Glossary

773 terms defined across the curriculum, each linked to the lesson where it is developed. Use the search box; try minimal-pair drilling (Phase 0.5) on any confusable terms.

$L^p$ convergence: $\E|X_n-X|^p\to0$; mean-square is $p=2$. §7.6

Absolute convergence: ∑|a_n| converges; it implies convergence and permits rearrangement. §2.7

Acceptance–rejection: Sample from an easy proposal $g$, keep points with probability $f(x)/(Mg(x))$ to hit target $f$. §13.1

Adapted / non-anticipating: An integrand whose value at time t uses only information up to t (measurable w.r.t. the filtration). §9.1

Adapted process: $(X_n)$ with each $X_n$ $\F_n$-measurable: its value is known once time $n$ is reached. §7.7

Adapted process: $X_n$ is $\F_n$-measurable - known at time $n$. §8.2

ADF test: Augmented Dickey-Fuller: a hypothesis test whose null is a unit root (non-stationarity). §12.3

Adjacency matrix: $A_{ij}=1$ iff there is an edge $i\to j$; then $(A^n)_{ij}$ counts walks of length exactly $n$ from $i$ to $j$. §19.13

Adverse selection: The risk of trading against a better-informed counterparty; a component of the spread even absent costs. §16.2

Adverse selection: Losses from filling informed traders whose orders predict the next price move. §16.5

Adverse selection: The tendency to be filled by better-informed traders precisely when the price is about to move against you. §18.7

Affine function: A map $x\mapsto Ax+b$; both convex and concave, and it preserves convexity under composition. §10.1

AIC / BIC: Analytic scores balancing fit against parameter count; BIC penalizes complexity more heavily as $n$ grows. §11.3

Algebraic multiplicity: The multiplicity of $\lambda$ as a root of the characteristic polynomial. §4.4

Almgren–Chriss: The canonical mean–variance execution model with linear permanent/temporary impact and price risk. §16.4

Almgren–Chriss: A mean–variance framework trading expected impact cost against the variance of execution cost. §18.6

Almost everywhere: A property holding except on a null set; written ‘a.e.’ §6.2

Almost sure convergence: $\Prob(\lim_n \bar X_n=\mu)=1$; the whole random sequence settles, not just its distribution. §7.5

Almost sure convergence: $X_n\to X$ with probability 1. §7.6

Amdahl’s law: The bound on total speedup when you accelerate only part of a program: limited by the un-accelerated fraction. §17.5

Antiderivative: A function F with F′=f; unique up to an additive constant. §2.6

Antithetic variates: Pairing each draw $Z$ with its mirror $-Z$ so negatively-correlated payoffs average to a lower-variance estimate. §13.3

AR($p$): Autoregression: $X_t=\sum_{i=1}^p\phi_i X_{t-i}+\varepsilon_t$; today is a linear function of its own past plus a shock. §12.2

Arbitrage: A self-financing strategy with zero cost today and, tomorrow, a nonnegative payoff that is strictly positive with positive probability - risk-free profit. §14.1

Arbitrary-precision integer: Python’s int: exact, unbounded, cost grows with digit count ($O(d^2)$ schoolbook, $O(d^{1.585})$ Karatsuba for big $d$). §19.4

ARCH($q$: $\sigma_t^2=\omega+\sum_{i=1}^q\alpha_i r_{t-i}^2$; conditional variance driven by recent squared returns. §12.4

ARIMA($p,d,q$): An ARMA($p,q$) fitted to the series after differencing $d$ times: $\phi(L)(1-L)^d X_t=\theta(L)\varepsilon_t$. §12.3

ARMA($p,q$): Combines both: $\phi(L)X_t=\theta(L)\varepsilon_t$; parsimonious for series with both features. §12.2

Asian option: A path-dependent claim on the average price $\bar S=\tfrac1m\sum S_{t_j}$; no simple closed form under GBM, a natural Monte Carlo target. §13.5

Associativity: The reason this works at all: $A^{2m}=(A^m)^2$ requires only that matrix multiplication be associative, which it is. §19.13

Autocorrelation (ACF): $\rho(h)=\gamma(h)/\gamma(0)$; correlation at lag $h$, with $\rho(0)=1$. §12.1

Autocovariance: $\gamma(h)=\Cov(X_t,X_{t+h})$, a function of lag $h$ under stationarity. §12.1

Avellaneda–Stoikov: A stochastic-control model giving optimal bid/ask quotes under inventory risk over a horizon. §16.5

Bézout’s identity: There exist integers $x,y$ with $ax+by=\gcd(a,b)$; the gcd is the smallest positive integer combination of $a$ and $b$. §19.1

Back substitution: Solving $Ux=y$ bottom-to-top in $O(n^2)$ work. §5.2

Backtest overfitting: Selecting a strategy by searching many variants, so the winner's performance is largely luck (selection bias). §11.7

Backtest overfitting: Selecting a strategy from many trials so its performance is largely luck; apparent Sharpe inflated by the search. §12.6

Backtracking: DFS over partial solutions; extend, test feasibility, and undo. The gain comes entirely from failing FAST. §19.10

Backward induction: Pricing a tree by computing terminal payoffs and rolling one-period risk-neutral values back to the root. §14.2

Backward stability: An algorithm is backward stable if its computed answer is the exact answer to a slightly perturbed input. §5.1

Bagging: Bootstrap AGGregatING: average many trees fit on bootstrap resamples to cut variance. §11.6

Base case: The smallest instance you verify directly; without it the whole argument collapses. §1.4

Baseline: A simple benchmark the model must beat to be worth its complexity (e.g. buy-and-hold, zero-signal). §18.8

Basis: A linearly independent spanning set; every vector has unique coordinates in it. §4.1

Bayes classifier: Assign to the class with the highest posterior $\Prob(G=k\mid x)$; the theoretical error-minimizing rule. §11.5

Bayes’ theorem: $\Prob(A\mid B)=\Prob(B\mid A)\Prob(A)/\Prob(B)$; inverts the direction of conditioning. §7.3

Bell number: $B_n=\sum_k S(n,k)$: all set partitions of an $n$-set. $B_0..B_5=1,1,2,5,15,52$. §19.11

Best approximation: No fraction with denominator $\le k_k$ is closer to $x$ than $h_k/k_k$. Convergents are the ONLY such fractions. §19.12

Best bid / best ask: The highest resting buy price and lowest resting sell price; their gap is the spread. §16.1

BFS: Breadth-first search from a source; visits vertices in order of edge-count distance, giving shortest paths in UNWEIGHTED graphs. $O(V+E)$. §19.9

Bias: The systematic error $\E[\hat\theta]-\theta$; zero bias means correct on average across resamples. §11.1

Bias controls: Procedures that remove survivorship, look-ahead, and multiple-testing bias from the study. §18.8

Bid–ask spread: The gap $P_a-P_b$; the round-trip cost of immediacy and the market maker’s gross compensation. §16.2

Bid–ask spread: The gap between the best buy and sell quotes; the market maker’s gross compensation per round trip. §18.7

Bidirectional recall: Practicing both symbol→meaning and meaning→symbol (and equation↔concept). §0.5

Big-O: $f=O(g)$ iff $\exists C,n_0:\ f(n)\le Cg(n)\ \forall n\ge n_0$. An upper bound - it says nothing about tightness. §19.14

Big-Theta: $f=\Theta(g)$ iff $f=O(g)$ AND $f=\Omega(g)$. This is what you usually mean when you say ‘the complexity is’. §19.14

Bijection principle: Two finite sets have the same size iff a bijection exists between them. Every clean counting proof is secretly a bijection. §19.5

Binary exponentiation: Square-and-multiply: $a^b$ from the binary digits of $b$ using $\le 2\log_2 b$ modular multiplications. §19.3

Binary search on the answer: When $P(x)$ is monotone in $x$, find the threshold in $O(\log\text{range})$ evaluations. Also called parametric search. §19.10

Binding constraint: One satisfied with equality at the optimum, so its gradient enters the stationarity condition. §3.5

Binomial coefficient: $\binom nk=\frac{n!}{k!(n-k)!}$: the number of $k$-subsets of an $n$-set; also the coefficient of $x^k$ in $(1+x)^n$. §19.5

Bitmask: An integer whose $i$-th bit records membership of element $i$. Union = OR, intersection = AND, symmetric difference = XOR, complement = XOR with the full mask. §19.8

Black–Scholes formula: Closed-form European option price under GBM with constant $\sigma$ and $r$. §18.3

Black–Scholes PDE: The PDE $V_t+\tfrac12\sigma^2S^2V_{SS}+rSV_S-rV=0$ governing any European derivative under GBM. §14.4

BLUE: Best Linear Unbiased Estimator: minimum variance among all linear unbiased estimators. §11.2

Boosting: Sequentially adding weak learners, each fit to the current residuals/gradient, reducing bias. §11.6

Borel sigma-algebra: The smallest sigma-algebra containing all open sets; the natural domain for measuring on $\mathbb{R}$. §6.2

Boundary case: An input at the edge of validity (zero volatility, expiry $T=0$, empty array) where naive code often breaks. §17.2

Bounded sequence: There is M with |a_n| ≤ M for all n. §1.5

Box–Muller transform: A pair of uniforms mapped to a pair of independent standard normals via polar coordinates. §13.1

Branch-and-bound: Backtracking + an admissible bound on the best completion; prune any branch whose bound is worse than the incumbent. §19.10

Broadcasting: NumPy’s rule for combining arrays of different shapes by virtually stretching size-1 dimensions, with no data copy. §17.1

Brownian motion: A process $(B_t)_{t\ge0}$ with $B_0=0$, independent stationary Gaussian increments, and continuous paths. §8.3

Brownian motion: A process $W_t$ with $W_0=0$, independent Gaussian increments $W_t-W_s\sim\Normal(0,t-s)$, and continuous paths. §18.2

Butterfly arbitrage: A violation where the implied risk-neutral density goes negative; forbidden. §15.5

Cache locality: Data laid out contiguously so the CPU cache is used well; a major reason contiguous arrays beat pointer-chasing. §17.5

Calendar arbitrage: A violation where total variance decreases with maturity for fixed moneyness; forbidden. §15.5

Calibration: Choosing model parameters/functions so model prices match all quoted option prices. §15.3

CART: Classification And Regression Trees: recursive binary splits chosen to most reduce an impurity measure. §11.6

Cartesian product: The set A×B of all ordered pairs (a,b) with a in A and b in B; ordered means (a,b) ≠ (b,a) in general. §1.1

Catalan number: $C_n=\frac1{n+1}\binom{2n}{n}$: counts balanced bracketings, binary trees, monotone lattice paths below the diagonal, triangulations. §19.6

Catastrophic cancellation: Loss of significant digits when subtracting two nearly equal, individually rounded numbers. §5.1

Catastrophic cancellation: Subtracting two nearly equal inexact numbers: the leading digits cancel, promoting tiny relative errors into huge ones. §19.4

Cauchy sequence: A sequence whose terms get arbitrarily close to each other: $d(x_m,x_n)\to0$. §6.1

CDF: $F_X(x)=\Prob(X\le x)$: non-decreasing, right-continuous, with limits 0 and 1. §7.1

Central limit theorem: For i.i.d. with mean $\mu$, variance $\sigma^2$, $\sqrt n(\bar X_n-\mu)/\sigma\Rightarrow\Normal(0,1)$. §7.6

Central limit theorem: Normalized sums of i.i.d. finite-variance variables converge in distribution to a normal. §18.2

Chain rule: (f∘g)′(x) = f′(g(x))·g′(x); differentiate outer, keep inner, times inner′. §2.3

Chapman-Kolmogorov: $P^{(m+n)}=P^{(m)}P^{(n)}$; $n$-step probabilities are matrix powers $P^n$. §8.1

Characteristic function: $\phi_X(t)=\E[e^{itX}]$; always exists, uniquely determines the law. §7.4

Characteristic function: $\E[e^{iu\ln S_T}]$; known in closed form for Heston, enabling Fourier pricing. §15.4

Characteristic polynomial: $p(\lambda)=\det(A-\lambda I)$, whose roots are the eigenvalues. §4.3

Characteristic polynomial: $x^k-c_1x^{k-1}-\cdots-c_k=0$; its roots $r_i$ give the basis solutions $r_i^n$ (times $n^j$ for a root of multiplicity $j+1$). §19.6

Chebyshev inequality: $\Prob(|X-\mu|\ge k\sigma)\le 1/k^2$; a distribution-free spread bound. §7.2

Chinese Remainder Theorem: For pairwise coprime $n_1..n_k$, the map $x\mapsto(x\bmod n_i)$ is a ring isomorphism $\Z/N\Z\cong\prod\Z/n_i\Z$, $N=\prod n_i$. §19.3

Cholesky decomposition: Factoring a symmetric positive-definite $\Sigma=LL^\top$ with $L$ lower-triangular; used for correlated draws. §18.1

Cholesky factor: Lower-triangular $L$ with positive diagonal such that $A=LL^\top$. §5.4

Chunk: A single retrievable unit built from previously separate pieces (e.g. ‘integration by parts’ as one move). §0.1

Class imbalance: When one class is rare (defaults, crashes); accuracy is dominated by the majority and hides model quality. §11.5

Closed form: A non-recursive formula giving a_n directly from n. §1.4

Cointegration: Two or more $I(1)$ series whose linear combination is $I(0)$ (stationary): a shared stochastic trend / long-run equilibrium. §12.6

Column space: The range $\operatorname{col}(A)=\{Ax\}$; its dimension is the rank. §4.2

Compact: A set for which every open cover has a finite subcover; in $\mathbb{R}^n$, closed and bounded. §6.1

Companion matrix: The $k\times k$ matrix that shifts a state vector of the last $k$ terms and appends the new one; its characteristic polynomial IS the recurrence’s. §19.13

Compilation: Translating source to machine code ahead of run time, so no interpreter overhead is paid per operation. §17.5

Complete market: Every claim can be replicated; then the price is unique and equals its discounted $\mathbb{Q}$-expectation. §14.2

Complete market: One in which every contingent claim is replicable by a self-financing strategy; then prices are unique. §14.3

Complete space: A metric space in which every Cauchy sequence converges to a point of the space. §6.1

Composition: An ORDERED sum. There are $2^{n-1}$ compositions of $n$ - a much easier count than $p(n)$, and a common source of confusion. §19.11

Concavity: f″>0 means convex (cup up); f″<0 means concave (cap down). §2.5

Concept-to-equation: Recalling the formula from the idea (‘variance of a sum of independent vars’ → formula). §0.5

Condition number: How much a problem amplifies relative input error; for solving $Ax=b$ it is $\kappa(A)=\lVert A\rVert\,\lVert A^{-1}\rVert$. §5.1

Condition number: For a quadratic, $\kappa=\lambda_{\max}/\lambda_{\min}$ of the Hessian; large $\kappa$ means slow zig-zag descent. §10.4

Condition number: How much a solution amplifies input error; large $\kappa$ warns of numerical instability. §18.1

Conditional expectation: $\E[X\mid\mathcal{G}]$: the $\mathcal{G}$-measurable random variable matching $X$’s integral on every $\mathcal{G}$-event. §7.3

Conditional probability: $\Prob(A\mid B)=\Prob(A\cap B)/\Prob(B)$ for $\Prob(B)\gt 0$. §7.3

Conditional variance: $\sigma_t^2=\Var(r_t\mid\mathcal F_{t-1})$, the variance given the past; time-varying in ARCH/GARCH. §12.4

Confidence interval: A random interval $\hat\theta_N\pm z\,s/\sqrt{N}$ that covers $\theta$ with the stated probability as $N\to\infty$. §13.2

Congruence: $a\equiv b\pmod n$ iff $n\mid a-b$; an equivalence relation whose classes are the $n$ residues. §19.3

Conjugate gradients: An iterative solver for symmetric positive-definite systems converging in terms of $\sqrt{\kappa}$. §5.5

Consistency: A sequence of estimators with $\hat\theta_n\to\theta$ in probability as $n\to\infty$. §11.1

Constraint set: The feasible region $\{x: g(x)=c\}$ over which $f$ is optimized. §3.5

Continued fraction: $[a_0;a_1,a_2,\dots]=a_0+\cfrac{1}{a_1+\cfrac{1}{a_2+\cdots}}$ with $a_0\in\Z$ and $a_i\ge1$ integers. §19.12

Continuity: A map with $x_n\to x\Rightarrow f(x_n)\to f(x)$; equivalently preimages of open sets are open. §6.1

Continuity at c: f is continuous at c when lim_{x→c} f(x)=f(c): the limit exists and equals the value. §2.1

Continuous compounding: Growth governed by dA/dt=rA, giving A(t)=A_0 e^{rt}. §2.2

Control variate: A correlated quantity $C$ with known mean $\E[C]$ used to correct the estimator: $Y-b(C-\E[C])$. §13.3

Convergence: (a_n) converges to L if its terms are eventually arbitrarily close to L; written a_n → L. §1.5

Convergence in distribution: $X_n\Rightarrow X$ if $F_{X_n}(x)\to F_X(x)$ at every continuity point of $F_X$. §7.6

Convergence in probability: $\bar X_n\to\mu$ if $\Prob(|\bar X_n-\mu|\gt \varepsilon)\to0$ for every $\varepsilon\gt 0$. §7.5

Convergence in probability: $X_n\xrightarrow{p}X$ if $\Prob(|X_n-X|\gt \varepsilon)\to0$. §7.6

Convergent: The rational $h_k/k_k$ obtained by truncating after $a_k$. Convergents alternate around $x$ and are in lowest terms automatically. §19.12

Converse / contrapositive: Of P⇒Q: converse is Q⇒P; contrapositive is ¬Q⇒¬P (logically equivalent to the original). §1.2

Convex function: One whose graph lies below its chords; equivalently $H\succeq 0$ everywhere for twice-differentiable $f$. §3.4

Convex function: A function whose domain is convex and whose graph lies below its chords: $f(\theta x+(1-\theta)y)\le\theta f(x)+(1-\theta)f(y)$. §10.1

Convex program: An optimization problem with convex objective and convex feasible set. §10.2

Convex set: A set $C$ containing the whole segment between any two of its points: $x,y\in C\Rightarrow\theta x+(1-\theta)y\in C$ for $\theta\in[0,1]$. §10.1

Convexity: (1/P) d²P/dy², the second-order curvature correction to duration. §2.4

Convolution: The law of $X+Y$ for independent $X,Y$; its transform is the product $\phi_X\phi_Y$. §7.4

Convolution: $[x^n]A(x)B(x)=\sum_{k}a_kb_{n-k}$ - the algebraic shadow of ‘split the structure into two independent parts’. §19.6

Coprime: $\gcd(a,b)=1$. Coprimality is what makes modular inverses, CRT, and Farey/Pell arguments work. §19.1

Correlated normals: A vector $X=\mu+LZ$ built from i.i.d. standard normals $Z$ so that $\Cov(X)=LL^\top=\Sigma$. §5.4

Correlation $\rho$: Correlation between the spot and variance shocks; its sign sets the skew direction. §15.4

Counterexample: A single instance that refutes a universal claim; disproves ‘for all’ statements. §1.3

Coupling: The degree to which one module depends on the internals of another; tight coupling makes changes ripple. §17.4

Covariance function: $\Cov(B_s,B_t)=\min(s,t)$. §8.3

Covariance function: $c(s,t)=\Cov(X_s,X_t)$; for BM, $c(s,t)=\min(s,t)$. §8.5

Covariance matrix: $\Sigma=\E[(X-\mu)(X-\mu)^\top]$; symmetric PSD, encoding all variances and covariances. §4.6

Covariance matrix: Symmetric positive-semidefinite $\Sigma$ with $\Sigma_{ij}=\Cov(X_i,X_j)$. §5.4

Covariance matrix $\Sigma$: PSD matrix of asset return covariances; $w^\top\Sigma w$ is portfolio variance. §10.5

Critical point: A point where f′=0 or f′ is undefined; the only candidates for interior extrema. §2.5

Critical point: A point where $\nabla f=0$ (or the gradient fails to exist); a candidate extremum. §3.4

Crossover point: The $n$ beyond which an asymptotically better algorithm actually beats a worse one with a smaller constant. It is often much larger than you expect. §19.14

CRRA utility: Constant relative risk aversion $u(W)=W^{1-\gamma}/(1-\gamma)$ with risk-aversion parameter $\gamma\gt 0$. §14.5

Cut property: For any partition of $V$ into two nonempty parts, the cheapest edge crossing the cut belongs to some MST. This one lemma proves both Kruskal and Prim. §19.9

d1, d2: The standardized moneyness terms $d_{1,2}=\tfrac{\ln(S/K)+(r\pm\tfrac12\sigma^2)T}{\sigma\sqrt T}$. §14.4

Data leakage: Information from outside the training fold (or from the future) contaminating the fit, inflating measured performance. §11.7

Data leakage: Information from the test period (or future) contaminating training, inflating apparent performance. §18.5

Data pipeline: An ordered set of stages - ingest, clean, transform, store, serve - each with a defined input, output, and guarantee. §17.6

Data snooping / overfitting: Selecting a strategy after many trials so it fits noise; the reported in-sample performance is upward-biased. §16.6

Decision boundary: The set where two classes are equally probable; linear for logistic and LDA, quadratic for QDA. §11.5

Defective matrix: One lacking a full eigenbasis (some eigenvalue’s geometric < algebraic multiplicity); not diagonalizable. §4.4

Definite integral: ∫_a^b f dx = limit of Riemann sums as the mesh → 0; the signed area under f. §2.6

Deliberate practice: Focused practice on well-defined sub-skills just beyond current ability, with immediate feedback and correction, guided by known effective methods. §0.3

Delta Δ: Sensitivity of the option value to the underlying, $\partial V/\partial S$; the hedge ratio. §15.1

Delta-hedged portfolio: Long the option, short $\Delta=V_S$ shares; instantaneously risk-free, so it must earn $r$. §14.4

Delta-hedging: Continuously holding $-\Delta$ units of the underlying so the portfolio is instantaneously insensitive to $S$. §15.1

Depth: The quantity available at each price level; how much you can trade before moving the price. §16.1

Derangement: A permutation with no fixed point; $D_n=n!\sum_{k=0}^n(-1)^k/k!\approx n!/e$. §19.5

Derivative: f′(x)=lim_{h→0}(f(x+h)−f(x))/h when the limit exists; the instantaneous rate. §2.2

Design matrix: The $n\times p$ matrix $X$ of predictors (often with a leading column of ones for the intercept). §11.2

Desirable difficulty: A struggle that slows short-term performance but improves long-term retention and transfer. §0.2

Determinant: The signed factor $\det A$ by which $A$ scales oriented volume; zero iff $A$ is singular. §4.3

DFS: Depth-first search; the natural tool for connectivity, cycle detection, topological order, and articulation points. $O(V+E)$. §19.9

Diagonalizable: $A=PDP^{-1}$ with $D$ diagonal; the columns of $P$ are eigenvectors. §4.4

Difference quotient: (f(x+h)−f(x))/h, the average rate of change / secant slope over a step h. §2.2

Differencing: The transform $\nabla X_t=X_t-X_{t-1}=(1-L)X_t$ that removes a unit root / linear trend. §12.3

Differentiable: Having a derivative at the point; requires the secant slopes to converge from both sides. §2.2

Diffuse mode: A relaxed, associative brain state that connects distant ideas; where many insights consolidate. §0.1

Diffusion (volatility): The $dW$ coefficient; the local standard deviation rate. §9.2

Diffusive scaling: $\mathrm{sd}(S_n)=\sqrt n$: displacement grows like the square root of time. §8.2

Dijkstra: Shortest paths from a source with NON-NEGATIVE weights: repeatedly settle the nearest unsettled vertex. $O((V+E)\log V)$ with a binary heap. §19.9

Dimension: The number of vectors in any basis - an invariant of the space. §4.1

Direct proof: Assume the hypothesis P and derive the conclusion Q by a chain of valid steps. §1.3

Directional derivative: The rate $D_u f=\nabla f\cdot u$ of change along a unit vector $u$. §3.2

Dirichlet function: The indicator of the rationals; Riemann-nonintegrable but Lebesgue-integrable with integral 0. §6.3

Discounted price: The price divided by the money-market account, $\tilde S_t=S_t/R^t$; martingale-ness of $\tilde S$ under $\mathbb{Q}$ encodes no-arbitrage. §14.2

Discrepancy: A measure of how far a point set deviates from perfect uniformity; QMC error is bounded by discrepancy via Koksma–Hlawka. §13.5

Discretization bias: The systematic error from replacing the continuous SDE by a finite-step scheme; it does not vanish as $N\to\infty$ at fixed $\Delta t$. §13.4

Distribution (law): The pushforward measure $\mu_X(B)=\Prob(X\in B)$ on $\R$; all a random variable’s probabilistic content. §7.1

Divergence: Failure to converge to any finite L; e.g. oscillation or growth without bound. §1.5

Divides: $d\mid n$ means $n=dk$ for some integer $k$. Note $d\mid 0$ for every $d$, and only $0\mid 0$. §19.1

Division algorithm: For $a\in\Z,\ b\gt 0$ there exist unique $q,r$ with $a=qb+r$ and $0\le r\lt b$. §19.1

Dominated convergence (DCT): If $f_n\to f$ a.e. and $|f_n|\le g\in L^1$, then $\int f_n\to\int f$. §6.4

Dominating function: An integrable $g$ bounding all $|f_n|$; the hypothesis that licenses DCT. §6.4

Donsker’s theorem: The rescaled random walk $S_{\lfloor nt\rfloor}/\sqrt n$ converges in distribution to Brownian motion. §8.3

Double integral: The limit $\iint_R f\,dA$ of Riemann sums of $f$ over a plane region $R$. §3.3

Drift: The $dt$ coefficient of an Itô process; the local mean rate of change. §9.2

DRY (Don’t Repeat Yourself): Every piece of knowledge has a single, authoritative representation; duplication of knowledge, not just code, is the enemy. §17.4

dtype: The element type of an array (e.g. float64, int64); mixing or defaulting to object silently kills performance. §17.1

Dual function: The infimum $g(\lambda,\nu)=\inf_x L(x,\lambda,\nu)$; concave, and a lower bound on the optimum. §10.3

Dupire equation: The PDE expressing $\sigma_{\text{loc}}^2$ in terms of strike/maturity derivatives of the call surface. §15.3

Duration: −(1/P) dP/dy, the first-order sensitivity of a bond price to its yield. §2.4

Effective degrees of freedom: For ridge, $\sum_j d_j^2/(d_j^2+\lambda)\le p$; complexity falls smoothly as $\lambda$ rises. §11.4

Effective spread: $2|P_{\text{trade}}-\text{mid}|$; the realized round-trip cost, often below the quoted spread. §16.2

Effective vol: The observation that $\sigma_{\text{imp}}$ behaves like an average of $\sigma_{\text{loc}}$ along paths to the strike. §15.3

Efficacy vs. plausibility: Whether a technique works in controlled tests, vs. whether it merely sounds mechanistically reasonable. §0.4

Efficient frontier: The set of trajectories with minimal expected cost for each level of cost variance. §16.4

Eigenbasis: A basis of the space consisting entirely of eigenvectors of $A$. §4.4

Eigenspace: The subspace $\ker(A-\lambda I)$ of all eigenvectors for a given $\lambda$ (plus 0). §4.3

Eigenvalue: The scalar $\lambda$ in $Av=\lambda v$; roots of the characteristic polynomial. §4.3

Eigenvalue growth: If $A$ is diagonalisable with eigenvalues $\lambda_i$, then $a_n=\sum_i c_i\lambda_i^n$ - the characteristic-root formula of 19.6, in matrix clothing. §19.13

Eigenvector: A nonzero $v$ with $Av=\lambda v$; a direction the map only stretches. §4.3

Elastic net: A blend $\alpha\|\beta\|_1+(1-\alpha)\|\beta\|_2^2$ combining lasso sparsity with ridge stability under collinearity. §11.4

Environment pin: An exact record of package versions (e.g. a lockfile) so the same code runs the same everywhere. §17.3

Epigraph: The set $\{(x,t):f(x)\le t\}$ above the graph; $f$ is convex iff its epigraph is a convex set. §10.1

Epsilon-delta: ∀ε>0 ∃δ>0: 0<|x−c|<δ ⇒ |f(x)−L|<ε. §2.1

Epsilon-N definition: ∀ε>0 ∃N such that n≥N ⇒ |a_n − L| < ε. §1.5

Equation-to-concept: Reading a formula and stating what it means and when it applies. §0.5

Equivalence relation: A reflexive, symmetric and transitive relation; it carves a set into disjoint equivalence classes. §1.1

Equivalent martingale measure: A measure $\Q\sim\Prob$ under which discounted prices are martingales; its existence is no-arbitrage. §8.5

Equivalent martingale measure (EMM): A probability $\mathbb{Q}$ equivalent to $\Prob$ (same null sets) under which discounted asset prices are martingales; also called a risk-neutral measure. §14.3

Equivalent measures: $\Prob\sim\Q$: they agree on which events have probability zero (mutually absolutely continuous). §8.5

Equivalent measures: Two probability measures $\Prob,\mathbb{Q}$ that agree on which events have probability zero (same null sets). §9.4

Equivalent measures: Two measures with the same events of probability zero; they agree on what is possible, disagree on how likely. §14.3

Error log: A running record of mistakes with their causes, used to schedule targeted retraining. §0.3

Error-correction model: A representation where changes respond to the lagged equilibrium error: $\Delta y_t=\alpha(y_{t-1}-\beta x_{t-1})+\dots$. §12.6

Escape of mass: Failure of interchange when probability/mass drifts to infinity or spikes, e.g. $n\mathbf{1}_{(0,1/n)}$. §6.4

Estimator: A function $\hat\theta=T(X_1,\dots,X_n)$ of the data used to approximate an unknown parameter; itself a random variable. §11.1

Euclid’s lemma: If $p$ is prime and $p\mid ab$ then $p\mid a$ or $p\mid b$. This, not existence, is the hard half of unique factorization. §19.2

Euclidean space: The set $\R^n$ of ordered n-tuples with vector addition, scalar multiplication, and the dot product. §3.1

Euler–Maruyama: The discretization $X_{k+1}=X_k+a\,\Delta t+b\sqrt{\Delta t}\,Z$, $Z\sim\Normal(0,1)$. §9.3

Euler–Maruyama: The first-order scheme $X_{k+1}=X_k+a(X_k)\,\Delta t+b(X_k)\,\Delta W_k$ with $\Delta W_k\sim\Normal(0,\Delta t)$. §13.4

Euler’s product: $\sum_{n\ge0}p(n)x^n=\prod_{k\ge1}\frac{1}{1-x^k}$: one factor per part size, each contributing a geometric series of multiplicities. §19.11

Euler’s theorem: For $\gcd(a,n)=1$: $a^{\varphi(n)}\equiv1\pmod n$; so exponents may be reduced mod $\varphi(n)$. §19.3

Evaluation vs. endorsement: Reviewing a claim (possibly to debunk it) is not the same as recommending it. §0.4

Evidence classification: A rubric rating a claim by the strength and convergence of the evidence supporting it, from strong to contradicted. §0.4

Executive summary: A concise, honest statement of question, method, result, uncertainty, and limitations. §18.8

Expanding schedule: Review intervals that grow (1d, 3d, 7d, …) as an item is repeatedly recalled - the basis of SR. §0.2

Expectation: $\E[X]=\int_\Omega X\,d\Prob=\int_\R x\,d\mu_X$; the Lebesgue integral / probability-weighted average. §7.2

Expected utility: Ranking gambles by $\E[u(W)]$ for an increasing concave $u$; concavity encodes risk aversion. §14.5

Experiment tracking: Logging each run’s config, code version, data hash, and metrics so a result maps back to its inputs. §17.3

Explained variance: The eigenvalue $\lambda_i$ of $\Sigma$, the variance captured by component $i$. §4.7

Explained variance ratio: The share $\lambda_j/\sum_k\lambda_k$ of total variance captured by component $j$. §11.7

Exponential martingale: The density process $Z_t=\exp(-\int_0^t\theta\,dW-\tfrac12\int_0^t\theta^2 du)$. §9.4

Fatou's lemma: For $f_n\ge0$, $\int\liminf f_n\le\liminf\int f_n$; a one-sided inequality, always valid. §6.4

Feasible set: The set of $x$ satisfying all constraints; convex when constraints are convex/affine. §10.2

Feedback loop: The cycle attempt → evaluate → correct → retry that drives skill gains; its speed and accuracy set the learning rate. §0.3

Feller condition: $2\kappa\theta\ge\xi^2$: guarantees the variance process stays strictly positive. §15.4

Fermat’s little theorem: For prime $p$ and $p\nmid a$: $a^{p-1}\equiv1\pmod p$. Hence $a^{-1}\equiv a^{p-2}$. §19.3

Fermat’s theorem: If f has a local extremum at an interior point where it is differentiable, then f′=0 there. §2.5

Feynman–Kac: The identity: the solution of a linear parabolic PDE equals an expectation over a diffusion path. §9.5

Fill intensity: The arrival rate of market orders hitting a quote, decreasing in how far the quote is from the mid. §16.5

Filtering vs smoothing: Filtering uses data up to $t$; smoothing uses the whole sample to re-estimate past states. §12.5

Filtration: An increasing family $\F_0\subseteq\F_1\subseteq\cdots$ of sigma-algebras; $\F_n$ is the information available at time $n$. §7.7

Filtration: Increasing sigma-algebras $\F_0\subseteq\F_1\subseteq\cdots$; $\F_n=\sigma(\xi_1,\dots,\xi_n)$ is the natural one. §8.2

Finite difference: Approximating a derivative by a difference quotient; central differences have $O(h^2)$ truncation error. §18.1

First Fundamental Theorem (FTAP1): No arbitrage $\Leftrightarrow$ at least one EMM exists. §14.3

First-derivative test: f′ changing + to − marks a local max; − to + a local min. §2.5

First-order optimality: At a minimum of a smooth convex $f$, the gradient vanishes: $\nabla f(x^\star)=0$. §18.1

Floating-point number: A value $\pm(1.f)_2\times 2^{e}$ with a finite mantissa; only finitely many exist in any range. §5.1

Focused mode: Tight, effortful attention on material you already partly understand; how you follow a derivation step by step. §0.1

Forecast-error variance: The variance of $X_{t+h}-\hat X_{t+h\mid t}$; grows with $h$ toward the unconditional variance. §12.3

Forgetting curve: The roughly exponential decay of retrievability after learning, reset upward by each successful recall. §0.2

Forward equation: A PDE for the price as a function of strike and maturity (Fokker–Planck in the density), not spot and time. §15.3

Forward error: The difference between the computed and true answer; bounded by (condition)×(backward error). §5.1

Forward smile: The implied-vol smile the model predicts for options starting at a future date - a dynamics property. §15.3

Forward substitution: Solving $Ly=b$ top-to-bottom in $O(n^2)$ work. §5.2

FTC Part 1: d/dx ∫_a^x f(t)dt = f(x): integration and differentiation are inverse operations. §2.6

FTC Part 2: ∫_a^b f dx = F(b)−F(a) for any antiderivative F of f. §2.6

Fubini–Tonelli: Iterated integrals equal the double integral: for $f\ge0$ (Tonelli) or $f\in L^1$ (Fubini), $\int\!\!\int f\,d\mu\,d\nu=\int\!\!\int f\,d\nu\,d\mu$. §6.5

Fubini’s theorem: For integrable $f$, the double integral equals either iterated integral, so the order may be swapped. §3.3

Function: A relation f from A to B in which every a in A is paired with exactly one b in B, written f: A → B. §1.1

Fundamental solution: The smallest positive solution $(x_1,y_1)$; all others come from $x_n+y_n\sqrt D=(x_1+y_1\sqrt D)^n$. §19.12

Gamma Γ: Curvature $\partial^2 V/\partial S^2$; how fast delta moves, so how often you must re-hedge. §15.1

Ganzfeld / psi claims: Alleged extrasensory information transfer; examined by the Army-commissioned reviews and judged unsupported. §0.4

GARCH(1,1): A model $\sigma_t^2=\omega+\alpha\epsilon_{t-1}^2+\beta\sigma_{t-1}^2$ capturing volatility clustering. §18.4

GARCH($p,q$: Adds lagged variances: $\sigma_t^2=\omega+\sum\alpha_i r_{t-i}^2+\sum\beta_j\sigma_{t-j}^2$. §12.4

Gaussian law: $\Normal(\mu,\sigma^2)$ with density $\tfrac{1}{\sqrt{2\pi}\sigma}e^{-(x-\mu)^2/2\sigma^2}$; $\phi(t)=e^{i\mu t-\sigma^2 t^2/2}$. §7.4

Gaussian process: A process all of whose finite-dimensional marginals $(X_{t_1},\dots,X_{t_k})$ are jointly Gaussian; determined by mean and covariance functions. §8.5

Geometric Brownian motion: The solution of $dS=\mu S\,dt+\sigma S\,dW$; an exponential of a Brownian motion with drift. §9.3

Geometric Brownian motion: The asset model $dS=\mu S\,dt+\sigma S\,dW$, solving to a lognormal $S_t$. §18.3

Geometric multiplicity: The dimension $\dim\ker(A-\lambda I)$ of the eigenspace. §4.4

Geometric series: ∑ ar^n; converges iff |r|<1, to a/(1−r). §2.7

Girsanov’s theorem: Under a suitable exponential density, $\tilde B_t=B_t+\theta t$ becomes a Brownian motion (a martingale) under the new measure. §8.5

Girsanov's theorem: Result: subtracting a drift from $W$ corresponds to an explicit change of measure with a known density. §9.4

Global (absolute) extremum: The largest/smallest value over the whole domain, possibly at an endpoint. §2.5

Global minimizer: A point $x^*$ with $f(x^*)\le f(x)$ for all feasible $x$. §3.4

Global mutable state: Hidden state (a module-level RNG, a cached file) that makes runs depend on order - the enemy of reproducibility. §17.3

Global vs local minimum: Global: best over the whole feasible set. Local: best within a neighborhood. For convex problems they coincide. §10.2

Golden ratio: $\varphi=\frac{1+\sqrt5}{2}\approx1.618$: the dominant characteristic root of Fibonacci, so $F_n\sim\varphi^n/\sqrt5$. §19.6

Gradient: The vector $\nabla f=(\partial f/\partial x_1,\dots,\partial f/\partial x_n)$ of first partials. §3.2

Gradient descent: The iteration $x_{k+1}=x_k-t\,\nabla f(x_k)$; step downhill along the negative gradient. §10.4

Gram–Schmidt: An algorithm turning any independent list into an orthonormal basis of the same span. §4.5

Gram-Schmidt: Sequentially subtracting projections onto prior vectors to orthonormalize a basis. §5.3

Graph: $G=(V,E)$; directed or not, weighted or not. In this phase the graph is often implicit: vertices are states, edges are moves. §19.9

Greatest common divisor: The largest $d$ dividing both $a$ and $b$; equivalently the non-negative generator of the ideal $a\Z+b\Z$. §19.1

Greeks: Sensitivities of price to inputs: delta $\partial V/\partial S$, gamma, vega, theta, rho. §18.3

Gross return $R$: One plus the risk-free rate over the period; $\$1$ in the bond becomes $\$R$ tomorrow. §14.1

GROUP BY: A SQL clause that partitions rows into groups so an aggregate (SUM, AVG, COUNT) is computed per group. §17.6

Growth factor: The largest magnitude appearing during elimination relative to $A$; controls LU stability. §5.2

Grundy number (nim-value): $g(v)=\operatorname{mex}\{g(u): v\to u\}$; a position is losing for the player to move iff its Grundy value is 0. §19.7

h-step forecast: The conditional expectation $\hat X_{t+h\mid t}=\E[X_{t+h}\mid \mathcal F_t]$, the minimum-MSE predictor. §12.3

Hat matrix: The projection $H=X(X^\top X)^{-1}X^\top$ mapping $y$ to fitted values $\hat y=Hy$. §11.2

Held–Karp: The bitmask DP for TSP: state $(\text{visited set},\ \text{current city})$, cost $O(2^n n^2)$ time and $O(2^n n)$ memory. §19.8

Hessian: The symmetric matrix $H_{ij}=\partial^2 f/\partial x_i\partial x_j$ of second partials. §3.2

Heston model: Variance follows a square-root (CIR) mean-reverting diffusion, correlated with the spot’s Brownian. §15.4

Homoscedasticity: Constant error variance $\Var(\varepsilon_i)=\sigma^2$ across observations. §11.2

Hot path: The small fraction of code that consumes most of the runtime; the only place optimization pays. §17.5

Householder reflector: An orthogonal matrix $H=I-2vv^\top/v^\top v$ that zeros a column below the diagonal, giving stable QR. §5.3

Hölder's inequality: $\int|fg|\le\lVert f\rVert_p\lVert g\rVert_q$ for $1/p+1/q=1$; source of Cauchy–Schwarz at $p=q=2$. §6.5

i.i.d.: Independent and identically distributed - the standard sampling assumption. §7.5

Idempotence: Re-running a stage yields the same result and no duplicates; essential for reliable, restartable pipelines. §17.6

IEEE-754 double: 64 bits = 1 sign + 11 exponent + 52 stored mantissa bits; represents $\pm(1.f)\times2^{e}$ with 53 bits of significand precision. §19.4

IGARCH: The boundary $\alpha+\beta=1$: shocks to variance never die out (integrated volatility). §12.4

Illusion of competence: Feeling you know material because it looks familiar, without being able to reproduce it. §0.1

Implementation shortfall: Total cost = execution price minus the decision (arrival) price, across the whole order. §16.3

Implementation shortfall: Realized cost vs. the arrival (decision) price: the honest all-in measure of execution quality. §18.6

Implication: ‘P ⇒ Q’ (if P then Q); false only when P is true and Q is false. §1.2

Implicit differentiation: Differentiating both sides of F(x,y)=0 treating y as a function of x, then solving for y′. §2.3

Implied volatility: The $\sigma$ that makes the Black–Scholes price match a quoted market price; the market’s language for option prices. §14.4

Implied volatility: The value of $\sigma$ that makes the Black–Scholes price equal the observed market price of an option. §15.2

Implied volatility: The $\sigma$ that makes the Black–Scholes price equal the observed market price of an option. §18.4

Importance sampling: Sampling from a tilted density $g$ and reweighting by the likelihood ratio $f/g$ to concentrate effort where the payoff matters. §13.3

Impurity: A node's heterogeneity: Gini $\sum_k \hat p_k(1-\hat p_k)$ or entropy for classification, RSS for regression. §11.6

Inclusion–exclusion: | union | = sum of sizes − pairwise intersections + triple intersections − …; the signed correction for overcounting. §19.5

Incomplete market: Some claims cannot be replicated; multiple EMMs exist and no-arbitrage pins a claim only to a price interval. §14.3

Increments: $S_n-S_m$ for $n\gt m$; independent and stationary for a random walk. §8.2

Independent events: $\Prob(A\cap B)=\Prob(A)\Prob(B)$; knowing one gives no information about the other. §7.3

Independent increments: For $t_0\lt \cdots\lt t_k$, the increments $B_{t_{i}}-B_{t_{i-1}}$ are mutually independent. §8.3

Independent increments: Non-overlapping increments of $W$ are independent - the Markov backbone of the process. §18.2

Index alignment: pandas matches Series/DataFrame values by label before arithmetic; mismatched labels produce NaN, not an error. §17.1

Inductive hypothesis: The assumed truth of P(k) (or all j≤k) used to establish the next case. §1.4

Infinitesimal generator: The operator $\mathcal{L}=a\partial_x+\tfrac12 b^2\partial_{xx}$ governing the diffusion's dynamics. §9.5

Injective / surjective / bijective: One-to-one / onto / both at once; a bijection is exactly a map with a two-sided inverse. §1.1

Inner product: A map $\langle\cdot,\cdot\rangle$ that is linear, symmetric, and positive-definite; generalizes the dot product. §4.5

Innovation: The one-step forecast error $y_t-H\hat x_{t\mid t-1}$; a white-noise sequence if the model is correct. §12.5

Integer partition: A multiset of positive integers summing to $n$; order does not matter. $p(4)=5$: 4, 3+1, 2+2, 2+1+1, 1+1+1+1. §19.11

Integer square root: math.isqrt(n): the exact $\lfloor\sqrt n\rfloor$ with no floating point anywhere; the only safe way to test perfect squares for huge $n$. §19.4

Integrable function: An $f$ with $\int|f|\,d\mu\lt \infty$; the space is denoted $L^1(\mu)$. §6.3

Integrated of order $d$: A series $I(d)$ that becomes stationary after $d$ differences; a random walk is $I(1)$. §12.3

Interleaving: Mixing problem types in one session so you practice choosing methods, not just executing them. §0.1

Interleaving: Mixing categories of problems within a session, forcing retrieval of which method applies. §0.2

Intermediate Value Theorem: A continuous f on [a,b] attains every value between f(a) and f(b). §2.1

Inventory cost: Compensation a market maker demands for holding an unwanted position away from its target. §16.2

Inventory risk: The price risk from the net position a market maker accumulates when fills are one-sided. §16.5

Inventory risk: The risk from holding a net long/short position accumulated by one-sided fills; exposed to price moves. §18.7

Inverse-transform method: Sampling $X=F^{-1}(U)$ with $U\sim\mathrm{Unif}(0,1)$ to realize any CDF $F$. §13.1

Invertibility: MA is invertible (writable as a convergent AR($\infty$)) iff all roots of $\theta(z)=0$ lie strictly outside the unit circle. §12.2

Invertible map: A bijective linear map; for square $A$ equivalent to full rank and trivial null space. §4.2

Irreducible / aperiodic: Irreducible: every state reaches every other; aperiodic: gcd of return times is 1. §8.1

Irreducible error: The noise variance $\sigma^2$ that no model can remove; the floor of prediction error. §11.1

Itô correction: The second-order term $\tfrac12 f_{xx}b^2\,dt$ absent from deterministic calculus. §9.2

Itô integral: The L²-limit of integrals of simple processes; evaluated at the LEFT endpoint of each subinterval. §9.1

Itô isometry: The identity equating the L² norm of the integral to the L² norm of the integrand in time. §9.1

Itô process: A process $dX=a\,dt+b\,dW$ with adapted drift $a$ and diffusion $b$. §9.2

Itô’s lemma: The chain rule for Itô processes: $df=f_t\,dt+f_x\,dX+\tfrac12 f_{xx}\,d\langle X\rangle$, with the extra second-order term. §18.3

Itô's lemma: The stochastic chain rule: it adds a $\tfrac12 f_{xx}(dX)^2$ term to the ordinary chain rule. §9.2

Iterated integral: Evaluation $\int\!\!\int f\,dy\,dx$ one variable at a time, inner limits possibly depending on the outer. §3.3

Ito multiplication rule: $(dB_t)^2=dt,\ (dt)^2=0,\ dt\,dB_t=0$; the algebra of second-order terms. §8.4

Jacobian: The $m\times n$ matrix $J_{ij}=\partial F_i/\partial x_j$ of a vector field $F:\R^n\to\R^m$. §3.2

Jacobian determinant: The factor $|\det J|$ by which a change of variables rescales area/volume elements. §3.3

Jensen inequality: For convex $\varphi$, $\varphi(\E X)\le \E[\varphi(X)]$; reversed for concave $\varphi$. §7.2

JOIN: Combining rows from two tables on a key (e.g. ticker+date), the tabular analogue of a merge. §17.6

K-fold CV: Split data into $K$ folds; fit on $K-1$, validate on the held-out fold, rotate, average. §11.3

k-means: Partition points into $K$ clusters minimizing within-cluster squared distance to centroids; non-convex, local optima. §11.7

Kalman gain: $K_t$, the optimal weight on the new observation's surprise; blends prediction and measurement by their precisions. §12.5

Kernel trick: Replacing inner products $x^\top x'$ with a kernel $K(x,x')$ to fit nonlinear boundaries without explicit features. §11.6

Kill switch: An automated control that halts trading when limits (loss, position, error rate) are breached. §16.6

Killing / discount rate: The $-rv$ term; it discounts (or ‘kills’) value at rate $r$ along the path. §9.5

KKT conditions: Stationarity, primal & dual feasibility, and complementary slackness - necessary and (convex case) sufficient for optimality. §10.3

Krylov subspace: $\mathrm{span}\{b,Ab,\dots,A^{k-1}b\}$; the search space for CG and GMRES. §5.5

L^p space: Measurable $f$ with $\lVert f\rVert_p=(\int|f|^p d\mu)^{1/p}\lt \infty$, functions identified when equal a.e. §6.5

Lag operator: $L$ with $LX_t=X_{t-1}$; polynomials $\phi(L),\theta(L)$ encode the model compactly. §12.2

Lagrange multiplier: The scalar $\lambda$ linking objective and constraint gradients at an optimum. §3.5

Lagrange remainder: R_n=f^{(n+1)}(ξ)(x−a)^{n+1}/(n+1)! for some ξ between a and x; the exact error. §2.4

Lagrangian: The function $\mathcal{L}(x,\lambda)=f(x)-\lambda\,(g(x)-c)$ whose stationarity encodes the conditions. §3.5

Lagrangian: The function $L(x,\lambda,\nu)=f_0(x)+\sum_i\lambda_i f_i(x)+\sum_j\nu_j(a_j^\top x-b_j)$ folding constraints into the objective. §10.3

Lasso: Least squares with an $\ell_1$ penalty $\lambda\|\beta\|_1$; convex, induces sparsity (variable selection). §10.5

Lasso: Least squares with an $\ell_1$ penalty $\lambda\|\beta\|_1$; performs shrinkage and variable selection (exact zeros). §11.4

Latency: The delay between signal, order, and fill; ignoring it makes fast strategies look better than reality. §16.6

Law of one price: Two portfolios with identical payoffs in every state must have identical prices today, or an arbitrage exists. §14.1

Layer-cake formula: $\int f\,d\mu=\int_0^\infty\mu(\{f\gt t\})\,dt$ for $f\ge0$; integration by horizontal slices. §6.3

LDA: Linear Discriminant Analysis: Gaussian class densities with a shared covariance, giving a linear decision boundary. §11.5

Least common multiple: $\operatorname{lcm}(a,b)=|ab|/\gcd(a,b)$ for nonzero $a,b$ - compute the gcd first to avoid overflow in fixed-width languages. §19.1

Least squares: Minimizing $\lVert Ax-b\rVert^2$ by projecting $b$ onto the column space of $A$. §4.5

Least squares: Minimizing $\lVert Ax-b\rVert_2$ over $x$; solved by $Rx=Q^\top b$. §5.3

Least squares: Finding $x$ minimizing $\|Ax-b\|_2^2$; solved stably by QR, not by forming $A^\top A$ blindly. §18.1

Lebesgue integral: $\int f\,d\mu=\sup\{\int s\,d\mu: 0\le s\le f,\ s\ \text{simple}\}$ for $f\ge0$. §6.3

Lebesgue measure: The translation-invariant measure on $\mathbb{R}^n$ assigning length/area/volume, extending intervals $\mu([a,b])=b-a$. §6.2

Lemma: A smaller proved result used as a stepping stone toward a theorem. §1.3

Level set: The set $\{x: f(x)=c\}$; for $n=2$ a level curve, for $n=3$ a level surface. §3.1

Likelihood: The data density viewed as a function of the parameter, $L(\theta)=\prod_i f(x_i;\theta)$; the MLE maximizes it. §11.1

Likelihood ratio: The weight $f(X)/g(X)$ that debiases an importance-sampling estimator drawn from $g$ instead of $f$. §13.3

Likelihood-ratio method: A Greek estimator differentiating the density rather than the payoff: $\partial_\theta\E[Y]=\E[Y\,\partial_\theta\log f_\theta]$. §13.5

Limit: L is the limit of f at c if f(x) can be forced arbitrarily close to L by taking x close enough (but not equal) to c. §2.1

Limit order: An order to buy/sell a quantity at a stated price or better; rests in the book providing liquidity. §16.1

Limit order book (LOB): The set of all resting limit orders, organized by price level and time priority on each side. §16.1

Linear independence: No nontrivial combination gives zero: $\sum c_i v_i=0\Rightarrow c_i=0$ for all $i$. §4.1

Linear map: A function $T:V\to W$ with $T(u+v)=Tu+Tv$ and $T(cv)=cTv$. §4.2

Linear recurrence: $a_n=c_1a_{n-1}+\cdots+c_ka_{n-k}$ with constant $c_i$; determined by $k$ initial values. §19.6

Linearization: The degree-1 Taylor polynomial f(a)+f′(a)(x−a); the tangent-line approximation. §2.4

Lipschitz / linear-growth: Conditions on $a,b$ guaranteeing a unique strong solution exists. §9.3

Liquidity: The ease of trading size quickly at low cost; measured by spread (tightness), depth, and resiliency. §16.2

A deterministic function giving the instantaneous vol when the spot is $S$ at time $t$. §15.3

Log-Euler (exact GBM): Simulating $\log S$ with the exact increment $(\mu-\tfrac12\sigma^2)\Delta t+\sigma\sqrt{\Delta t}Z$, which reproduces GBM without bias. §13.4

Log-likelihood (Bernoulli): $\ell(\beta)=\sum_i[y_i\log p_i+(1-y_i)\log(1-p_i)]$; concave, so its maximizer is unique. §11.5

Logit / log-odds: The transform $\log\frac{p}{1-p}$ mapping a probability to the whole real line; logistic regression makes it linear in $x$. §11.5

Lognormal: A variable whose logarithm is normal; $S_t$ under GBM is lognormal. §9.3

LOOCV: Leave-one-out CV: $K=n$; nearly unbiased but high variance and expensive. §11.3

Look-ahead bias: Using data not available at decision time - a special, time-flavored leakage. §11.7

Look-ahead bias: Using information not available at decision time; the most common way backtests cheat. §12.6

Look-ahead bias: Using information in the backtest that would not have been available at the decision time; inflates returns. §16.6

Loop invariant: A property true before the loop, preserved by each iteration, and strong enough at exit to give the result. The standard correctness proof. §19.14

Loss of orthogonality: Rounding makes classical GS columns drift from orthogonal; measured by $\lVert Q^\top Q-I\rVert$. §5.3

Low-rank approximation: The best rank-$k$ fit $A_k=\sum_{i\le k}\sigma_i u_i v_i^\top$ (Eckart–Young). §4.7

Lowbit: $x\ \&\ (-x)$ isolates the lowest set bit - the standard way to iterate over the elements of a mask in $O(\text{popcount})$. §19.8

LU factorization: Writing $A=LU$ with $L$ unit lower-triangular and $U$ upper-triangular. §5.2

MA($q$): Moving average: $X_t=\varepsilon_t+\sum_{j=1}^q\theta_j\varepsilon_{t-j}$; today is a weighted window of recent shocks. §12.2

Machine epsilon: The gap between 1 and the next representable double, $\epsilon_{\text{mach}}\approx 1.1\times10^{-16}$; bounds relative rounding error. §5.1

Machine epsilon: $\varepsilon=2^{-52}\approx2.22\times10^{-16}$: the gap between 1 and the next representable double. Relative rounding error is $\le\varepsilon/2$. §19.4

Maclaurin series: A Taylor series centered at a=0. §2.4

Margin: The distance from the decision hyperplane to the nearest training point; SVMs maximize it. §11.6

Marginal quantity: In economics/finance, the derivative of a total with respect to quantity (marginal cost, marginal utility). §2.2

Market impact: The adverse price move caused by your own trading; the dominant cost for large orders. §16.3

Market impact: The adverse price move caused by your own trading; larger and faster orders push price against you. §18.6

Market maker: A liquidity provider who continuously quotes bid and ask, aiming to earn the spread across many round trips. §16.5

Market maker: A trader who continuously posts bid and ask quotes, earning the spread by providing liquidity. §18.7

Market order: An order to trade immediately against the best available prices; consumes liquidity. §16.1

Market price of risk: The quantity $\theta=(\mu-r)/\sigma$; excess return per unit of volatility. §9.4

Markov inequality: For $X\ge0$, $\Prob(X\ge a)\le \E[X]/a$. §7.2

Markov property: $\Prob(X_{n+1}=j\mid X_n=i,\text{past})=\Prob(X_{n+1}=j\mid X_n=i)$: the future depends on the past only through the present. §8.1

Martingale: An adapted, integrable $(M_n)$ with $\E[M_{n+1}\mid\F_n]=M_n$; a fair game. §7.7

Martingale: A process whose conditional expected future value equals its present value; the Itô integral is one. §9.1

Martingale: A process with $\E_{\mathbb{Q}}[\tilde S_{t+1}\mid\mathcal F_t]=\tilde S_t$: no predictable drift after discounting. §14.2

Martingale: A process whose conditional expected future value equals its current value; the mathematical form of ‘no arbitrage’. §18.3

Matrix power by squaring: Same square-and-multiply as 19.3 with matrix multiplication as the operation: $O(\log n)$ multiplications, each $O(k^3)$. §19.13

Matrix representation: The array whose columns are the images $T v_j$ of a basis, written in the target basis. §4.2

Mean reversion $\kappa$: The speed at which variance is pulled back toward its long-run level $\theta$. §15.4

Mean–variance efficiency: A portfolio with the least variance for its expected return; the set of such portfolios is the efficient frontier. §14.5

Mean-squared error: Expected squared distance to the truth, $\E[(\hat\theta-\theta)^2]$; the standard risk under squared loss. §11.1

Mean-variance / Markowitz: Trade off return against variance: $\max\ \mu^\top w-\tfrac{\gamma}{2}w^\top\Sigma w$. §10.5

Measurable function: $f$ with $\{x:f(x)\gt a\}\in\mathcal{F}$ for every $a$; the class we can integrate. §6.3

Measure: A function $\mu:\mathcal{F}\to[0,\infty]$ with $\mu(\emptyset)=0$ and countable additivity on disjoint sets. §6.2

Meet in the middle: Split the input in half, enumerate both halves ($2^{n/2}$ each), and join by sorting/hashing. Turns $2^n$ into $2^{n/2}\log$. §19.10

Memoization: Top-down recursion + a cache. Computes only the reachable states; easiest to write from a recurrence. §19.7

Mental representation: A domain-specific structure (a chunk-of-chunks) that lets experts perceive patterns and plan solutions others cannot see. §0.3

Merton problem: Continuous-time optimal consumption/investment; for CRRA the optimal risky fraction is the constant $w^*=(\mu-r)/(\gamma\sigma^2)$. §14.5

Metric: A function $d(x,y)$ that is nonnegative, symmetric, zero iff $x=y$, and obeys the triangle inequality. §6.1

mex: Minimum EXcludant: the smallest non-negative integer not in a set. $\operatorname{mex}\{0,1,3\}=2$. §19.7

Micro-price: A depth-weighted mid $(P_a Q_b+P_b Q_a)/(Q_a+Q_b)$ that leans toward the heavier side. §16.1

Milstein scheme: A refinement adding the $\tfrac12 b\,b'\big((\Delta W)^2-\Delta t\big)$ term to raise strong order to 1. §13.4

Minimal pair: Two easily-confused items studied together to sharpen the distinction (e.g. $\subset$ vs $\in$). §0.5

Minimum spanning tree: A cycle-free subset of edges connecting all vertices with minimum total weight. Kruskal (sort + union–find) or Prim (grow with a heap). §19.9

Minimum-variance portfolio: Weights minimizing $w^\top\Sigma w$ subject to $\mathbf{1}^\top w=1$. §3.5

Minimum-variance portfolio: Weights minimizing $w^\top\Sigma w$ subject to $\mathbf1^\top w=1$ (fully invested). §10.5

Model assumptions: Constant $\sigma$ and $r$, GBM dynamics, no jumps, continuous frictionless trading, no dividends - idealizations, each violable. §14.4

Model risk: The risk that the model is wrong or overfit, so realized performance falls short of the backtest. §18.5

Moment: $\E[X^k]$ (raw) or $\E[(X-\mu)^k]$ (central); the $k$-th shape descriptor. §7.2

Moment generating function: $M_X(t)=\E[e^{tX}]$; when finite near 0, its derivatives at 0 give the moments. §7.4

Moneyness: A normalized strike, e.g. $K/S$, $\ln(K/S)$, or $\ln(K/F)/(\sigma\sqrt{T})$ (standardized). §15.2

Monotone convergence (MCT): If $0\le f_n\uparrow f$ then $\int f_n\to\int f$; limits pass through for increasing nonnegative sequences. §6.4

Monotone sequence: Non-increasing or non-decreasing for all n. §1.5

Monte Carlo estimator: The sample average $\hat\theta_N=\tfrac1N\sum_{i=1}^N Y_i$ of i.i.d. draws $Y_i$ with $\E[Y_i]=\theta$. §13.2

Multinomial coefficient: $\binom{n}{k_1,\dots,k_r}=\frac{n!}{k_1!\cdots k_r!}$: arrangements of a multiset; the count of ways to split $n$ labelled items into labelled groups of given sizes. §19.5

Multiple testing: Trying many strategies inflates the chance one looks good by luck; demands a higher bar or correction. §18.5

Multiplication table: The formal rules $(dt)^2=dt\,dW=0$, $(dW)^2=dt$ used to expand differentials. §9.2

Multiplicative function: $f$ with $f(mn)=f(m)f(n)$ whenever $\gcd(m,n)=1$. Examples: $\tau$ (divisor count), $\sigma$ (divisor sum), $\varphi$ (totient), $\mu$ (Möbius). §19.2

n-th term test: If a_n does not → 0, the series diverges (a necessary, not sufficient, condition). §2.7

ndarray: NumPy’s homogeneous, fixed-dtype, contiguous n-dimensional array; the substrate of all quant numerics in Python. §17.1

Nearest-PD repair: Projecting an indefinite estimated covariance to the closest positive-definite matrix so Cholesky succeeds. §5.4

Necessary condition: Q is necessary for P when P ⇒ Q: P cannot hold unless Q does. §1.2

Newton–Raphson: A root-finder $\sigma_{n+1}=\sigma_n-(C(\sigma_n)-C_{mkt})/\text{vega}(\sigma_n)$ exploiting the known derivative. §15.2

Newton's method: The iteration $x_{k+1}=x_k-[\nabla^2 f(x_k)]^{-1}\nabla f(x_k)$; uses curvature. §10.4

No-arbitrage: No self-financing strategy turns zero initial wealth into a sure profit; equivalent to existence of $\mathbb{Q}$. §9.6

Norm: The length $\lVert x\rVert=\sqrt{x\cdot x}$; measures distance and induces the metric on $\R^n$. §3.1

Normal equations: The system $A^\top A x = A^\top b$; correct but conditioned like $\kappa(A)^2$. §5.3

Normal equations: The linear system $X^\top X\beta=X^\top y$ whose solution is the OLS estimate. §11.2

Notation fluency: Automatic reading of symbols so attention is free for reasoning, not decoding. §0.5

Novikov condition: A sufficient integrability condition $\E[e^{\frac12\int\theta^2 dt}]\lt \infty$ ensuring $Z$ is a true martingale. §9.4

Null set: A set of measure zero; e.g. any countable set has Lebesgue measure 0. §6.2

Null space: The kernel $\ker T=\{v:Tv=0\}$; its dimension is the nullity. §4.2

Numeraire: The asset prices are expressed in; the money-market account $B_t=e^{rt}$ is the standard choice. §9.6

Observation equation: $y_t=H x_t+v_t$, $v_t\sim\Normal(0,R)$; the noisy measurement of the state. §12.5

One-period market: Two dates $t=0,1$ and finitely many states; assets are a risk-free bond and a risky stock with known state payoffs. §14.1

One-sided limit: The limit taken as x approaches c only from the left (c−) or right (c+). §2.1

One-standard-error rule: Choose the simplest model whose CV error is within one standard error of the minimum. §11.3

Open set: A set in which every point has a ball entirely inside it; the basis of topology. §6.1

Operations budget: A rough count of primitive operations you can afford: $\sim10^8$ simple ops/second in C, $\sim10^6\!-\!10^7$ in pure Python. §19.14

Optimal coefficient: The variance-minimizing $b^*=\Cov(Y,C)/\Var(C)$ for a control variate. §13.3

Optimal execution: Choosing how to split a parent order over time to minimize expected cost plus a penalty on its risk. §16.4

Optimal substructure: An optimal solution is built from optimal solutions of subproblems. Without it, DP is simply invalid. §19.7

Optimality condition: A test a point must satisfy to be optimal; over a convex set it is a variational inequality. §10.2

Optimism: The gap $\E[\text{test}]-\E[\text{train}]$; grows with model complexity and with fitting noise. §11.3

Optional stopping: Under integrability/boundedness conditions, $\E[M_\tau]=\E[M_0]$ for a martingale. §7.7

Oracle: A trusted reference answer - a closed-form value, a slow-but-correct implementation, or a mathematical identity. §17.2

Order-processing cost: The fixed operational cost (fees, technology) of providing quotes, a component of the spread. §16.2

Ordinary generating function (OGF): $A(x)=\sum_{n\ge0}a_nx^n$: a formal power series that encodes the whole sequence as one object. §19.6

Orientation predicate: The sign of the cross product $(b-a)\times(c-a)$: +, 0 or − for counter-clockwise, collinear, clockwise. Exact in integer arithmetic. §19.10

Orthogonal complement: $U^\perp=\{v:\langle v,u\rangle=0\ \forall u\in U\}$; $V=U\oplus U^\perp$. §4.5

Orthogonal projection: The closest point $\operatorname{proj}_U x$ in a subspace $U$ to a given $x$. §4.5

Orthogonality: Components are independent: changing one has no unintended effect on another; effects are ‘at right angles’. §17.4

Orthonormal set: Vectors that are mutually orthogonal and of unit norm: $\langle q_i,q_j\rangle=\delta_{ij}$. §4.5

Out-of-sample / walk-forward: Evaluating on data not used to design or select the strategy; the only credible performance estimate. §16.6

Overlapping subproblems: The naive recursion revisits the same subproblem exponentially often; caching collapses the recursion tree into a DAG. §19.7

PACF: Partial autocorrelation at lag $h$: the correlation of $X_t$ and $X_{t+h}$ after removing the linear effect of the intervening lags. §12.1

Parabolic PDE: A PDE of heat-equation type: first order in time, second order in space. §9.5

Partial derivative: The rate $\partial f/\partial x_i$ with all other variables held fixed. §3.2

Partial pivoting: Row-swapping to put the largest available entry on the pivot, giving $PA=LU$. §5.2

Participation rate: Your trading as a fraction of market volume; a key driver of temporary impact. §16.3

Participation rate: The fraction of market volume your order represents; higher rates mean more impact. §18.6

Partition: A family of non-empty, pairwise-disjoint subsets whose union is the whole set. §1.1

Partition mesh: $\|\Pi\|=\max_k(t_k-t_{k-1})$; the size of the largest sub-interval. §8.4

Path limit: The value approached by $f$ as $x$ tends to a point along a chosen curve; all paths must agree for a limit to exist. §3.1

Pathwise derivative: A Greek estimator differentiating the payoff along each path: $\partial_\theta\E[Y]=\E[\partial_\theta Y]$ when the payoff is Lipschitz. §13.5

PCA: Principal Component Analysis: orthogonal directions of maximal variance, the eigenvectors of the covariance matrix. §11.7

Pell’s equation: $x^2-Dy^2=1$ for non-square $D\gt 0$; always has infinitely many integer solutions, generated from a fundamental one. §19.12

Pentagonal number theorem: $\prod_{k\ge1}(1-x^k)=\sum_{j\in\Z}(-1)^j x^{j(3j-1)/2}$; it yields a recurrence for $p(n)$ with only $O(\sqrt n)$ terms. §19.11

Period: The number of draws before a PRNG’s output sequence repeats; must vastly exceed the sample size used. §13.1

Permanent impact: A lasting shift in the efficient price because trading reveals information (Kyle’s lambda). §16.3

Permutation matrix: A reordering of the identity, $P$, encoding the row swaps; orthogonal with $P^{-1}=P^\top$. §5.2

Persistence: $\alpha+\beta$ in GARCH(1,1); how slowly volatility shocks decay; near 1 means very persistent. §12.4

Persistence: In GARCH, $\alpha+\beta$; close to 1 means shocks to variance decay slowly. §18.4

Physical measure $\Prob$: The real-world probability estimated from data; used for risk, forecasting, and P&L. §9.6

Point-in-time (PIT): Data as it was known on a past date, with no later revisions leaked in - the antidote to look-ahead bias. §17.6

Poisson law: Counts of rare events; $\Prob(N=k)=e^{-\lambda}\lambda^k/k!$, mean = variance = $\lambda$. §7.4

Polar coordinates: The map $x=r\cos\theta,\ y=r\sin\theta$ with area element $dA=r\,dr\,d\theta$. §3.3

Popcount: The number of set bits. Python: bin(x).count('1') or x.bit_count() (3.10+). §19.8

Positive definite: A symmetric matrix with $x^\top Hx\gt 0$ for all $x\neq 0$; equivalently all eigenvalues positive. §3.4

Positive definite: Symmetric with $x^\top Ax\gt 0$ for all $x\neq0$; equivalently all eigenvalues $\gt 0$. §4.6

Positive definite: Symmetric $A$ with $x^\top A x\gt 0$ for all $x\ne0$; equivalently all eigenvalues positive. §5.4

Positive semidefinite: Symmetric with $x^\top Ax\ge0$; eigenvalues $\ge0$ (covariances live here). §4.6

Positive semidefinite: $x^\top A x\ge0$ for all $x$; allows zero eigenvalues (a singular covariance). §5.4

Power iteration: Repeated multiplication $x\leftarrow Ax/\lVert Ax\rVert$ converging to the dominant eigenvector. §4.7

Power iteration: Repeatedly applying $A$ and normalizing; converges to the dominant eigenvector. §5.5

Power rule: d/dx x^n = n x^{n-1} for any real n. §2.3

Predictable process: $H_n$ is $\F_{n-1}$-measurable - chosen before the time-$n$ move (a trading position). §8.2

Predictable variation: For $B$, the compensator making $B_t^2-t$ a martingale is exactly $[B]_t=t$. §8.4

Prediction interval: A band, e.g. $\hat X_{t+h\mid t}\pm1.96\,\sigma_h$, quantifying forecast uncertainty at horizon $h$. §12.3

Present value: Today’s worth of future money, discounted at rate r; a future dollar at time t is worth e^{−rt}. §2.6

Price formation: The process by which order flow and information are incorporated into the quoted mid-price over time. §16.2

Price–time priority: Matching rule: best price first, and within a price, earliest order first (FIFO queue). §16.1

Prime: An integer $p\gt 1$ whose only positive divisors are 1 and $p$. 1 is not prime - that convention is what makes factorization unique. §19.2

Principal component: An eigenvector of the covariance matrix; a direction of maximal variance in the data. §4.7

Probability measure: A set function $\Prob:\F\to[0,1]$ with $\Prob(\Omega)=1$ that is countably additive on disjoint events. §7.1

Probability space: A measure space $(\Omega,\mathcal{F},\mathbb{P})$ with $\mathbb{P}(\Omega)=1$; expectation is the integral against $\mathbb{P}$. §6.5

Product measure: On $X\times Y$, the measure with $(\mu\times\nu)(A\times B)=\mu(A)\nu(B)$; underlies joint distributions and independence. §6.5

Product rule: (fg)′ = f′g + fg′. §2.3

Profiling: Measuring where a program actually spends time (per function/line) rather than guessing. §17.5

Projection: The nearest feasible point to a given $z$: $\Pi_C(z)=\argmin_{x\in C}\|x-z\|_2$; well-defined and unique for convex $C$. §10.2

Proof by contradiction: Assume the statement is false, derive a logical impossibility, conclude it must be true. §1.3

Proof by contrapositive: Prove ¬Q ⇒ ¬P, which is logically equivalent to P ⇒ Q. §1.3

Property-based test: A test asserting an invariant that must hold for many random inputs (monotonicity, parity, symmetry), not one fixed case. §17.2

Proposition: A statement that is definitely true or false (not both). §1.2

Prototype: Throwaway code built to answer one question (is this feasible?), then discarded - unlike a tracer bullet. §17.4

Pruning / constraint propagation: Discarding a partial solution the moment it cannot be completed. Reduces the effective branching factor, not the worst-case exponent. §19.10

Pseudo-polynomial: Polynomial in the numeric VALUE of an input but exponential in its bit length (e.g. the $O(nW)$ knapsack DP). §19.14

Pseudo-random number generator (PRNG): A deterministic recursion that, seeded once, emits a stream statistically indistinguishable from i.i.d. uniforms on $[0,1)$. §13.1

Publication bias: The tendency for positive results to be published and null results to be hidden, inflating apparent efficacy. §0.4

Purposeful practice: Goal-directed practice with feedback, but without an established field-tested method - a step below deliberate. §0.3

QR algorithm: Iterating $A_k=Q_kR_k,\ A_{k+1}=R_kQ_k$; converges to (block) triangular Schur form revealing eigenvalues. §5.5

QR factorization: Writing $A=QR$ with $Q$ orthonormal columns and $R$ upper-triangular. §5.3

Quadratic convergence: Error squares each step ($e_{k+1}\approx c\,e_k^2$) near the optimum; Newton's hallmark. §10.4

Quadratic form: A function $q(x)=x^\top Ax$ with symmetric $A$; its level sets are ellipsoids when $A\succ0$. §4.6

Quadratic surd: $\sqrt D$ for non-square $D$; by Lagrange its continued fraction is eventually periodic: $[a_0;\overline{a_1,\dots,a_r}]$. §19.12

Quadratic variation: $[f]_t=\lim_{\|\Pi\|\to0}\sum_k (f(t_{k})-f(t_{k-1}))^2$ over partitions $\Pi$ of $[0,t]$. §8.4

Quadratic variation: The limit of summed squared increments; for Brownian motion on [0,t] it equals t, not 0. §9.1

Quadratic variation: The limit $\sum(W_{t_{i+1}}-W_{t_i})^2\to t$; nonzero, unlike for smooth functions. §18.2

Quadrature: Numerical integration, e.g. the trapezoidal or Simpson rule, approximating $\int f$ by weighted samples. §18.1

Quasi-Monte Carlo (QMC): Replacing random points by a deterministic low-discrepancy sequence (Sobol, Halton) to fill space more evenly. §13.5

Quote skew: Shifting bid/ask asymmetrically to encourage trades that reduce inventory. §18.7

Quotient rule: (f/g)′ = (f′g − fg′)/g². §2.3

Radius of convergence: The R such that a power series ∑c_n(x−a)^n converges for |x−a|<R. §2.7

Radon–Nikodym derivative: The density $Z=d\mathbb{Q}/d\Prob$ re-weighting outcomes; $\mathbb{Q}(A)=\E_\Prob[Z\,\ind_A]$. §9.4

Radon-Nikodym derivative: The density $Z=d\Q/d\Prob\ge0$ with $\E_\Prob[Z]=1$ that re-weights $\Prob$ into $\Q$. §8.5

Random forest: Bagging plus random feature subsampling at each split, decorrelating the trees for extra variance reduction. §11.6

Random variable: A measurable map $X:\Omega\to\R$: preimages of Borel sets are events. §7.1

Rank: The dimension of the column space, equal to the dimension of the row space. §4.2

Ratio test: If lim|a_{n+1}/a_n|=L, the series converges (absolutely) for L<1, diverges for L>1. §2.7

Rational arithmetic: fractions.Fraction: exact $p/q$ kept in lowest terms via gcd - correct, but the denominators can explode. §19.4

Rayleigh quotient: $\rho(v)=\dfrac{v^\top A v}{v^\top v}$; best scalar eigenvalue estimate for a given $v$. §5.5

Realized variance: The empirical quadratic variation $\sum(\Delta B)^2$ of a price path; converges to $\int\sigma^2\,dt$. §8.4

Realized volatility: An estimate of $\sigma$ from historical returns, e.g. $\sqrt{252}\cdot\text{sd of daily returns}$. §18.4

Recurrent / transient: A state is recurrent if the chain returns to it with probability 1, else transient. §8.1

Recursive definition: A definition of a_n in terms of earlier terms plus explicit initial values. §1.4

Regime change / structural break: A shift in the data-generating process (policy, liquidity, crisis) that breaks a previously fitted relationship. §12.6

Region of integration: The domain $R$; its description (as x- or y-simple) sets the inner and outer limits. §3.3

Regression test: A test that pins a previously fixed bug so it can never silently return. §17.2

Regularization: Penalizing model complexity (e.g. ridge/lasso $\lambda$) to reduce variance at the cost of some bias. §18.5

Regularization path: The trajectory of $\hat\beta(\lambda)$ as the penalty varies from 0 (OLS) to $\infty$ (all zero). §11.4

Relation: Any subset R of A×B; we write a R b to mean (a,b) is in R. §1.1

Removable / jump discontinuity: A hole that a single redefinition would fix / a genuine step where left and right limits differ. §2.1

Replicating portfolio: Holdings $(\Delta,B)$ in stock and bond whose date-1 payoff equals the claim’s in every state. §14.1

Replication: Matching a derivative's payoff with a dynamic portfolio of the underlying and cash. §9.6

Reproducibility: Given the same code, data, environment, and seed, you get bit-for-bit (or within-tolerance) the same result. §17.3

Reproducibility (seed): Fixing the generator’s initial state so a stochastic run can be replayed exactly for debugging and testing. §13.1

Research question: A precise, falsifiable statement of what you are testing and under what conditions. §18.8

Reservation price: The market maker’s inventory-adjusted fair value; the mid around which it centers its quotes. §16.5

Reservation price: An inventory-adjusted fair value around which the maker centers quotes (Avellaneda–Stoikov). §18.7

Residual: The gap $e=y-\hat y=(I-H)y$, orthogonal to every column of $X$. §11.2

Rho ρ: Sensitivity to the interest rate $\partial V/\partial r$; usually the smallest first-order risk. §15.1

Ridge regression: Least squares with an $\ell_2$ penalty $\lambda\|\beta\|_2^2$; shrinks coefficients, convex, closed form. §10.5

Ridge regression: Least squares with an $\ell_2$ penalty $\lambda\|\beta\|_2^2$; shrinks coefficients toward zero, never exactly to zero. §11.4

Riemann sum: ∑ f(x_i*) Δx, an approximation of area by rectangles over a partition. §2.6

Riesz–Fischer: $L^p$ is a complete normed space (Banach); $L^2$ is a Hilbert space with inner product $\langle f,g\rangle=\int fg$. §6.5

Risk analysis: Quantifying drawdown, tail risk, exposures, and scenario behavior of the result. §18.8

Risk aversion $\gamma$: The weight on variance; larger $\gamma$ gives more conservative portfolios. §10.5

Risk aversion $\lambda$: The weight on cost variance; larger $\lambda$ means more urgency (faster liquidation). §16.4

Risk-neutral density: The pricing distribution $q(S_T)$ implied by option prices; recovered via Breeden–Litzenberger. §15.2

Risk-neutral measure: An equivalent measure $\Q$ under which discounted asset prices are martingales; drift becomes $r$. §18.3

An equivalent measure under which discounted tradable prices are martingales; used only for pricing. §9.6

The probability under which every traded asset’s discounted price is a martingale; the pricing measure, distinct from real-world $\Prob$. §14.2

Risk-neutral price: The no-arbitrage value $V_0=e^{-rT}\E_{\mathbb{Q}}[\text{payoff}]$, an expectation under the pricing measure $\mathbb{Q}$, not the real-world $\Prob$. §13.5

Root-mean-square error: The overall accuracy $\sqrt{\E[(\hat\theta_N-\theta)^2]}$, which for an unbiased estimator equals the standard error. §13.2

Saddle point: A critical point that is a min in some directions and a max in others; the Hessian is indefinite. §3.4

Sample mean: $\bar X_n=\tfrac1n\sum_{i=1}^n X_i$; the empirical average of $n$ draws. §7.5

Sample space: The set $\Omega$ of all elementary outcomes of an experiment. §7.1

Sample standard deviation: The estimate $s$ of $\sigma$ from the data, using the $N-1$ (Bessel) denominator. §13.2

Scalar field: A function $f:\R^n\to\R$ assigning a number to each point, e.g. temperature or a portfolio’s loss. §3.1

Scaling law: Brownian increments scale like $\sqrt{\Delta t}$, not $\Delta t$; the root of the $\sqrt{dt}$ in simulation. §18.2

SDE: An equation $dX=a(t,X)dt+b(t,X)dW$ specifying an Itô process by its local drift and diffusion. §9.3

Second Fundamental Theorem (FTAP2): An arbitrage-free market is complete $\Leftrightarrow$ the EMM is unique. §14.3

Second-derivative test: At a critical point, f″<0 ⇒ local max, f″>0 ⇒ local min, f″=0 inconclusive. §2.5

Second-order test: Classifies a critical point by the definiteness of the Hessian there. §3.4

Seed: The initial state of a pseudo-random generator; fixing it makes ‘random’ draws deterministic and repeatable. §17.3

Segmented sieve: Sieve an interval $[L,R]$ using primes up to $\sqrt R$, so memory is $O(R-L)$ rather than $O(R)$. §19.2

Self-financing: A trading strategy whose value changes only through market moves, with no external cash injected or withdrawn. §15.1

Self-financing portfolio: A trading strategy whose value changes only through asset returns, with no external cash in/out. §9.6

Self-financing strategy: A dynamic portfolio rebalanced with no external cash injection or withdrawal after inception. §14.2

Sequence: A function from the naturals to the reals, written (a_n); the ordered list a_1,a_2,…. §1.5

Series: The formal infinite sum ∑ a_n; it converges to S if its partial sums s_N=∑_{n≤N} a_n → S. §2.7

Set: An unordered collection of distinct objects called its elements; specified by roster {1,2,3} or by a rule {x : P(x)}. §1.1

Shadow price: The rate $d f^*/dc=\lambda$ at which the optimal value improves as the constraint loosens. §3.5

Sharpe ratio: Excess return per unit of volatility, $(\mu_p-r)/\sigma_p$; the slope of the capital market line. §14.5

Shoelace formula: The area of a polygon from its vertices: $2A=\big|\sum_i (x_iy_{i+1}-x_{i+1}y_i)\big|$ - integer-exact for lattice polygons. §19.10

Shrinkage factor: In the SVD basis, ridge multiplies the $j$th component by $d_j^2/(d_j^2+\lambda)\in(0,1)$. §11.4

Sieve of Eratosthenes: Cross out multiples of each prime $p$ starting at $p^2$; survivors are prime. Cost $O(n\log\log n)$. §19.2

Sigma-algebra: A collection $\mathcal{F}$ containing $X$ and closed under complement and countable unions. §6.2

Sigma-algebra: A collection $\F$ of subsets of $\Omega$ closed under complement and countable union, containing $\Omega$; the admissible events. §7.1

Sigma-algebra as information: A sub-sigma-algebra $\mathcal{G}\subseteq\F$ models ‘what is known’; measurability w.r.t. $\mathcal{G}$ means observable. §7.3

Sigmoid: The inverse logit $\sigma(z)=1/(1+e^{-z})$, squashing a linear score into $(0,1)$. §11.5

Similar matrices: $A$ and $B=P^{-1}AP$ for invertible $P$; same map in different bases. §4.4

Simple function: A finite combination $\sum_i c_i\mathbf{1}_{A_i}$ of indicators of measurable sets $A_i$. §6.3

Simple process: A step-function integrand, constant on a partition, for which the integral is defined by hand. §9.1

Simple random walk: $S_n=\sum_{i=1}^n \xi_i$ with i.i.d. $\xi_i=\pm1$; symmetric if each sign has probability 1/2. §8.2

Single source of truth: The one place a fact lives (a constant, a config, a function) so a change is made once and propagates. §17.4

Singular value: A diagonal entry $\sigma_i\ge0$ of $\Sigma$; $\sigma_i=\sqrt{\lambda_i(A^\top A)}$. §4.7

Singular value decomposition: $A=U\Sigma V^\top$ with orthogonal $U,V$ and nonnegative diagonal $\Sigma$. §4.7

Skewing quotes: Shifting both quotes to encourage trades that reduce inventory (e.g. lower both to sell down a long). §16.5

Slater's condition: A strictly feasible point exists ($f_i(x)\lt 0$, equalities met); guarantees strong duality for convex problems. §10.3

Sleep learning (hypnopaedia): The claim that information presented during sleep is learned; reviewed and not supported for cognitive content. §0.4

Slippage: Realized execution price minus a benchmark (arrival mid or VWAP). §16.3

Slippage: The gap between assumed and realized execution price from spread, impact, and delay. §16.6

Slutsky’s theorem: If $X_n\Rightarrow X$ and $Y_n\xrightarrow{p}c$, then $X_n+Y_n\Rightarrow X+c$ and $X_nY_n\Rightarrow cX$. §7.6

Smallest prime factor (SPF) sieve: An array where spf[k] is $k$’s least prime factor; dividing repeatedly factors any $k\le n$ in $O(\log k)$. §19.2

Soft-thresholding: The operator $S_\lambda(z)=\text{sign}(z)(|z|-\lambda)_+$; the lasso solution under orthonormal predictors. §11.4

Source map: An explicit mapping from each method used to the phase/book that justifies it. §18.8

Spacing effect: Reviews distributed over time produce more durable memory than the same reviews massed together. §0.2

Span: The set $\operatorname{span}(v_1,\dots,v_k)=\{\sum c_i v_i\}$ of all linear combinations. §4.1

Spectral theorem: Every real symmetric matrix is $A=Q\Lambda Q^\top$ with orthonormal $Q$ and real $\Lambda$. §4.6

Spurious regression: A high-$R^2$, significant-looking regression between independent $I(1)$ series - an artifact of common trends, not a real relationship. §12.6

SQL: Structured Query Language: a declarative language for selecting, filtering, aggregating, and joining tabular data. §17.6

Square-root law: Empirical rule: impact scales roughly as $\propto\sigma\sqrt{Q/V}$, sublinear in size. §16.3

Standard error: The estimated standard deviation of a coefficient estimate, the basis of $t$-tests and intervals. §11.2

Standard error: The standard deviation of the estimator, $\mathrm{SE}=\sigma/\sqrt{N}$, estimated by $s/\sqrt{N}$. §13.2

Standard error: The standard deviation of an estimator; for a mean of $n$ draws it is $\sigma/\sqrt n$. §18.2

Standard form: Minimize $f_0(x)$ s.t. $f_i(x)\le0$ (convex) and $Ax=b$ (affine). §10.2

Stars and bars: The number of ways to write $n$ as an ordered sum of $k$ non-negative integers is $\binom{n+k-1}{k-1}$. §19.5

State compression: Encoding an exponential-but-small state (a subset, a profile of a grid row) as an integer so it can index a DP array. §19.8

State covariance: $P_t$, the uncertainty of the state estimate; propagated and updated each step. §12.5

State equation: $x_t=F x_{t-1}+w_t$, $w_t\sim\Normal(0,Q)$; the hidden dynamics. §12.5

State prices: Nonnegative numbers $\psi_s$ pricing an $\$1$-in-state-$s$ security; a claim’s price is $\sum_s\psi_s\,\text{payoff}_s$. §14.1

State space: The set of distinct arguments the recurrence takes. DP cost = |states| × cost per transition. Designing the state IS the problem. §19.7

State vector: $v_n=(a_n,a_{n-1},\dots,a_{n-k+1})^\top$; the recurrence is exactly $v_n=Av_{n-1}$, hence $v_n=A^{n-1}v_1$. §19.13

State-space model: A latent state evolving by a transition equation, observed noisily through a measurement equation. §12.5

Static typing: Types fixed and known at compile time (as in C++), enabling the compiler to emit specialized machine code. §17.5

Stationarity condition: AR is stationary iff all roots of $\phi(z)=0$ lie strictly outside the unit circle. §12.2

Stationary distribution: A row vector $\pi\ge0$, $\sum\pi_i=1$, with $\pi P=\pi$; invariant under one step. §8.1

Stationary increments: $B_{t}-B_{s}\sim\Normal(0,t-s)$ depends only on the gap $t-s$. §8.3

Step size / learning rate: The scalar $t\gt 0$; too large diverges, too small crawls; line search adapts it. §10.4

Sticky delta (moneyness): Dynamics in which the smile is a fixed function of moneyness and rides with the spot. §15.5

Sticky strike: Dynamics in which implied vol at a fixed strike stays put as spot moves. §15.5

Stirling number (2nd kind): $S(n,k)$: the number of ways to partition a SET of $n$ labelled elements into $k$ nonempty unlabelled blocks. $S(n,k)=k\,S(n-1,k)+S(n-1,k-1)$. §19.11

Stochastic volatility: A model in which volatility itself follows a random process driven by its own Brownian motion. §15.4

Stopping time: A random time $\tau$ with $\{\tau\le n\}\in\F_n$ for all $n$: the decision to stop uses only past information. §7.7

Stratified sampling: Partitioning the sample space into strata and sampling each in fixed proportion to remove between-stratum variance. §13.3

Strict stationarity: The full joint distribution is invariant to time shifts: $(X_{t_1},\dots,X_{t_k})$ and $(X_{t_1+h},\dots,X_{t_k+h})$ agree. §12.1

Strictly convex: Strict inequality for $x\ne y,\ \theta\in(0,1)$; guarantees a unique minimizer if one exists. §10.1

Strong convergence: Path-wise accuracy: $\E|X^{\Delta t}_T-X_T|\le C\,\Delta t^{\gamma}$; Euler has strong order $\gamma=\tfrac12$. §13.4

Strong convexity: There is $\mu\gt 0$ with $\nabla^2 f\succeq\mu I$; gives linear convergence. §10.4

Strong duality: When $d^\star=p^\star$ (zero gap); holds for convex problems under a constraint qualification. §10.3

Strong induction: Assume P holds for all values up to k to prove P(k+1); equivalent in power to weak induction. §1.4

Strong law (SLLN): For i.i.d. with finite mean, $\bar X_n\to\mu$ almost surely (Kolmogorov). §7.5

Strong solution: A process adapted to the driving Brownian filtration satisfying the SDE for a given $W$ and $X_0$. §9.3

Sublevel set: The set $\{x:f(x)\le\alpha\}$; convex for every $\alpha$ when $f$ is convex. §10.1

Submartingale / supermartingale: $\E[M_{n+1}\mid\F_n]\ge M_n$ (favorable) / $\le M_n$ (unfavorable). §7.7

Submask enumeration: s = (s-1) & mask walks all submasks of mask in decreasing order; over all masks this totals $3^n$ steps, not $4^n$. §19.8

Subspace: A nonempty subset closed under addition and scalar multiplication; automatically contains $0$. §4.1

Sufficient condition: P is sufficient for Q when P ⇒ Q: P alone guarantees Q. §1.2

Survivorship bias: Studying only assets that survived, silently dropping the delisted/defaulted ones and overstating returns. §11.7

Survivorship bias: Testing only on assets that survived to today, omitting delisted/failed names; inflates returns. §16.6

SVD: $A=U\Sigma V^\top$ with orthogonal $U,V$ and nonnegative singular values on $\Sigma$. §5.5

SVI: Stochastic Volatility Inspired parameterization of a total-variance slice with five parameters. §15.5

Symmetric matrix: $A=A^\top$; the natural class for covariance, Hessians, and Gram matrices. §4.6

Tabulation: Bottom-up filling of an array in a topological order of the dependency DAG. Faster constants, easy memory reduction. §19.7

Tangency portfolio: The risky portfolio maximizing the Sharpe ratio; with a risk-free asset, all investors hold it plus cash (two-fund separation). §14.5

Tangent line: The line through (x,f(x)) with slope f′(x); the best local linear fit to the graph. §2.2

Taylor polynomial: P_n(x)=∑_{k=0}^n f^{(k)}(a)(x−a)^k/k!, the best degree-n polynomial matching f and its derivatives at a. §2.4

Temporary impact: A transient price concession for demanding immediacy that decays after you stop trading. §16.3

Terminal condition: The payoff $v(T,x)=h(x)$ that anchors the backward PDE at maturity. §9.5

Test error: Expected loss on independent data from the same distribution; the quantity we actually care about. §11.3

Testing effect: Retrieving information strengthens memory more than re-studying it for the same time. §0.2

Theta Θ: Time decay $\partial V/\partial t$; the price you pay (or earn) for holding the position as time passes. §15.1

Timing risk: Variance of cost from price moves while the position is still open; grows the slower you trade. §16.4

Timing risk: The risk that price drifts while you execute slowly; grows with volatility and horizon. §18.6

Tolerance: The allowed gap atol/rtol in a floating comparison, chosen from the algorithm’s error, not arbitrarily. §17.2

Total (first-order) variation: $\sum_k|f(t_k)-f(t_{k-1})|$; finite for smooth paths, infinite for BM. §8.4

Total derivative: The best linear approximation $f(a+h)\approx f(a)+\nabla f(a)\cdot h$; differentiability means this error is $o(\lVert h\rVert)$. §3.2

Total implied variance: $w(k,T)=\sigma_{\text{imp}}^2(k,T)\,T$, the natural coordinate for surface arbitrage conditions. §15.3

Total variance: $w(k,T)=\sigma_{\text{imp}}^2(k,T)\,T$ in log-moneyness $k=\ln(K/F)$; the natural no-arbitrage coordinate. §15.5

Tower property: $\E[\E[X\mid\mathcal{G}]]=\E[X]$; more generally $\E[\E[X\mid\mathcal{G}]\mid\mathcal{H}]=\E[X\mid\mathcal{H}]$ for $\mathcal{H}\subseteq\mathcal{G}$. §7.3

Trace: The sum of diagonal entries $\tr A$, equal to the sum of eigenvalues. §4.3

Tracer bullet: A thin end-to-end skeleton of the real system, built early to hit the target and then fleshed out. §17.4

Trading trajectory: The planned remaining holdings $x_k$ (or trade sizes $n_k$) over the execution horizon. §16.4

Training error: Average loss on the same data used to fit; optimistically low, decreasing with complexity. §11.3

Transaction cost: The cost of trading (spread, commission, slippage) that erodes gross returns; often decisive. §18.5

Transition matrix: $P=(p_{ij})$ with $p_{ij}=\Prob(X_{n+1}=j\mid X_n=i)$; rows are probability vectors (stochastic matrix). §8.1

TWAP: Time-weighted average price: trade equal amounts each interval; the $\lambda\to0$ Almgren–Chriss solution. §16.4

TWAP / VWAP: Time- (or volume-) weighted average price: standard execution benchmarks and schedules. §18.6

Unbiasedness: An estimator with $\E[\hat\theta_N]=\theta$ for every $N$; the sample mean is unbiased by linearity of expectation. §13.2

Unconditional variance: $\omega/(1-\alpha-\beta)$ for stationary GARCH(1,1); the long-run average variance. §12.4

Uniform integrability: A sharpening of domination controlling tails uniformly; the general condition behind $L^1$ convergence. §6.4

Union–find: Disjoint-set structure with union by rank + path compression; near-constant $\alpha(n)$ amortised per operation. §19.9

Uniqueness theorem: Equal characteristic functions imply equal laws; convergence of $\phi$ gives convergence in distribution (Levy). §7.4

Unit / invertible residue: $a$ with $\gcd(a,n)=1$; exactly these have an inverse mod $n$, and they form a group $(\Z/n\Z)^\times$ of size $\varphi(n)$. §19.3

Unit root: A root on the unit circle (e.g. a random walk); the series is non-stationary and must be differenced. §12.1

Unit test: A small automated check that a function returns the expected output on specified inputs, run on every change. §17.2

Universal / existential quantifier: ∀ (for all) and ∃ (there exists); binds a variable over a domain. §1.2

Value function: The function $v(t,x)=\E[\text{payoff}\mid X_t=x]$ (possibly discounted) that solves the PDE. §9.5

VAR($p$: Vector autoregression: $x_t=c+\sum_{i=1}^p \Phi_i x_{t-i}+\varepsilon_t$ for a vector $x_t$ of series. §12.6

Variance: $\Var(X)=\E[(X-\E X)^2]=\E[X^2]-(\E X)^2$; mean-squared spread. §7.2

Variance of an estimator: The spread $\Var(\hat\theta)$ of the estimate across hypothetical repeated samples. §11.1

Variant / measure: A non-negative integer that strictly decreases each iteration - the termination half of the proof (well-ordering, as in Euclid). §19.14

Vector field: A function $F:\R^n\to\R^m$ assigning a vector to each point, e.g. a gradient or a force. §3.1

Vector space: A set with addition and scalar multiplication satisfying the eight axioms (closure, associativity, identity, inverses, distributivity). §4.1

Vectorization: Expressing a computation as whole-array operations so the inner loop runs in compiled C, not the Python interpreter. §17.1

Vectorized reduction: A whole-array aggregate such as sum, mean, or @ that collapses an axis in compiled code. §17.1

Vega: Sensitivity of price to volatility, $\partial V/\partial\sigma$; positive for vanilla calls and puts. §14.4

Vega: $\partial C/\partial\sigma\gt 0$: because price is strictly increasing in $\sigma$, implied vol is unique when it exists. §15.2

Vega ν: Sensitivity to volatility $\partial V/\partial\sigma$; not a Greek letter, but the risk that dominates a smile. §15.1

Version control: A system (e.g. git) that records every change as a commit, so any past state can be recovered exactly. §17.3

Visual association: Attaching a vivid image to a symbol/formula to aid retrieval (Fluent Forever’s core trick). §0.5

Vol of vol $\xi$: The volatility of the variance process; controls the convexity (curvature) of the smile. §15.4

Volatility clustering: The empirical tendency of large moves to follow large moves: $|r_t|$ is autocorrelated even when $r_t$ is not. §12.4

Volatility clustering: The tendency of large moves to follow large moves; autocorrelation in squared returns. §18.4

Volatility skew: An asymmetric smile (equities): implied vol rises for low strikes (OTM puts), reflecting crash fear. §15.2

Volatility smile: Implied vol plotted against strike/moneyness that is higher for OTM puts and calls than ATM - a U shape. §15.2

Volatility smile: The empirical pattern that implied vol varies with strike/moneyness, contradicting constant-$\sigma$ BS. §18.4

Volatility surface: The map $(K,T)\mapsto\sigma_{\text{imp}}(K,T)$ of implied vols across all strikes and maturities. §15.5

Walk-forward validation: Training on a past window and testing on the next, rolling forward - the time-series analogue of cross-validation. §18.5

Weak (ordinary) induction: Prove P(1), then P(k)⇒P(k+1); conclude P(n) for all n≥1. §1.4

Weak convergence: Distributional accuracy: $|\E f(X^{\Delta t}_T)-\E f(X_T)|\le C\,\Delta t^{\beta}$; Euler has weak order $\beta=1$. §13.4

Weak duality: Always: $g(\lambda,\nu)\le p^\star$ for $\lambda\ge0$; the best such bound is the dual optimum $d^\star\le p^\star$. §10.3

Weak law (WLLN): For i.i.d. with finite mean, $\bar X_n\to\mu$ in probability. §7.5

Weak stationarity: Constant mean, constant variance, and autocovariance depending only on the lag $h$, not on $t$. §12.1

White noise: Uncorrelated, mean-zero, constant-variance sequence; $\rho(h)=0$ for $h\ne0$; the residual ideal. §12.1

Wiener process: Synonym for standard Brownian motion; the measure it induces on path space is Wiener measure. §8.3

Without loss of generality: A justified reduction to a representative case when symmetry makes the others identical. §1.3

Working memory: The ~4-slot mental scratchpad; chunking is how experts fit hard problems into it. §0.1

Yule-Walker equations: Linear system $\rho(k)=\sum_i\phi_i\rho(k-i)$ relating AR coefficients to the ACF; the basis of one estimator. §12.2

Zone of proximal difficulty: The band of tasks hard enough to require effort but not so hard they can’t be completed with focus. §0.3