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Tag: foundations
64 items with this tag.
Sep 12, 2026
M.1 Linear Algebra & Matrices
foundations
linear-algebra
matrices-decompositions
svd
index-hub
Sep 12, 2026
M.1.1 Linear Algebra from Zero
foundations
linear-algebra
intuition
eigen-decomposition
Sep 12, 2026
M.1.2 Vector Spaces, Matrices & the Geometry of Returns
foundations
linear-algebra
vector-spaces
linear-independence
gram-schmidt
Sep 12, 2026
M.1.3 Linear Systems & Matrix Decompositions (LU, Cholesky)
foundations
linear-algebra
gaussian-elimination
cholesky
lu-decomposition
Sep 12, 2026
M.1.4 Eigenvalues & Covariance
foundations
linear-algebra
spectral-theorem
covariance
positive-semidefinite
jacobi
Sep 12, 2026
M.1.5 SVD, PCA & Linear Regression
foundations
linear-algebra
svd
pca
least-squares
ridge
Sep 12, 2026
M.1.6 Advanced Extensions
foundations
linear-algebra
random-matrix-theory
marchenko-pastur
condition-number
ill-conditioning
Sep 12, 2026
M.2 Calculus & Optimization
foundations
calculus
optimization
convexity
index-hub
Sep 12, 2026
M.2.1 Calculus & Optimization from Zero
foundations
calculus
intuition
derivative
Sep 12, 2026
M.2.2 Single-Variable Calculus
foundations
calculus
taylor-series
single-variable
Sep 12, 2026
M.2.3 Multivariable Calculus
foundations
calculus
gradient
hessian
jacobian
Sep 12, 2026
M.2.4 Constrained Optimization
foundations
optimization
lagrange-multiplier
kkt
markowitz
Sep 12, 2026
M.2.5 Gradient Descent & Newton's Method
foundations
optimization
gradient-descent
newton-method
convergence
Sep 12, 2026
M.2.6 Advanced Extensions
foundations
optimization
convexity
duality
lasso
applications
Sep 12, 2026
M.3 Probability & Measure Theory
foundations
probability-and-measure-theory
sigma-algebra
martingales
conditional-expectation
index-hub
Sep 12, 2026
M.3.1 Probability & Measure Theory from Zero
foundations
probability-and-measure-theory
intuition
law-of-large-numbers
central-limit-theorem
Sep 12, 2026
M.3.2 Probability Spaces & Filtrations
foundations
probability-and-measure-theory
sigma-algebra
filtration
measurability
Sep 12, 2026
M.3.3 Distributions & Expectation
foundations
probability-and-measure-theory
random-variables
distributions
expectation
independence
Sep 12, 2026
M.3.4 Conditional Expectation
foundations
probability-and-measure-theory
conditional-expectation
tower-property
partial-averaging
Sep 12, 2026
M.3.5 Martingales
foundations
probability-and-measure-theory
martingales
risk-neutral-measure
radon-nikodym
Sep 12, 2026
M.3.6 Advanced Extensions
foundations
probability-and-measure-theory
measure-theory
radon-nikodym
convergence-theorems
lebesgue-integral
Oct 03, 2026
M.4 Stochastic Calculus
foundations
stochastic-calculus
brownian-motion
ito
girsanov
index-hub
Sep 12, 2026
M.4.1 Stochastic Calculus from Zero
foundations
stochastic-calculus
intuition
brownian-motion
Sep 12, 2026
M.4.2 Brownian Motion & Martingales
foundations
stochastic-calculus
brownian-motion
martingales
quadratic-variation
Sep 12, 2026
M.4.3 The Itô Integral & the Itô–Doeblin Lemma
foundations
stochastic-calculus
ito
doeblin
quadratic-variation
Sep 12, 2026
M.4.4 Stochastic Differential Equations & Simulation
foundations
stochastic-calculus
sde
simulation
vasicek
cir
euler
milstein
Sep 12, 2026
M.4.5 Girsanov's Theorem & the Risk-Neutral Measure
foundations
stochastic-calculus
girsanov
risk-neutral
radon-nikodym
market-price-of-risk
Sep 12, 2026
M.4.6 Advanced Extensions
foundations
stochastic-calculus
feynman-kac
martingale-representation
fundamental-theorems
completeness
Oct 03, 2026
M.5 Statistics & Inference
foundations
statistics-and-inference
point-estimation
hypothesis-testing
index-hub
Sep 12, 2026
M.5.1 Statistics & Inference from Zero
foundations
statistics-and-inference
intuition
sampling-distribution
law-of-large-numbers
Sep 12, 2026
M.5.2 Point Estimation
foundations
statistics-and-inference
maximum-likelihood
method-of-moments
bias-variance
cramer-rao
Sep 12, 2026
M.5.3 The CLT & Sampling
foundations
statistics-and-inference
central-limit-theorem
law-of-large-numbers
standard-error
sampling-distributions
Sep 12, 2026
M.5.4 Confidence Intervals & Hypothesis Testing
foundations
statistics-and-inference
confidence-intervals
hypothesis-testing
p-values
multiple-testing
Sep 12, 2026
M.5.5 Bias–Variance, Cross-Validation & Model Selection
foundations
statistics-and-inference
bias-variance
cross-validation
model-selection
overfitting
Sep 12, 2026
M.5.6 Advanced Extensions
foundations
statistics-and-inference
bootstrap
asymptotic-theory
backtesting
data-snooping
Sep 12, 2026
M.6 Econometrics & Time Series
foundations
econometrics-timeseries
arma-garch
index-hub
Sep 12, 2026
M.6.1 Econometrics & Time Series from Zero
foundations
econometrics-timeseries
intuition
returns
stationarity
Sep 12, 2026
M.6.2 Stationarity & ARMA Models
foundations
econometrics-timeseries
stationarity
arma
acf-pacf
Sep 12, 2026
M.6.3 Forecasting & Unit Roots
foundations
econometrics-timeseries
forecasting
unit-roots
adf
Sep 12, 2026
M.6.4 Volatility Modeling
foundations
econometrics-timeseries
garch
arch
volatility-clustering
Sep 12, 2026
M.6.5 Cointegration & Multivariate Models
foundations
econometrics-timeseries
cointegration
var
error-correction
Sep 12, 2026
M.6.6 Advanced Extensions
foundations
econometrics-timeseries
state-space
kalman-filter
markov-switching
Sep 12, 2026
M.7 Bayesian Statistics
foundations
bayesian-statistics
bayes-theorem
conjugate-priors
posterior-inference
mcmc
index-hub
Sep 12, 2026
M.7.1 Bayesian Statistics from Zero
foundations
bayesian-statistics
intuition
bayes-theorem
conjugate-priors
beta-bernoulli
Sep 12, 2026
M.7.2 Bayes' Theorem, Priors & Conjugate Families
foundations
bayesian-statistics
bayes-theorem
conjugate-priors
prior-specification
normal-normal
gamma-poisson
Sep 12, 2026
M.7.3 Posterior Inference
foundations
bayesian-statistics
posterior-inference
credible-interval
posterior-predictive
bayes-estimator
Sep 12, 2026
M.7.4 Bayesian Inference & Regularization
foundations
bayesian-statistics
regularization
ridge
lasso
map-estimation
shrinkage
Sep 12, 2026
M.7.5 Markov Chain Monte Carlo
foundations
bayesian-statistics
mcmc
metropolis-hastings
gibbs-sampling
convergence
ffbs
Sep 12, 2026
M.7.6 Advanced Extensions
foundations
bayesian-statistics
hierarchical-models
shrinkage
random-effects
empirical-bayes
applications
Sep 12, 2026
M.8 Numerical Methods
foundations
numerical-methods
finite-difference
monte-carlo
index-hub
Sep 12, 2026
M.8.1 Numerical Methods from Zero
foundations
numerical-methods
intuition
error-analysis
Sep 12, 2026
M.8.2 Finite-Difference Methods
foundations
numerical-methods
finite-difference
stability
pde
Sep 12, 2026
M.8.3 Monte Carlo
foundations
numerical-methods
monte-carlo
variance-reduction
sampling
Sep 12, 2026
M.8.4 Numerical Optimization & Root-Finding
foundations
numerical-methods
optimization
root-finding
newton
Sep 12, 2026
M.8.5 Numerical Linear Algebra
foundations
numerical-methods
linear-algebra
eigenvalues
conditioning
Sep 12, 2026
M.8.6 Advanced Extensions
foundations
numerical-methods
quasi-monte-carlo
mcmc
high-dimensional
Sep 12, 2026
M.9 Ergodicity & Statistical Mechanics
foundations
ergodicity
statistical-mechanics
kelly-criterion
ruin-theory
index-hub
Sep 12, 2026
M.9.1 Ergodicity from Zero
foundations
ergodicity
intuition
growth
Sep 12, 2026
M.9.2 Ensemble vs Time Averages
foundations
ergodicity
time-average
ensemble-average
law-of-large-numbers
Sep 12, 2026
M.9.3 Multiplicative Growth
foundations
growth-rate
volatility-drag
geometric-mean
log-utility
Sep 12, 2026
M.9.4 The Kelly Criterion
foundations
kelly-criterion
bet-sizing
log-utility
growth-optimal
Sep 12, 2026
M.9.5 Ruin & Drawdown
foundations
ruin-theory
drawdown
gamblers-ruin
overbetting
Sep 12, 2026
M.9.6 Advanced Extensions
foundations
kelly-criterion
portfolio-growth
estimation-error
ergodicity-economics
Sep 12, 2026
Math Foundations
foundations
mathematics
statistics
first-principles