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Number Theory

Rational numbers in decimal

Rational numbers in decimal — In decimal representation, rational numbers either terminate after a finite number of digits or produce a repeating sequence. Conversely, any repeating decimal can be converted

Continued Fractions

Continued Fractions —

First-order methods for stochastic optimization

First-order methods for stochastic optimization — Optimization, particularly deterministic (convex) optimization, is essential to many learning algorithms (regression, support vector machines, matrix factorization etc). This post discusses first-order/gradient-based optimization approaches that