BOJ 10803 — Making Squares: A Verified Recurrence Bound
Archived technical note: BOJ 10803 — Making Squares: A Verified Recurrence Bound.
Category
Math
10 articles.
2022-05-31
Fast Fourier Transform (FFT)
A radix-2 FFT guide: DFT normalization, butterfly decomposition, polynomial convolution, and the limits of floating-point integer results.
Bolzano–Weierstrass Theorem
A proof that every bounded sequence in finite-dimensional Euclidean space has a convergent subsequence, with the compactness distinction.
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.
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.