Mathematics Study Notes

A single, navigable reference for the mathematics behind machine learning interviews: probability, inferential statistics, and linear algebra. Every page leads with intuition, keeps the formalism right beside it, and ends with the interview questions that topic tends to attract. Read a track in order, or jump straight to the page you need ten minutes before a screen.

How this site is organized

Three tracks, seven sections. The probability track moves from counting and conditioning, through random variables and distributions, into advanced probability theory, with a standalone distribution cheat sheet. The inference track turns probability into estimators, intervals, and tests. The linear algebra track is the computational language underneath regression, covariance, PCA, and optimization. Use the tabs at the top, or the map below.

The section graph

The arrows show prerequisites: follow them forward and nothing on a later page will surprise you.

flowchart TB
  Prob1["Probability Foundations<br/>counting, events, Bayes"]
  Prob2["Random Variables & Distributions<br/>discrete and continuous families"]
  Prob3["Advanced Probability<br/>multivariate, limits, Markov chains"]
  DistSheet["Distribution Cheat Sheet<br/>18-distribution lookup grid"]
  Infer1["Estimation & Inference<br/>MLE, confidence intervals, OLS"]
  Infer2["Hypothesis Testing & Bayesian<br/>tests, p-values, MAP"]
  LinearAlg["Linear Algebra for ML<br/>matrices, rank, decompositions"]

  Prob1 --> Prob2
  Prob2 --> Prob3
  Prob3 --> DistSheet
  Prob3 --> Infer1
  Infer1 --> Infer2
  LinearAlg --> Infer1
  LinearAlg --> Prob3

Reading paths

• Probability path: Foundations then Random Variables & Distributions then Advanced Probability then the Distribution Cheat Sheet.
• Inference path: Estimation & Inference then Hypothesis Testing & Bayesian Inference. This path leans on the probability sequence, especially distributions, the law of large numbers, the central limit theorem, and likelihood.
• Linear algebra support path: read Linear Algebra for ML in parallel with inference and ML topics. It supports ordinary least squares, principal component analysis, covariance, Markov matrices, optimization, pseudo-inverses, and the singular value decomposition.

The seven sections

Section	What it builds	Start here
Probability Foundations	Counting, conditioning, Bayes, paradoxes, random walks	Open
Random Variables & Distributions	Discrete and continuous families, expectation, variance	Open
Advanced Probability	Normal theory, moment-generating functions, covariance, limits, Markov chains	Open
Distribution Cheat Sheet	Side-by-side lookup of eighteen distributions	Open
Estimation & Inference	Likelihood, maximum likelihood estimation, bias, confidence intervals, ordinary least squares	Open
Hypothesis Testing & Bayesian Inference	Tests, p-values, errors, power, Bayesian estimation	Open
Linear Algebra for ML	Matrices, rank, definiteness, decompositions, matrix calculus	Open