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Concepts5

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📐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

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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∑MathIntermediate

Probability Axioms & Rules

Kolmogorov’s axioms define probability as a measure on events: non-negativity, normalization, and countable additivity.

#kolmogorov axioms#probability measure#sample space+12
∑MathAdvanced

Stirling Numbers of Second Kind

Stirling numbers of the second kind S(n,k) count how many ways to split n labeled items into k non-empty, unlabeled groups.

#stirling numbers of the second kind
Advanced
Filtering by:
#inclusion-exclusion
#set partitions
#bell numbers
+12
∑MathIntermediate

Derangements

A derangement is a permutation with no element left in its original position, often written as !n or D(n).

#derangement#subfactorial#inclusion-exclusion+11
∑MathIntermediate

Inclusion-Exclusion Principle

The Inclusion-Exclusion Principle (IEP) corrects overcounting by alternately adding and subtracting sizes of intersections of sets.

#inclusion-exclusion#derangements#surjections+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