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Concepts140

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

All Beginner Intermediate Advanced

∑MathIntermediate

Binomial Theorem and Identities

The binomial theorem expands (x + y)^n into a sum of terms using binomial coefficients that count how many ways to choose k items from n.

#binomial theorem#binomial coefficient#pascal's triangle+12

∑MathIntermediate

Stars and Bars

Stars and Bars counts the ways to distribute n identical items into k distinct bins using combinations.

#stars and bars

#combinatorics

#binomial coefficient

+12

∑MathAdvanced

Primitive Roots

A primitive root modulo n is a number g that cycles through all units modulo n when you repeatedly multiply by g, so its multiplicative order equals \(\varphi(n)\).

#primitive root#multiplicative order#euler totient+10

∑MathAdvanced

Discrete Logarithm

The discrete logarithm problem asks for x such that g^x ≡ h (mod p) in a multiplicative group modulo a prime p.

#discrete logarithm#baby-step giant-step#pollard rho dlp+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

Miller-Rabin Primality Test

Miller–Rabin is a fast primality test that uses modular exponentiation to detect compositeness with very high reliability.

#miller-rabin#primality test#probable prime+11

∑MathIntermediate

Permutations and Combinations

Permutations count ordered selections, while combinations count unordered selections.

#permutations#combinations#binomial coefficient+12

∑MathAdvanced

Quadratic Residues

A quadratic residue modulo an odd prime p is any a for which x^2 ≡ a (mod p) has a solution; exactly half of the nonzero classes are residues.

#quadratic residues#legendre symbol#euler criterion+12

∑MathAdvanced

Möbius Function and Inversion

The Möbius function μ(n) is 0 if n has a squared prime factor, otherwise it is (-1)^k where k is the number of distinct prime factors.

#mobius function#mobius inversion#dirichlet convolution+12

∑MathAdvanced

Divisor Function Sums

Summing the divisor function d(i) up to n equals counting lattice points under the hyperbola xy ≤ n, which can be done in O(√n) using floor-division blocks.

#divisor function#euler totient#mobius function+11

∑MathIntermediate

Multiplicative Functions

A multiplicative function is an arithmetic function f with f(mn) = f(m)f(n) whenever gcd(m, n) = 1.

#multiplicative function#dirichlet convolution#mobius function+12

∑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