01
Harvard · Statistics 110
Probability, Stat 110
Joe Blitzstein · Harvard University
Models are probability machines. Loss functions, Naive Bayes, and how a model expresses uncertainty all come straight from here.
- Full lecture series
- Free textbook
- edX: 10 weeks, 5–10 hrs/week
- Free to audit
- Basics & FoundationsSample spaces, events, counting methods, story proofs
- Conditional ProbabilityConditioning, independence, Bayes' Rule
- Discrete Random VariablesPMFs, expectation, variance; Binomial, Negative Binomial, Poisson
- Continuous Random VariablesPDFs, CDFs; Normal, Uniform, Exponential, Beta, Gamma
- Expectation & TransformationsMoment generating functions, covariance, correlation, conditional expectation
- Multivariate DistributionsJoint, conditional and marginal distributions; Multinomial, Multivariate Normal
- Limit TheoremsLaw of Large Numbers, Central Limit Theorem
- Stochastic ProcessesMarkov chains, transition probabilities, stationary distributions, convergence
02
3Blue1Brown · YouTube series
Essence of Calculus
Grant Sanderson · 3Blue1Brown
Gradient descent and backpropagation are derivatives in disguise. This is the visual version that makes them click.
- 12 short videos
- Visual, no heavy algebra
- Free
- Introduction & Circle AreaSlicing a circle into rings to go from finite sums to continuous area
- LimitsWhat it means for one value to approach another
- DerivativesRate of change as the nudge shrinks to zero; sum, product and chain rules
- Integrals & the Fundamental TheoremArea under a curve; why differentiation and integration are inverses
- Advanced & Bonus TopicsTaylor series, divergence and curl, and the backpropagation calculus behind neural nets
03
3Blue1Brown · YouTube series
Essence of Linear Algebra
Grant Sanderson · 3Blue1Brown
Data, weights and embeddings are all vectors and matrices. This series shows matrices as transformations of space, which is how models actually use them.
- 16 short videos
- Visual, intuition-first
- Free
- VectorsPhysics, CS and maths views; addition and scalar multiplication
- Linear Combinations, Span & BasisHow scaling and adding vectors builds a span; basis vectors and coordinates
- Linear Transformations & MatricesFunctions that keep grid lines parallel and the origin fixed
- Matrix Multiplication as CompositionApplying one transformation after another
- 3D Linear TransformationsThe same ideas, extended to 3D space
- DeterminantsHow area or volume scales, orientation flips, dimensional collapse
- Inverse Matrices, Column Space & Null SpaceSolving Ax = v, and when an answer exists
- Nonsquare MatricesMapping between different dimensions
- Dot Products & DualityProjections and what a dot product really measures
- Cross ProductsAreas from cross products and their link to transformations
- Cramer's RuleSolving linear systems geometrically with determinants
- Change of BasisTranslating vectors and matrices between coordinate systems
- Eigenvectors & EigenvaluesVectors that only get scaled, never knocked off their span