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Concepts98

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
∑MathIntermediate

Vectors & Vector Spaces

A vector is an element you can add and scale, and a vector space is any collection of such elements closed under these operations.

#vector space#basis#span+12
∑MathIntermediate

Legendre's Formula

Legendre's formula gives the exponent of a prime p in n! by summing how many multiples of p, p^2, p^3, ... are ≤ n.

#legendre's formula#p-adic valuation
45678
Advanced
#binomial divisibility
+10
∑MathIntermediate

Harmonic Lemma

The Harmonic Lemma says that the values of \lfloor n/i \rfloor only change about 2\sqrt{n} times, so you can iterate those value blocks in O(\sqrt{n}) instead of O(n).

#harmonic lemma#integer division trick#block decomposition+12
∑MathIntermediate

Sprague-Grundy Theorem

Sprague–Grundy theory turns every finite impartial game (normal play) into an equivalent Nim heap with a size called the Grundy number.

#sprague-grundy#grundy number#mex+11
∑MathIntermediate

Game Theory - Nim

Nim is a two-player impartial game with several piles where a move removes any positive number of stones from exactly one pile.

#nim#game theory#xor+11
∑MathIntermediate

Game Theory - Calculation Techniques

Sprague–Grundy theory converts any impartial, normal-play game into an equivalent Nim heap using a Grundy number.

#sprague-grundy#grundy numbers#nim-sum+12
∑MathIntermediate

Variance and Covariance

Variance measures how spread out a random variable is around its mean, while covariance measures how two variables move together.

#variance#covariance#standard deviation+12
∑MathIntermediate

Linearity of Expectation Applications

Linearity of expectation says the expected value of a sum equals the sum of expected values, even if the variables are dependent.

#linearity of expectation#indicator variables#expected inversions+12
∑MathIntermediate

Expected Value

Expected value is the long-run average outcome of a random variable if you could repeat the experiment many times.

#expected value#linearity of expectation#indicator variables+12
∑MathIntermediate

Bayes' Theorem

Bayes' Theorem tells you how to update the probability of a hypothesis after seeing new evidence.

#bayes' theorem#posterior probability#prior probability+11
∑MathIntermediate

Probability Fundamentals

Probability quantifies uncertainty by assigning numbers between 0 and 1 to events in a sample space.

#probability#sample space#conditional probability+12
∑MathIntermediate

Catalan Numbers

Catalan numbers count many 'non-crossing' and 'well-formed' structures like balanced parentheses, binary trees, Dyck paths, and triangulations of a convex polygon.

#catalan numbers#balanced parentheses#dyck paths+12