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Basic Mathematics and Topics for Audio Engineers

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a work in progress.

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Basic Mathematics
Algebra
Abstract algebra
Calculus
Category theory
Commutative algebra
Aliasing
Anti-aliasing filter
Approximation theory
Balian–Low theorem
Band-pass filter
Bandlimiting
Baseband
Borel measure
Cheung–Marks theorem
Complex analysis
Compressed sensing
Computability theory
Conditional convergence
Continuous signal
Convex optimization
Convolution
Derivative
Differential equation
Diffusion equation
Digital-to-analog converter
Dirac comb
Dirac delta function
Discrete-time Fourier transform
Discrete-time signal
Distribution (mathematics)
Duality (mathematics)
Elementary algebra
Exponential type
Field (mathematics)
Final value theorem
Foundations of mathematics
Fourier analysis
Fourier series
Fourier transform
Frequency
Functional analysis
Fundamental theorem of algebra
Fundamental theorem of calculus
Geometric algebra
Geometric calculus
Geometric series
Group theory
Gödel's incompleteness theorems
Harmonic analysis
Heaviside step function
Hertz
Holomorphic function
Improper integral
Initial value theorem
Integral
Integral equation
Integral transform
Interpolation
Inverse Laplace transform
Laplace transform
Lebesgue integration
Linear algebra
Linearity
Locally integrable function
Low-pass filter
Mathematical analysis
Mathematical logic
Matrix (mathematics)
Measure (mathematics)
Mellin transform
Model theory
Moiré pattern
Moment (mathematics)
Multidimensional sampling
Multilinear algebra
Naive set theory
Necessity and sufficiency
Nonuniform sampling
Numerical stability
Nyquist frequency
Nyquist ISI criterion
Nyquist rate
Nyquist–Shannon sampling theorem
Operational calculus
Operator theory
Ordinary differential equation
Partial differential equation
Partial fraction decomposition
Pathological (mathematics)
Periodic function
Periodic summation
Poisson summation formula
Pole (complex analysis)
Potential theory
Probability density function
Probability measure
Proof theory
Real analysis
Reconstruction from zero crossings
Rectangular function
Recurrence relation
Ring theory
S transform
Sampling (signal processing)
Shannon–Hartley theorem
Signal (electrical engineering)
Sinc filter
Sinc function
Single-sideband modulation
Special functions
Spectrum
Step function
Time–frequency analysis
Topos
Two-sided Laplace transform
Undersampling
Universal algebra
Vector calculus
Vector-valued function
Whittaker–Shannon interpolation formula
Z-transform
Zero-order hold