders  
Pyramids  5.3.5  Pyramids  
Prisms  5.3.6  Prisms  
Polyhedra  5.3.7  Polyhedra  
6.6.0  Analytic Geometry  5.4.0  Analytic Geometry  
Cartesian Coordinates  5.4.1  Cartesian Coordinates  
Lines  5.4.2  Lines  
Circles  5.4.3  Circles  
Planes  5.4.4  Planes  
Conics  5.4.5  Conics  
Polar Coordinates  5.4.6  Polar Coordinates  
Parametric Curves  5.4.7  Parametric Curves  
Surfaces  5.4.8  Surfaces  
Distance Formula  5.4.9  Distance Formula  
6.7.0  Discrete Mathematics  4.0.0  Discrete Mathematics  
Cellular Automata  4.1.0  Cellular Automata  
Combinatorics  4.2.0  Combinatorics  
Game Theory  4.3.0  Game Theory  
Algorithms  4.4.0  Algorithms  
Recursion  4.5.0  Recursion  
Graph Theory  4.6.0  Graph Theory  
Linear Programming  4.7.0  Linear Programming  
Order and Lattices  4.8.0  Order and Lattices  
Theory of Computation  4.9.0  Theory of Computation  
Chaos  4.10  Chaos  
6.8.0  Data Sets  9.1.0  Data  
Data Collection  9.1.1  Data Collection  
Data Representation  9.1.2  Data Representation  
6.9.0  Single Variable Calculus  6.1.0  Single Variable  
Functions  6.1.1  Functions  
Limits  6.1.2  Limits  
Continuity  6.1.3  Continuity  
Differentiation  6.1.4  Differentiation  
Integration  6.1.5  Integration  
Series  6.1.6  Series  
6.10.0  Multivariate Calculus  6.2.0  Several Variables  
Functions of Several Variables  6.2.1  Functions of Several Variables  
Limits  6.2.2  Limits  
Continuity  6.2.3  Continuity  
Partial Derivatives  6.2.4  Partial Derivatives  
Multiple Integrals  6.2.5  Multiple Integrals  
Taylor Series  6.2.6  Taylor Series  
6.11.0  Advanced Calculus  6.3.0  Advanced Calculus  
Vector Valued Functions  6.3.1  Vector Valued Functions  
Line Integrals  6.3.2  Line Integrals  
Surface Integrals  6.3.3  Surface Integrals  
Stokes Theorem  6.3.4  Stokes Theorem  
Curvilinear Coordinates  6.3.5  Curvilinear Coordinates  
Linear Spaces  6.3.6  Linear Spaces  
Fourier Series  6.3.7  Fourier Series  
Orthogonal Functions  6.3.8  Orthogonal Functions  
Tensor Calculus  6.4.0  Tensor Calculus  
Calculus of Variations  6.5.0  Calculus of Variations  
Operational Calculus  6.6.0  Operational Calculus  
6.12.0  Logic and Foundations  2.0.0  Logic and Foundations  
Logic  2.1.0  Logic  
Set Theory  2.2.0  Set Theory  
Computability and Decidability  2.3.0  Computability and Decidability  
Model Theory  2.4.0  Model Theory  
6.13.0  Linear Algebra  3.2.0  Linear Algebra  
Systems of Linear Equations  3.2.1  Systems of Linear Equations  
Matrix Algebra  3.2.2  Matrix Algebra  
Vectors in R3  3.2.3  Vectors in R3  
Vector Spaces  3.2.4  Vector Spaces  
Linear Transformations  3.2.5  Linear Transformations  
Eigenvalues and Eigenvectors  3.2.6  Eigenvalues and Eigenvectors  
Inner Product Spaces  3.2.7  Inner Product Spaces  
6.14.0  Abstract Algebra  3.3.0  Abstract Algebra  
Groups  3.3.1  Groups  
Rings and Ideals  3.3.2  Rings and Ideals  
Fields  3.3.3  Fields  
Galois Theory  3.3.4  Galois Theory  
Multilinear Algebra  3.3.5  Multilinear Algebra  
Category Theory  3.5.0  Category Theory  
KTheory  3.6.0  KTheory  
Homological Algebra  3.7.0  Homological Algebra  
6.15.0  Number Theory  3.4.0  Number Theory  
Integers  3.4.1  Integers  
Primes  3.4.2  Primes  
Congruences  3.4.3  Congruences  
Diophantine Equations  3.4.4  Diophantine Equations  
Irrational Numbers  3.4.5  Irrational Numbers  
Coding Theory  3.4.7  Coding Theory  
Cryptography  3.4.8  Cryptography  
Modular Arithmetic  3.8.0  Modular Arithmetic  
6.16.0  Advanced Geometry  
Projective Geometry  5.5.0  Projective Geometry  
Differential Geometry  5.6.0  Differential Geometry  
Algebraic Geometry  5.7.0  Algebraic Geometry  
6.17.0  Topology  5.8.0  Topology  
Point Set Topology  5.8.1  Point Set Topology  
General Topology  5.8.2  General Topology  
Differential Topology  5.8.3  Differential Topology  
Algebraic Topology  5.8.4  Algebraic Topology  
6.18.0  Difference Equations  8.3.0  Difference Equations  
First Order  8.3.1  First Order  
Second Order  8.3.2  Second Order  
Linear Systems  8.3.3  Linear Systems  
Z Transforms  8.3.4  Z Transforms  
Orthogonal Polynomials  8.3.5  Orthogonal Polynomials  
6.19.0  Dynamical Systems  8.4.0  Dynamical Systems  
1D Maps  8.4.1  1D Maps  
2D Maps  8.4.2  2D Maps  
Lyapunov Exponents  8.4.3  Lyapunov Exponents  
Bifurcations  8.4.4  Bifurcations  
Fractals  8.4.5  Fractals  
Differentiable Dynamics  8.4.6  Differentiable Dynamics  
Conservative Dynamics  8.4.7  Conservative Dynamics  
Chaos  8.4.8  Chaos  
Complex Dynamical Systems  8.4.9  Complex Dynamical Systems  
6.20.0  Ordinary Differential Equations  8.1.0  Ordinary Differential Equations  
First Order  8.1.1  First Order  
Second Order  8.1.2  Second Order  
Linear Oscillations  8.1.3  Linear Oscillations  
Nonlinear Oscillations  8.1.4  Nonlinear Oscillations  
Systems of Differential Equations  8.1.5  Systems of Differential Equations  
Sturm Liouville Problems  8.1.6  Sturm Liouville Problems  
Special Functions  8.1.7  Special Functions  
Power Series Methods  8.1.8  Power Series Methods  
Laplace Transforms  8.1.9  Laplace Transforms  
6.21.0  Partial Differential Equations  8.2.0  Partial Differential Equations  
First Order  8.2.1  First Order  
Elliptic  8.2.2  Elliptic  
Parabolic  8.2.3  Parabolic  
Hyperbolic  8.2.4  Hyperbolic  
Integral Transforms  8.2.5  Integral Transforms  
Integral Equations  8.2.6  Integral Equations  
Potential Theory  8.2.7  Potential Theory  
Nonlinear Equations  8.2.8  Nonlinear Equations  
Symmetries and Integrability  8.2.9  Symmetries and Integrability  
6.22.0  Real Analysis  7.1.0  Real Analysis  
Metric Spaces  7.1.1  Metric Spaces  
Convergence  7.1.2  Convergence  
Continuity  7.1.3  Continuity  
Differentiation  7.1.4  Differentiation  
Integration  7.1.5  Integration  
Measure Theory  7.1.6  Measure Theory  
6.23.0  Complex Analysis  7.2.0  Complex Analysis  
Convergence  7.2.1  Convergence  
Infinite Series  7.2.2  Infinite Series  
Analytic Functions  7.2.3  Analytic Functions  
Integration  7.2.4  Integration  
Contour Integrals  7.2.5  Contour Integrals  
Conformal Mappings  7.2.6  Conformal Mappings  
Several Complex Variables  7.2.7  Several Complex Variables  
6.24.0  Functional Analysis  7.6.0  Functional Analysis  
Hilbert Spaces  7.6.1  Hilbert Spaces  
Banach Spaces  7.6.2  Banach Spaces  
Topological Spaces  7.6.3  Topological Spaces  
Locally Convex Spaces  7.6.4  Locally Convex Spaces  
Bounded Operators  7.6.5  Bounded Operators  
Spectral Theorem  7.6.6  Spectral Theorem  
Unbounded Operators  7.6.7  Unbounded Operators  
Harmonic Analysis  7.7.0  Harmonic Analysis  
Global Analysis  7.8.0  Global Analysis  
6.25.0  Numerical Analysis  7.3.0  Numerical Analysis  
Computer Arithmetic  7.3.1  Computer Arithmetic  
Solutions of Equations  7.3.2  Solutions of Equations  
Solutions of Systems  7.3.3  Solutions of Systems  
Interpolation  7.3.4  Interpolation  
Numerical Differentiation  7.3.5  Numerical Differentiation  
Numerical Integration  7.3.6  Numerical Integration  
Numerical Solutions of ODEs  7.3.7  Numerical Solutions of ODEs  
Numerical Solutions of PDEs  7.3.8  Numerical Solutions of PDEs  
6.26.0  Statistics  9.2.0  Statistics  
Elementary Statistics  9.2.1  Elementary Statistics  
Sampling  9.2.2  Sampling  
Linear Regression  9.2.3  Linear Regression  
Nonlinear Regression  9.2.4  Nonlinear Regression  
Queuing Theory  9.2.5  Queuing Theory  
Bayesian Statistics  9.2.6  Bayesian Statistics  
Confidence Testing  9.2.7  Confidence Testing  
6.27.0  Probability  9.3.0  Probability  
Elementary Probability  9.3.1  Elementary Probability  
Random Variables  9.3.2  Random Variables  
Limit Theorems  9.3.3  Limit Theorems  
Brownian Motion  9.3.4  Brownian Motion  
Markov Chains  9.3.5  Markov Chains  
Probability Measures  9.3.6  Probability Measures  
Stochastic Processes  9.3.7  Stochastic Processes  
6.28.0  Signal Analysis  7.5.0  Signal Analysis  
Sampling Theory  7.5.1  Sampling Theory  
Filters  7.5.2  Filters  
Noise  7.5.3  Noise  
Data Compression  7.5.4  Data Compression  
Image Processing  7.5.5  Image Processing  
6.29.0  Integral Transforms  7.4.0  Integral Transforms  
Fourier Transforms  7.4.1  Fourier Transforms  
Laplace Transforms  7.4.2  Laplace Transforms  
Hankel Transforms  7.4.3  Hankel Transforms  
Wavelets  7.4.4  Wavelets  
Other Transforms  7.4.5  Other Transforms  
6.30.0  Applied Mathematics  10.0.0  Applied Mathematics  
Mathematical Physics  10.1.0  Mathematical Physics  
Mathematical Economics  10.2.0  Mathematical Economics  
Mathematical Biology  10.3.0  Mathematical Biology  
Mathematics for Business  10.4.0  Mathematics for Business  
Engineering Mathematics  10.5.0  Engineering Mathematics  
Mathematical Sociology  10.6.0  Mathematical Sociology  
Mathematics for Social Sciences  10.7.0  Mathematics for Social Sciences  
Mathematics for Computer Science  10.8.0  Mathematics for Computer Science  
Mathematics for Humanities  10.9.0  Mathematics for Humanities  
Consumer Mathematics  10.10.0  Consumer Mathematics  
6.31.0  Mathematics History  11.0.0  Mathematics History  
General  11.1.0  General  
Famous Problems  11.2.0  Famous Problems  
Biographies of Mathematicians  11.3.0  Biographies of Mathematicians 
Developed by: Dr.
Russell Herman and Dr. Gabriel Lugo based upon the Mathematics
taxonomy developed in 2002 by the Math NSDL
Taxonomy Committee of the Mathematical Sciences Conference Group on Digital
Educational Resources.
iLumina Digital Library Form ims_math.htm v1.01