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