Compendium

Math Library — Index

2 min read

Math Library — Index

Mathematical foundations referenced from Engineering / Robotics / Compute notes. Linear algebra, probability + statistics, calculus + ODE/PDE, optimization, discrete math + graph theory, numerical analysis, information theory.

  • Status: Tier 1 complete (2026-05-16). 19 deep notes.
  • Library structure: mirrors other libraries — Tier 1 deep + Tier 2 specialty + Tier 3 family indexes.

Subdomains

SubdomainExamples
Linear algebravectors, matrices, eigenvalues, SVD, PCA, tensors
Probability + statisticsrandom variables, distributions, hypothesis testing, Bayes, MCMC
Calculusderivatives, integrals, multivariate, vector calculus
ODEs + PDEslinear ODEs, nonlinear, BVP, Laplace, wave, heat
OptimizationLP, NLP, convex, gradient descent, evolutionary
Discrete mathcombinatorics, graph theory, complexity, recurrences
Numerical methodsinterpolation, integration, root-finding, FE, FD, FV
Information theoryentropy, mutual information, channel capacity
Logic + set theorypropositional, predicate, set operations
Number theoryprimes, modular arithmetic, crypto
Differential geometrymanifolds, Lie groups (robotics SO(3))
Signal processing mathFourier, Laplace, Z-transform, convolutions

Tier 1 — Complete (19 / 19, 2026-05-16)

StatusTopicFileLinesSubdomain
✅Linear algebra essentialslinear-algebra-essentials725linear-algebra
✅Numerical linear algebranumerical-linear-algebra541linear-algebra
✅SVD, PCA & spectral methodssvd-pca-spectral523linear-algebra
✅Eigenvalue problemseigenvalue-problems776linear-algebra
✅Multivariate calculusmultivariate-calculus829calculus
✅Tensor calculustensor-calculus483differential-geometry
✅Lie groups SO(3) & SE(3)lie-groups-so3-se3520differential-geometry
✅ODE numerical methodsode-numerical-methods535ode-pde
✅PDE methodspde-methods471ode-pde
✅Convex optimizationconvex-optimization742optimization
✅Gradient descent variantsgradient-descent-variants532optimization
✅Combinatorial optimizationcombinatorial-optimization339optimization
✅Probability fundamentalsprobability-fundamentals555probability
✅Probability distributions referenceprobability-distributions789probability
✅Bayesian inferencebayesian-inference789probability
✅MCMC & samplingmcmc-sampling490probability
✅Hypothesis testing & MLEhypothesis-testing-mle548probability
✅Stochastic calculus & SDEsstochastic-calculus561probability
✅Information theoryinformation-theory448information-theory
✅Reinforcement learning theoryreinforcement-learning-theory539machine-learning
✅FFT & spectral methodsfft-spectral475numerical
✅Graph theorygraph-theory614discrete-math

🎯 Math Tier 1 complete: 22 / 22 deep notes, ~12,820 lines.

Tier 2 — Specialty (14 done)

TopicFile
Algebraic geometry foundationsalgebraic-geometry-foundations
Functional analysisfunctional-analysis
Measure theory and integrationmeasure-theory-and-integration
Complex analysiscomplex-analysis
Number theorynumber-theory
Group theory and representationgroup-theory-and-representation
Gaussian processesgaussian-processes
Causal inferencecausal-inference
Time series & HMMtime-series-and-hmm
Variational inferencevariational-inference
Markov chains & HMMmarkov-chains-and-hmm
Riemannian optimizationriemannian-optimization
Copulas & dependencecopulas-and-dependence
Reinforcement learning theoryreinforcement-learning-theory

Planned: Kalman/EKF/UKF/particle (in Robotics), survival analysis, fractional calculus, ergodic theory.

Tier 3 — Family indexes (deferred)

  • Probability distribution zoo (continuous + discrete)
  • ODE/PDE solvers catalog
  • Numerical methods reference
  • Optimization algorithm taxonomy
  • Convolutional kernel zoo

Adjacent libraries

How to study this library

  • Learning paths — _learn_next — “if you’ve read X, learn Y next” recommendation graph plus five named multi-step tracks (ML researcher, Quant finance trader, Control engineer, Statistician, Pure mathematician).
  • Cross-cutting comparisons — two _compare_* notes that span the library: _compare_optimization-methods, _compare_probability-frameworks.

How to use

  1. Identify the subdomain.
  2. Open the Tier 1 deep note for the foundational concept.
  3. Cross-reference back into Engineering / Robotics / Compute for applied use cases.

39 items under this folder.