A/B Testing Statistics
Complete A/B testing methodology: sample size calculation, statistical power, minimum detectable effect, sequential testing, and the peeking problem.
Bayesian Statistics
Bayes theorem, prior and posterior distributions, MCMC sampling, credible intervals, and how Bayesian inference differs from frequentist approaches.
Calculus Essentials
Derivatives, integrals, the chain rule, partial derivatives, gradients — the calculus toolkit every data scientist and ML engineer needs.
Combinatorics & Probability
Permutations, combinations, the binomial theorem, counting rules, and fundamental probability concepts for problem solving and algorithm analysis.
Confidence Intervals
Z-intervals, t-intervals, bootstrap confidence intervals, margin of error, and proper interpretation of confidence levels.
Correlation & Covariance
Pearson and Spearman correlation, covariance matrices, interpreting correlation strength, and common correlation fallacies.
Descriptive Statistics
Complete guide to measures of central tendency, dispersion, and shape — mean, median, mode, variance, standard deviation, skewness, and kurtosis.
Dimensionality Reduction
PCA, t-SNE, UMAP — when to use each, explained variance, perplexity tuning, and practical dimensionality reduction strategies.
Discrete Mathematics
Discrete math essentials — propositional logic, predicates, quantifiers, proof techniques, relations, functions, and induction for computer science.
Experimental Design
Randomization, blocking, factorial designs, power analysis, sample size determination, and the fundamentals of sound experimental methodology.
Graph Theory Basics
Graph theory fundamentals — vertices, edges, directed/undirected, weighted graphs, BFS/DFS traversal, Dijkstra shortest path, and graph representations.
Hypothesis Testing
Complete framework for statistical hypothesis testing: null/alternative hypotheses, p-values, t-tests, chi-square, ANOVA, and Type I/II errors.
Information Theory
Entropy, KL divergence, mutual information, cross-entropy, and their critical applications in machine learning and data science.
Linear Algebra Basics
Essential linear algebra for data science and ML: vectors, matrices, eigenvalues, SVD, dot products, and norms.
Markov Chains
Transition matrices, steady state distributions, absorbing states, PageRank algorithm, and Markov chain applications in data science.
Monte Carlo Methods
Monte Carlo integration, importance sampling, MCMC, Gibbs sampling, and simulation-based techniques for estimation and inference.
Number Theory Basics
Number theory fundamentals — prime numbers, GCD/LCM, modular arithmetic, Euler's theorem, RSA basics, and primality testing for cryptography.
Optimization Methods
Gradient descent variants, SGD, Adam optimizer, convex vs non-convex optimization, loss landscapes, and practical tips for training machine learning models.
Probability Distributions
Complete reference for normal, binomial, Poisson, and exponential distributions with formulas, parameters, and use cases.
Regression Analysis
Linear, logistic, and polynomial regression: formulas, R-squared interpretation, residual analysis, and the core assumptions every modeler must verify.
Set Theory Basics
Set theory fundamentals — union, intersection, complement, Venn diagrams, cardinality, power sets, and set notation for discrete math and data science.
Statistical Distributions Cheatsheet
Every major probability distribution: PDF/PMF formulas, parameters, mean, variance, and real-world use cases in one comprehensive reference.
Statistical Power Analysis
Statistical power, Type I/II errors, effect size (Cohen's d), sample size determination, and power curves for A/B testing and experimental design.
Statistical Tests Guide
When to use each statistical test: parametric vs non-parametric, assumptions, test selection flowchart, and common pitfalls in test interpretation.
Time Series Analysis
ARIMA modeling, stationarity testing, ACF/PACF interpretation, decomposition, and forecasting methodologies for time-dependent data.