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Mathematics:


 
iLumina Mathematics Classification Scheme
6.0.0 Mathematics
 
6.1.0 Numbers and Computation
Number Concepts
Arithmetic
Patterns and Sequences
Measurement
 
6.2.0 Algebra
Graphing Techniques
Algebraic Manipulation
Functions
Equations
Inequalities
Matrices
Sequences and Series
Algebraic Proof
 
6.3.0 Trigonometry
Angles
Trigonometric Functions
Inverse Trigonometric Functions
Trigonometric Identities
Trigonometric Equations
Roots of Unity
Spherical Trigonometry
Fractal Geometry
 
6.4.0 Plane Geometry
Geometric Proof
Measurement
Lines and Planes
Angles
Triangles
Polygons
Circles
Patterns
Transformations
 
6.5.0 Solid Geometry
Dihedral Angles
Spheres
Cones
Cylinders
Pyramids
Prisms
Polyhedra
 
6.6.0 Analytic Geometry
Cartesian Coordinates
Lines
Circles
Planes
Conics
Polar Coordinates
Parametric Curves
Surfaces
Distance Formula
 
6.7.0 Discrete Mathematics
Cellular Automata
Combinatorics
Game Theory
Algorithms
Recursion
Graph Theory
Linear Programming
Order and Lattices
Theory of Computation
Chaos
 
6.8.0 Data Sets
Data Collection
Data Representation
 
6.9.0 Single Variable Calculus
Functions
Limits
Continuity
Differentiation
Integration
Series
 
6.10.0 Multivariate Calculus
Functions of Several Variables
Limits
Continuity
Partial Derivatives
Multiple Integrals
Taylor Series
 
6.11.0 Advanced Calculus
Vector Valued Functions
Line Integrals
Surface Integrals
Stokes Theorem
Curvilinear Coordinates
Linear Spaces
Fourier Series
Orthogonal Functions
Tensor Calculus
Calculus of Variations
Operational Calculus
 
6.12.0 Logic and Foundations
Logic
Set Theory
Computability and Decidability
Model Theory
 
6.13.0 Linear Algebra
Systems of Linear Equations
Matrix Algebra
Vectors in R3
Vector Spaces
Linear Transformations
Eigenvalues and Eigenvectors
Inner Product Spaces
 
6.14.0 Abstract Algebra
Groups
Rings and Ideals
Fields
Galois Theory
Multilinear Algebra
Category Theory
K-Theory
Homological Algebra
 
6.15.0 Number Theory
Integers
Primes
Congruences
Diophantine Equations
Irrational Numbers
Coding Theory
Cryptography
Modular Arithmetic
 
6.16.0 Advanced Geometry
Projective Geometry
Differential Geometry
Algebraic Geometry
 
6.17.0 Topology
Point Set Topology
General Topology
Differential Topology
Algebraic Topology
 
6.18.0 Difference Equations
First Order
Second Order
Linear Systems
Z Transforms
Orthogonal Polynomials
 
6.19.0 Dynamical Systems
1D Maps
2D Maps
Lyapunov Exponents
Bifurcations
Fractals
Differentiable Dynamics
Conservative Dynamics
Chaos
Complex Dynamical Systems
 
6.20.0 Ordinary Differential Equations
First Order
Second Order
Linear Oscillations
Nonlinear Oscillations
Systems of Differential Equations
Sturm Liouville Problems
Special Functions
Power Series Methods
Laplace Transforms
 
6.21.0 Partial Differential Equations
First Order
Elliptic
Parabolic
Hyperbolic
Integral Transforms
Integral Equations
Potential Theory
Nonlinear Equations
Symmetries and Integrability
 
6.22.0 Real Analysis
Metric Spaces
Convergence
Continuity
Differentiation
Integration
Measure Theory
 
6.23.0 Complex Analysis
Convergence
Infinite Series
Analytic Functions
Integration
Contour Integrals
Conformal Mappings
Several Complex Variables
 
6.24.0 Functional Analysis
Hilbert Spaces
Banach Spaces
Topological Spaces
Locally Convex Spaces
Bounded Operators
Spectral Theorem
Unbounded Operators
Harmonic Analysis
Global Analysis
 
6.25.0 Numerical Analysis
Computer Arithmetic
Solutions of Equations
Solutions of Systems
Interpolation
Numerical Differentiation
Numerical Integration
Numerical Solutions of ODEs
Numerical Solutions of PDEs
 
6.26.0 Statistics
Elementary Statistics
Sampling
Linear Regression
Nonlinear Regression
Queuing Theory
Bayesian Statistics
Confidence Testing
 
6.27.0 Probability
Elementary Probability
Random Variables
Limit Theorems
Brownian Motion
Markov Chains
Probability Measures
Stochastic Processes
 
6.28.0 Signal Analysis
Sampling Theory
Filters
Noise
Data Compression
Image Processing
 
6.29.0 Integral Transforms
Fourier Transforms
Laplace Transforms
Hankel Transforms
Wavelets
Other Transforms
 
6.30.0 Applied Mathematics
Mathematical Physics
Mathematical Economics
Mathematical Biology
Mathematics for Business
Engineering Mathematics
Mathematical Sociology
Mathematics for Social Sciences
Mathematics for Computer Science
Mathematics for Humanities
Consumer Mathematics
 
6.31.0 Mathematics History
General
Famous Problems
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. See the  mapping to the Math NSDL taoxonomy.

iLumina Digital Library Form ims_math.htm v1.01



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