🎓How I Study AIHISA
📖Read
📄Papers📰Blogs🎬Courses
💡Learn
🛤️Paths📚Topics💡Concepts🎴Shorts
🎯Practice
📝Daily Log🎯Prompts🧠Review
SearchSettings
How I Study AI - Learn AI Papers & Lectures the Easy Way

Concepts532

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

AllBeginnerIntermediateAdvanced
∑MathAdvanced

Generating Functions - EGF

Exponential generating functions (EGFs) encode a sequence (a_n) as A(x) = \sum_{n \ge 0} a_n \frac{x^n}{n!}, which naturally models labeled combinatorial objects.

#exponential generating function#egf#binomial convolution+11
∑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
2627282930
#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
∑MathAdvanced

Pólya Enumeration

Pólya Enumeration Theorem generalizes Burnside’s Lemma by turning counting under symmetry into a polynomial substitution problem.

#pólya enumeration#cycle index#burnside lemma+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
∑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#cauchy-frobenius#polya enumeration+12
∑MathAdvanced

Partition Function

The partition function p(n) counts the number of ways to write n as a sum of positive integers where order does not matter.

#partition function#integer partitions#euler pentagonal theorem+11
∑MathAdvanced

Generating Functions - OGF

An ordinary generating function (OGF) encodes a sequence (a_n) as a formal power series A(x) = \sum_{n \ge 0} a_n x^n.

#ordinary generating function#ogf#coefficient extraction+12
∑MathAdvanced

Stirling Numbers of First Kind

Stirling numbers of the first kind count permutations by their number of cycles and connect power polynomials to rising/falling factorials.

#stirling numbers of the first kind#unsigned cycle numbers#signed stirling numbers+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
∑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#set partitions#bell numbers+12