Fast Fourier Transform (FFT)
A radix-2 FFT guide: DFT normalization, butterfly decomposition, polynomial convolution, and the limits of floating-point integer results.
Subjects
Mathematics
Reviewed articles explicitly assigned to Mathematics. Only articles published in English appear here.
Bolzano–Weierstrass Theorem
A proof that every bounded sequence in finite-dimensional Euclidean space has a convergent subsequence, with the compactness distinction.
Max-flow min-cut theorem
A proof of the max-flow min-cut theorem using residual reachability, with a concrete flow-and-cut certificate.
Monotone Convergence Theorem
The monotone convergence theorem for real sequences, proved from the least-upper-bound property and illustrated with examples.
Nested Interval Theorem
The nested interval theorem: completeness gives a common point, while shrinking interval lengths make it unique.
Analysis Foundations: Metric Spaces, Order, and Limits
A grouped reference to algebraic, metric, order, completeness, and limit concepts used across introductory analysis.
Mathematical Foundations: A Compact Glossary
A compact, grouped reference to 19 foundational ideas in sets, algebraic structures, functions, and cardinality, with examples.
Bézout's Identity: Integers and Polynomials over a Field
Why the gcd of two integers is an integer linear combination, with a least-positive-combination proof and the field-only polynomial analogue.
The Euclidean Algorithm: Computing a Greatest Common Divisor
A proof and worked trace of the Euclidean algorithm, including its nonnegative-input C++ implementation and logarithmic step count.
Flow network
Learn feasible flows, residual forward and reverse arcs, augmenting paths, cut bounds, and when Ford–Fulkerson terminates.
De Moivre's Formula for Integer Powers
De Moivre's formula for positive, zero, and negative integer powers, proved with Euler's formula and illustrated by a cube calculation.