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Concepts12

Groups

📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

Category

🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginnerIntermediate
⚙️AlgorithmIntermediate

Overflow Prevention Techniques

Integer overflow happens when a computed value exceeds the range of its type; in C++ this silently wraps for unsigned and is undefined for signed, so prevention is crucial.

#overflow prevention#long long#__int128+11
∑MathAdvanced

Burnside's Lemma

Burnside's Lemma says the number of distinct objects up to a symmetry group equals the average number of objects fixed by each symmetry.

#burnside's lemma
Advanced
Filtering by:
#gcd
#cauchy-frobenius
#polya enumeration
+12
∑MathIntermediate

Linear Diophantine Equations

A linear Diophantine equation ax + by = c has integer solutions if and only if gcd(a, b) divides c.

#linear diophantine#extended euclidean algorithm#gcd+12
∑MathAdvanced

Pollard's Rho Factorization

Pollard's Rho is a randomized algorithm that finds a non-trivial factor of a composite integer by walking a pseudorandom sequence modulo n and extracting a factor with a gcd.

#pollard's rho#integer factorization#cycle detection+10
∑MathIntermediate

Euler's Totient Function

Euler's Totient Function φ(n) counts how many integers from 1 to n are coprime with n.

#euler totient#phi function#coprime count+12
∑MathIntermediate

Modular Arithmetic Basics

Modular arithmetic is arithmetic with wrap-around at a fixed modulus m, like numbers on a clock.

#modular arithmetic#mod#modulo c+++12
∑MathIntermediate

Modular Inverse

A modular inverse of a modulo m is a number a_inv such that a × a_inv ≡ 1 (mod m).

#modular inverse#extended euclidean algorithm#fermats little theorem+12
∑MathIntermediate

Chinese Remainder Theorem

The Chinese Remainder Theorem (CRT) reconstructs an integer from its remainders modulo pairwise coprime moduli and guarantees a unique answer modulo the product.

#chinese remainder theorem#crt#modular arithmetic+12
∑MathIntermediate

Prime Factorization

Prime factorization expresses any integer greater than 1 as a product of primes raised to powers, uniquely up to ordering.

#prime factorization#trial division#spf sieve+12
∑MathIntermediate

Extended Euclidean Algorithm

The Extended Euclidean Algorithm finds integers x and y such that ax + by = gcd(a, b) while also computing gcd(a, b).

#extended euclidean algorithm#bezout coefficients#gcd+12
∑MathIntermediate

GCD and Euclidean Algorithm

The greatest common divisor (gcd) of two integers is the largest integer that divides both without a remainder.

#gcd#euclidean algorithm#extended euclidean+12
🗂️Data StructureIntermediate

Sparse Table

A Sparse Table is a static range-query data structure that preprocesses an array in O(n \log n) time and answers many queries in O(1) time.

#sparse table#range minimum query#rmq+12