{
  "schema": "ml-prep/search@1",
  "items": [
    {
      "id": "mit-6-100l-finger-06",
      "title": "Bisection search finger exercise",
      "area": "programming",
      "area_title": "Programming",
      "topic": "data-structures",
      "topic_title": "Data Structures",
      "skills": [
        "binary-search",
        "loops",
        "conditionals"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "integer-arithmetic"
      ],
      "summary": "A small official exercise that separates binary-search reasoning from library use.",
      "path": "item/mit-6-100l-finger-06/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-06/"
    },
    {
      "id": "mit-6-100l-finger-11",
      "title": "List mutation and sorting finger exercise",
      "area": "programming",
      "area_title": "Programming",
      "topic": "python",
      "topic_title": "Python",
      "skills": [
        "lists-tuples",
        "mutability"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 8,
      "prerequisites": [
        "lists"
      ],
      "summary": "Directly tests in-place mutation and ordering semantics.",
      "path": "item/mit-6-100l-finger-11/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-11/"
    },
    {
      "id": "mit-6-100l-finger-14",
      "title": "Dictionary selection finger exercise",
      "area": "programming",
      "area_title": "Programming",
      "topic": "data-structures",
      "topic_title": "Data Structures",
      "skills": [
        "dictionaries-sets",
        "hash-map"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "dictionaries"
      ],
      "summary": "Uses dictionary iteration, filtering, and deterministic output ordering.",
      "path": "item/mit-6-100l-finger-14/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-14/"
    },
    {
      "id": "mit-6-100l-finger-15",
      "title": "Recursive power finger exercise",
      "area": "programming",
      "area_title": "Programming",
      "topic": "recursion",
      "topic_title": "Recursion",
      "skills": [
        "base-case",
        "recursive-trace",
        "recursive-implementation"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 7,
      "prerequisites": [
        "functions"
      ],
      "summary": "A minimal official check of base and recursive cases.",
      "path": "item/mit-6-100l-finger-15/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-15/"
    },
    {
      "id": "mit-6-100l-finger-16",
      "title": "Recursive flattening finger exercise",
      "area": "programming",
      "area_title": "Programming",
      "topic": "recursion",
      "topic_title": "Recursion",
      "skills": [
        "base-case",
        "recursive-implementation",
        "lists-tuples"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "recursion",
        "lists"
      ],
      "summary": "Adds recursive structural decomposition beyond a scalar recurrence.",
      "path": "item/mit-6-100l-finger-16/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-16/"
    },
    {
      "id": "mit-6-100l-finger-23",
      "title": "Asymptotic complexity finger exercise",
      "area": "programming",
      "area_title": "Programming",
      "topic": "python",
      "topic_title": "Python",
      "skills": [
        "complexity",
        "loops"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "loops"
      ],
      "summary": "Tests complexity from actual Python operations rather than memorized algorithm names.",
      "path": "item/mit-6-100l-finger-23/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-23/"
    },
    {
      "id": "google-mlcc-linear-regression-quiz",
      "title": "Linear regression knowledge check",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "regression",
      "topic_title": "Regression",
      "skills": [
        "linear-regression",
        "squared-loss",
        "gradient-update"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "algebra"
      ],
      "summary": "An authoritative interactive check of the regression objective and training loop.",
      "path": "item/google-mlcc-linear-regression-quiz/",
      "url": "https://mlprep.iwase.dev/item/google-mlcc-linear-regression-quiz/"
    },
    {
      "id": "google-mlcc-logistic-quiz",
      "title": "Logistic regression knowledge check",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "classification",
      "topic_title": "Classification",
      "skills": [
        "logistic-regression",
        "cross-entropy",
        "regularization"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "probability"
      ],
      "summary": "Checks probability interpretation, loss, and regularization on the official Google course.",
      "path": "item/google-mlcc-logistic-quiz/",
      "url": "https://mlprep.iwase.dev/item/google-mlcc-logistic-quiz/"
    },
    {
      "id": "google-mlcc-classification-quiz",
      "title": "Classification metrics knowledge check",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "classification",
      "topic_title": "Classification",
      "skills": [
        "confusion-matrix",
        "precision-recall",
        "decision-boundary"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "fractions"
      ],
      "summary": "Authoritative questions on threshold-dependent classification metrics.",
      "path": "item/google-mlcc-classification-quiz/",
      "url": "https://mlprep.iwase.dev/item/google-mlcc-classification-quiz/"
    },
    {
      "id": "google-mlcc-overfitting-quiz",
      "title": "Generalization and overfitting knowledge check",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "theory",
      "topic_title": "Theory",
      "skills": [
        "generalization",
        "overfitting",
        "train-validation-test",
        "model-complexity",
        "regularization"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "training-loss"
      ],
      "summary": "Covers the evaluation distinctions most often confused under time pressure.",
      "path": "item/google-mlcc-overfitting-quiz/",
      "url": "https://mlprep.iwase.dev/item/google-mlcc-overfitting-quiz/"
    },
    {
      "id": "google-mlcc-neural-network-quiz",
      "title": "Neural-network knowledge check",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "neural-networks",
      "topic_title": "Neural Networks",
      "skills": [
        "forward-pass",
        "activations",
        "backpropagation"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "linear-models"
      ],
      "summary": "A concise official check of architecture, activations, and training.",
      "path": "item/google-mlcc-neural-network-quiz/",
      "url": "https://mlprep.iwase.dev/item/google-mlcc-neural-network-quiz/"
    },
    {
      "id": "leetcode-20-valid-parentheses",
      "title": "Valid Parentheses",
      "area": "programming",
      "area_title": "Programming",
      "topic": "data-structures",
      "topic_title": "Data Structures",
      "skills": [
        "stack",
        "conditionals"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 12,
      "prerequisites": [
        "strings"
      ],
      "summary": "A standard stack invariant problem with immediate judge feedback on malformed nesting and edge cases.",
      "path": "item/leetcode-20-valid-parentheses/",
      "url": "https://mlprep.iwase.dev/item/leetcode-20-valid-parentheses/"
    },
    {
      "id": "leetcode-215-kth-largest",
      "title": "Kth Largest Element in an Array",
      "area": "programming",
      "area_title": "Programming",
      "topic": "data-structures",
      "topic_title": "Data Structures",
      "skills": [
        "heap",
        "complexity"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 20,
      "prerequisites": [
        "arrays",
        "priority-queues"
      ],
      "summary": "Requires selecting an appropriate heap or selection strategy under an explicit complexity target and provides judge feedback.",
      "path": "item/leetcode-215-kth-largest/",
      "url": "https://mlprep.iwase.dev/item/leetcode-215-kth-largest/"
    },
    {
      "id": "leetcode-704-binary-search",
      "title": "Binary Search",
      "area": "programming",
      "area_title": "Programming",
      "topic": "data-structures",
      "topic_title": "Data Structures",
      "skills": [
        "binary-search",
        "conditionals",
        "loops"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "sorted-arrays"
      ],
      "summary": "Tests interval invariants and termination on a canonical sorted-array search with judge feedback.",
      "path": "item/leetcode-704-binary-search/",
      "url": "https://mlprep.iwase.dev/item/leetcode-704-binary-search/"
    },
    {
      "id": "leetcode-752-open-the-lock",
      "title": "Open the Lock",
      "area": "programming",
      "area_title": "Programming",
      "topic": "data-structures",
      "topic_title": "Data Structures",
      "skills": [
        "queue",
        "bfs",
        "dictionaries-sets"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 25,
      "prerequisites": [
        "graphs",
        "shortest-path"
      ],
      "summary": "Models an implicit state graph and requires BFS with visited-state handling; submissions receive judge feedback.",
      "path": "item/leetcode-752-open-the-lock/",
      "url": "https://mlprep.iwase.dev/item/leetcode-752-open-the-lock/"
    },
    {
      "id": "leetcode-200-number-of-islands",
      "title": "Number of Islands",
      "area": "programming",
      "area_title": "Programming",
      "topic": "data-structures",
      "topic_title": "Data Structures",
      "skills": [
        "dfs",
        "bfs",
        "queue",
        "recursive-implementation"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 25,
      "prerequisites": [
        "grids",
        "graph-traversal"
      ],
      "summary": "Uses recursive or iterative flood fill to test traversal state, base cases, and component counting with judge feedback.",
      "path": "item/leetcode-200-number-of-islands/",
      "url": "https://mlprep.iwase.dev/item/leetcode-200-number-of-islands/"
    },
    {
      "id": "mit-18-02sc-f2010-exam2-q1",
      "title": "Gradient, tangent plane, linearization, and directional derivative",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "calculus",
      "topic_title": "Calculus",
      "skills": [
        "gradient",
        "directional-derivative"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 12,
      "prerequisites": [
        "partial-derivatives"
      ],
      "summary": "A fast diagnostic of the multivariable differential concepts most likely to transfer to ML.",
      "path": "item/mit-18-02sc-f2010-exam2-q1/",
      "url": "https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q1/"
    },
    {
      "id": "mit-18-02sc-f2010-exam2-q3",
      "title": "Critical points and constrained domain boundaries",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "calculus",
      "topic_title": "Calculus",
      "skills": [
        "critical-points"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 14,
      "prerequisites": [
        "partial-derivatives",
        "quadratic-functions"
      ],
      "summary": "Separates local critical-point classification from optimization over a constrained region.",
      "path": "item/mit-18-02sc-f2010-exam2-q3/",
      "url": "https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q3/"
    },
    {
      "id": "mit-18-02sc-f2010-exam2-q4",
      "title": "Multivariable chain rule under a change of variables",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "calculus",
      "topic_title": "Calculus",
      "skills": [
        "chain-rule",
        "partial-derivatives"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "partial-derivatives"
      ],
      "summary": "Tests symbolic chain-rule bookkeeping that directly supports backpropagation and reparameterization.",
      "path": "item/mit-18-02sc-f2010-exam2-q4/",
      "url": "https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q4/"
    },
    {
      "id": "mit-18-02sc-f2010-exam2-q5",
      "title": "Lagrange multiplier equations and tangent geometry",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "calculus",
      "topic_title": "Calculus",
      "skills": [
        "constrained-optimization"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "gradient",
        "implicit-surfaces"
      ],
      "summary": "Focuses on setting up constrained optimization and interpreting the shared normal direction.",
      "path": "item/mit-18-02sc-f2010-exam2-q5/",
      "url": "https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q5/"
    },
    {
      "id": "mit-18-02sc-f2010-exam2-q6",
      "title": "Total differentials and implicit differentiation",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "calculus",
      "topic_title": "Calculus",
      "skills": [
        "implicit-differentiation",
        "linear-systems"
      ],
      "priority": "supplementary",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "partial-derivatives"
      ],
      "summary": "Checks whether local differential constraints can be combined and solved without treating variables as independent.",
      "path": "item/mit-18-02sc-f2010-exam2-q6/",
      "url": "https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q6/"
    },
    {
      "id": "mit-18-05-s2022-exam1-q1b",
      "title": "Events, unions, and conditional probability",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "event-algebra",
        "inclusion-exclusion",
        "conditional-probability"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 6,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "A compact check of whether event notation and conditioning are operational rather than merely familiar.",
      "path": "item/mit-18-05-s2022-exam1-q1b/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q1b/"
    },
    {
      "id": "mit-18-05-s2022-exam1-q3",
      "title": "Joint tables, Bayes rule, and independence",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "bayes-rule",
        "independence"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 14,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "Uses one finite model to test joint and marginal probabilities, reverse conditioning, and independence.",
      "path": "item/mit-18-05-s2022-exam1-q3/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q3/"
    },
    {
      "id": "mit-18-05-s2022-exam1-q4",
      "title": "Diagnostic testing with base rates",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "bayes-rule",
        "conditional-probability"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 8,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "A short, discriminative Bayes calculation whose interpretation transfers directly to ML evaluation.",
      "path": "item/mit-18-05-s2022-exam1-q4/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q4/"
    },
    {
      "id": "mit-18-05-s2022-exam1-q5",
      "title": "Joint density, moments, covariance, and correlation",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "joint-marginal-conditional",
        "independence",
        "expectation",
        "variance"
      ],
      "priority": "core",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 24,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "Integrates continuous probability, moments, dependence, and a geometric integration region in one coherent problem.",
      "path": "item/mit-18-05-s2022-exam1-q5/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q5/"
    },
    {
      "id": "mit-18-05-s2022-exam1-q6",
      "title": "Central limit theorem for an aggregate",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "central-limit-theorem",
        "sums-of-random-variables"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "Tests whether the learner can propagate mean and variance and standardize an aggregate.",
      "path": "item/mit-18-05-s2022-exam1-q6/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q6/"
    },
    {
      "id": "mit-18-05-s2022-exam2-i2",
      "title": "Type I error, Type II error, and power",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "null-alternative",
        "type-errors-power"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 5,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "A rapid conceptual diagnostic that catches common confusion among significance, power, and error rates.",
      "path": "item/mit-18-05-s2022-exam2-i2/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-i2/"
    },
    {
      "id": "mit-18-05-s2022-exam2-ii1",
      "title": "Maximum likelihood estimation from a density",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "likelihood",
        "maximum-likelihood"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 12,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "Requires constructing and differentiating a likelihood rather than quoting an estimator.",
      "path": "item/mit-18-05-s2022-exam2-ii1/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-ii1/"
    },
    {
      "id": "mit-18-05-s2022-exam2-ii2",
      "title": "Bayesian posterior density and normalization",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "bayesian-updating"
      ],
      "priority": "core",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 15,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "Tests likelihood construction, prior multiplication, and posterior normalization in a finite-outcome model.",
      "path": "item/mit-18-05-s2022-exam2-ii2/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-ii2/"
    },
    {
      "id": "mit-18-05-s2022-exam2-ii4",
      "title": "One-sided test, critical value, and p-value",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "null-alternative",
        "p-values-critical-regions"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 12,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "Connects a rejection region, significance level, observed statistic, and p-value without relying on one mnemonic.",
      "path": "item/mit-18-05-s2022-exam2-ii4/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-ii4/"
    },
    {
      "id": "mit-18-05-s2022-exam2-ii5",
      "title": "Chi-square test for a contingency table",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "goodness-of-fit",
        "chi-square"
      ],
      "priority": "core",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 18,
      "prerequisites": [
        "basic-algebra"
      ],
      "summary": "Checks end-to-end statistical reasoning from hypotheses through expected counts to a justified decision.",
      "path": "item/mit-18-05-s2022-exam2-ii5/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-ii5/"
    },
    {
      "id": "mit-18-06-s2010-exam1-q2",
      "title": "Nullspace, column space, pivots, and block structure",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "linear-algebra",
      "topic_title": "Linear Algebra",
      "skills": [
        "matrix-operations",
        "linear-systems",
        "row-reduction",
        "subspaces",
        "rank",
        "rank-nullity"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 14,
      "prerequisites": [
        "linear-systems",
        "reduced-row-echelon-form"
      ],
      "summary": "Distinguishes procedural row reduction from geometric understanding of the four fundamental subspaces.",
      "path": "item/mit-18-06-s2010-exam1-q2/",
      "url": "https://mlprep.iwase.dev/item/mit-18-06-s2010-exam1-q2/"
    },
    {
      "id": "mit-18-06-s2010-exam2-q1",
      "title": "Projection matrix as geometry and spectrum",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "linear-algebra",
      "topic_title": "Linear Algebra",
      "skills": [
        "projection",
        "eigenvalues"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 15,
      "prerequisites": [
        "orthogonality",
        "outer-products"
      ],
      "summary": "Connects a projection formula to its subspaces and eigenstructure, a high-value ML pattern.",
      "path": "item/mit-18-06-s2010-exam2-q1/",
      "url": "https://mlprep.iwase.dev/item/mit-18-06-s2010-exam2-q1/"
    },
    {
      "id": "mit-18-06-s2010-exam2-q2",
      "title": "Least squares, QR, and orthonormal projection",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "linear-algebra",
      "topic_title": "Linear Algebra",
      "skills": [
        "least-squares",
        "normal-equations",
        "qr",
        "projection",
        "orthogonality"
      ],
      "priority": "core",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 18,
      "prerequisites": [
        "orthogonality",
        "matrix-inverse"
      ],
      "summary": "Tests the derivation and interpretation of least squares rather than formula recall alone.",
      "path": "item/mit-18-06-s2010-exam2-q2/",
      "url": "https://mlprep.iwase.dev/item/mit-18-06-s2010-exam2-q2/"
    },
    {
      "id": "mit-18-06-s2010-exam3-q1",
      "title": "Symmetry, orthogonality, and eigenspaces",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "linear-algebra",
      "topic_title": "Linear Algebra",
      "skills": [
        "symmetric-matrices",
        "eigenvalues",
        "diagonalization"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 16,
      "prerequisites": [
        "outer-products",
        "orthogonal-complements"
      ],
      "summary": "Uses a structured matrix to test proof, geometry, multiplicity, and trace in one compact question.",
      "path": "item/mit-18-06-s2010-exam3-q1/",
      "url": "https://mlprep.iwase.dev/item/mit-18-06-s2010-exam3-q1/"
    },
    {
      "id": "mit-18-06-s2010-exam3-q2",
      "title": "Positive definite and semidefinite transformations",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "linear-algebra",
      "topic_title": "Linear Algebra",
      "skills": [
        "positive-definiteness",
        "quadratic-forms"
      ],
      "priority": "core",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 14,
      "prerequisites": [
        "eigenvalues",
        "quadratic-forms"
      ],
      "summary": "Exercises three interchangeable tests for positive definiteness and a useful block-matrix argument.",
      "path": "item/mit-18-06-s2010-exam3-q2/",
      "url": "https://mlprep.iwase.dev/item/mit-18-06-s2010-exam3-q2/"
    },
    {
      "id": "mit-18-06-s2010-exam3-q3c",
      "title": "Singular value decomposition from the Gram matrix",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "linear-algebra",
      "topic_title": "Linear Algebra",
      "skills": [
        "svd",
        "orthogonality"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 10,
      "prerequisites": [
        "eigenvalues",
        "orthogonality"
      ],
      "summary": "A compact check that the learner can construct an SVD from the eigendecomposition of a Gram matrix.",
      "path": "item/mit-18-06-s2010-exam3-q3c/",
      "url": "https://mlprep.iwase.dev/item/mit-18-06-s2010-exam3-q3c/"
    },
    {
      "id": "mit-6-036-s2018-final-q9",
      "title": "Convolutional representation and detector design",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "convolution",
      "topic_title": "Convolution",
      "skills": [
        "convolution-operation",
        "output-shape",
        "receptive-field"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 18,
      "prerequisites": [
        "matrix-indexing",
        "relu"
      ],
      "summary": "Requires an actual convolution and composes small filters into a deeper detector instead of testing shape recall alone.",
      "path": "item/mit-6-036-s2018-final-q9/",
      "url": "https://mlprep.iwase.dev/item/mit-6-036-s2018-final-q9/"
    },
    {
      "id": "mit-6-036-s2019-final-q4",
      "title": "CNN shapes, pooling, and backpropagation",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "convolution",
      "topic_title": "Convolution",
      "skills": [
        "convolution-operation",
        "output-shape",
        "parameter-count",
        "pooling"
      ],
      "priority": "supplementary",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 25,
      "prerequisites": [
        "backpropagation",
        "max-pooling",
        "sgd"
      ],
      "summary": "Integrates convolutional shapes, loss choice, differentiation through convolution and pooling, and an SGD debugging decision.",
      "path": "item/mit-6-036-s2019-final-q4/",
      "url": "https://mlprep.iwase.dev/item/mit-6-036-s2019-final-q4/"
    },
    {
      "id": "mit-6-036-s2019-midterm-q5",
      "title": "Learning as optimization",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "optimization",
      "topic_title": "Optimization",
      "skills": [
        "objective-functions",
        "convexity",
        "optimization-diagnostics",
        "stationary-points"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 18,
      "prerequisites": [
        "derivatives",
        "gradient-descent",
        "loss-functions"
      ],
      "summary": "Derives an update and distinguishes slow, oscillating, and divergent learning-rate behavior from objective geometry.",
      "path": "item/mit-6-036-s2019-midterm-q5/",
      "url": "https://mlprep.iwase.dev/item/mit-6-036-s2019-midterm-q5/"
    },
    {
      "id": "mit-6-036-s2019-midterm-q4",
      "title": "Diagnose model evaluation failures",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "theory",
      "topic_title": "Theory",
      "skills": [
        "bias-variance",
        "generalization",
        "overfitting",
        "train-validation-test",
        "model-complexity"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 15,
      "prerequisites": [
        "classification-metrics"
      ],
      "summary": "Uses observed train and held-out behavior to separate overfitting, insufficient expressivity, data scarcity, and distribution shift.",
      "path": "item/mit-6-036-s2019-midterm-q4/",
      "url": "https://mlprep.iwase.dev/item/mit-6-036-s2019-midterm-q4/"
    },
    {
      "id": "mit-6-100l-finger-05",
      "title": "Even-indexed characters finger exercise",
      "area": "programming",
      "area_title": "Programming",
      "topic": "control-flow",
      "topic_title": "Control Flow",
      "skills": [
        "conditionals",
        "loops",
        "strings"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 5,
      "prerequisites": [
        "string-indexing"
      ],
      "summary": "Uses a compact string traversal to test index parity, loop state, and output construction.",
      "path": "item/mit-6-100l-finger-05/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-05/"
    },
    {
      "id": "mit-6-100l-finger-08",
      "title": "Compare character sets in two strings",
      "area": "programming",
      "area_title": "Programming",
      "topic": "control-flow",
      "topic_title": "Control Flow",
      "skills": [
        "conditionals",
        "loops",
        "strings"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 6,
      "prerequisites": [
        "membership"
      ],
      "summary": "Tests bidirectional membership reasoning rather than only one pass over one string.",
      "path": "item/mit-6-100l-finger-08/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-08/"
    },
    {
      "id": "mit-6-100l-finger-17",
      "title": "Circle class and value equality",
      "area": "programming",
      "area_title": "Programming",
      "topic": "python",
      "topic_title": "Python",
      "skills": [
        "classes",
        "value-equality",
        "functions"
      ],
      "priority": "supplementary",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 12,
      "prerequisites": [
        "methods",
        "object-state"
      ],
      "summary": "Exercises object state, accessors, mutation, and explicit value equality through a small class contract.",
      "path": "item/mit-6-100l-finger-17/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-17/"
    },
    {
      "id": "mit-6-100l-finger-19",
      "title": "Stack subclass implementation",
      "area": "programming",
      "area_title": "Programming",
      "topic": "data-structures",
      "topic_title": "Data Structures",
      "skills": [
        "stack",
        "classes",
        "lists-tuples"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 15,
      "prerequisites": [
        "lists",
        "methods"
      ],
      "summary": "Implements a LIFO abstraction while distinguishing inherited container behavior from stack-specific removal.",
      "path": "item/mit-6-100l-finger-19/",
      "url": "https://mlprep.iwase.dev/item/mit-6-100l-finger-19/"
    },
    {
      "id": "mit-18-01sc-f2010-final-foundations",
      "title": "Single-variable calculus foundation check",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "calculus",
      "topic_title": "Calculus",
      "skills": [
        "limits-continuity",
        "single-variable-calculus",
        "taylor-approximation"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 24,
      "prerequisites": [
        "polynomials"
      ],
      "summary": "Uses official exam questions to check differentiation, a limit, definite integration, and Taylor approximation independently.",
      "path": "item/mit-18-01sc-f2010-final-foundations/",
      "url": "https://mlprep.iwase.dev/item/mit-18-01sc-f2010-final-foundations/"
    },
    {
      "id": "mit-18-05-s2022-pset11-q1",
      "title": "Confidence intervals with known and unknown variance",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "confidence-intervals",
        "standard-error",
        "sampling-distributions"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "external",
      "estimated_minutes": 14,
      "prerequisites": [
        "gaussian-distribution"
      ],
      "summary": "Contrasts t and z intervals on the same data and extends the calculation to sample-size planning.",
      "path": "item/mit-18-05-s2022-pset11-q1/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-pset11-q1/"
    },
    {
      "id": "mit-18-05-s2022-pset6-q2",
      "title": "Simple linear regression from Gaussian maximum likelihood",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "simple-linear-regression",
        "maximum-likelihood",
        "likelihood"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 25,
      "prerequisites": [
        "gaussian-distribution",
        "partial-derivatives"
      ],
      "summary": "Derives a fitted line from an explicit Gaussian error model, linking regression, likelihood, and least squares.",
      "path": "item/mit-18-05-s2022-pset6-q2/",
      "url": "https://mlprep.iwase.dev/item/mit-18-05-s2022-pset6-q2/"
    },
    {
      "id": "original-la-foundations",
      "title": "Matrix fundamentals under time pressure",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "linear-algebra",
      "topic_title": "Linear Algebra",
      "skills": [
        "matrix-operations",
        "inverse",
        "determinant-trace",
        "matrix-norms"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 8,
      "prerequisites": [
        "matrix-arithmetic"
      ],
      "summary": "Original practice item.",
      "path": "item/original-la-foundations/",
      "url": "https://mlprep.iwase.dev/item/original-la-foundations/"
    },
    {
      "id": "original-la-basis-change",
      "title": "Basis, dimension, and coordinates",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "linear-algebra",
      "topic_title": "Linear Algebra",
      "skills": [
        "independence",
        "basis-dimension",
        "change-of-basis"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 8,
      "prerequisites": [
        "linear-combinations"
      ],
      "summary": "Original practice item.",
      "path": "item/original-la-basis-change/",
      "url": "https://mlprep.iwase.dev/item/original-la-basis-change/"
    },
    {
      "id": "original-la-low-rank",
      "title": "Low-rank error and explained variance",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "linear-algebra",
      "topic_title": "Linear Algebra",
      "skills": [
        "svd",
        "low-rank-approximation",
        "pca-connection",
        "svd-pca"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 8,
      "prerequisites": [
        "singular-values"
      ],
      "summary": "Original practice item.",
      "path": "item/original-la-low-rank/",
      "url": "https://mlprep.iwase.dev/item/original-la-low-rank/"
    },
    {
      "id": "original-calc-jacobian",
      "title": "Jacobian and chain rule",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "calculus",
      "topic_title": "Calculus",
      "skills": [
        "partial-derivatives",
        "jacobian",
        "chain-rule",
        "gradient"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 10,
      "prerequisites": [
        "partial-derivatives"
      ],
      "summary": "Original practice item.",
      "path": "item/original-calc-jacobian/",
      "url": "https://mlprep.iwase.dev/item/original-calc-jacobian/"
    },
    {
      "id": "original-calc-matrix",
      "title": "Matrix gradient and Hessian",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "calculus",
      "topic_title": "Calculus",
      "skills": [
        "matrix-calculus",
        "gradient",
        "hessian",
        "convexity"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 10,
      "prerequisites": [
        "matrix-multiplication",
        "chain-rule"
      ],
      "summary": "Original practice item.",
      "path": "item/original-calc-matrix/",
      "url": "https://mlprep.iwase.dev/item/original-calc-matrix/"
    },
    {
      "id": "original-prob-distributions",
      "title": "Recognize distribution moments",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "discrete-random-variables",
        "continuous-random-variables",
        "named-distributions",
        "sums-of-random-variables",
        "expectation",
        "variance"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 8,
      "prerequisites": [
        "random-variables"
      ],
      "summary": "Original practice item.",
      "path": "item/original-prob-distributions/",
      "url": "https://mlprep.iwase.dev/item/original-prob-distributions/"
    },
    {
      "id": "original-prob-total-variance",
      "title": "Conditional expectation and total variance",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "conditional-expectation",
        "total-expectation-variance",
        "expectation",
        "variance"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 8,
      "prerequisites": [
        "conditional-probability"
      ],
      "summary": "Original practice item.",
      "path": "item/original-prob-total-variance/",
      "url": "https://mlprep.iwase.dev/item/original-prob-total-variance/"
    },
    {
      "id": "original-prob-gaussian",
      "title": "Linear transform of a multivariate Gaussian",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "multivariate-gaussian",
        "transformations",
        "covariance-correlation"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 8,
      "prerequisites": [
        "matrix-multiplication",
        "gaussian-distribution"
      ],
      "summary": "Original practice item.",
      "path": "item/original-prob-gaussian/",
      "url": "https://mlprep.iwase.dev/item/original-prob-gaussian/"
    },
    {
      "id": "original-prob-foundations",
      "title": "Counting, total probability, and independence",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "counting",
        "conditional-probability",
        "independence"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 7,
      "prerequisites": [
        "fractions"
      ],
      "summary": "Original practice item.",
      "path": "item/original-prob-foundations/",
      "url": "https://mlprep.iwase.dev/item/original-prob-foundations/"
    },
    {
      "id": "original-prob-lln",
      "title": "LLN versus CLT",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "law-of-large-numbers",
        "central-limit-theorem"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 5,
      "prerequisites": [
        "expectation",
        "variance"
      ],
      "summary": "Original practice item.",
      "path": "item/original-prob-lln/",
      "url": "https://mlprep.iwase.dev/item/original-prob-lln/"
    },
    {
      "id": "original-stats-estimator",
      "title": "Bias, variance, MSE, and consistency",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "samples-statistics",
        "sampling-distributions",
        "estimator-bias-variance-mse",
        "consistency",
        "standard-error"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 7,
      "prerequisites": [
        "expectation",
        "variance"
      ],
      "summary": "Original practice item.",
      "path": "item/original-stats-estimator/",
      "url": "https://mlprep.iwase.dev/item/original-stats-estimator/"
    },
    {
      "id": "original-stats-mom-map",
      "title": "Method of moments and Bayesian updating",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "method-of-moments",
        "map",
        "bayesian-updating",
        "likelihood"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 10,
      "prerequisites": [
        "exponential-distribution",
        "beta-distribution"
      ],
      "summary": "Original practice item.",
      "path": "item/original-stats-mom-map/",
      "url": "https://mlprep.iwase.dev/item/original-stats-mom-map/"
    },
    {
      "id": "original-ml-regression",
      "title": "Linear regression objective and gradient",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "regression",
      "topic_title": "Regression",
      "skills": [
        "linear-regression",
        "squared-loss",
        "regression-gradient"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 8,
      "prerequisites": [
        "matrix-multiplication",
        "derivatives"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-regression/",
      "url": "https://mlprep.iwase.dev/item/original-ml-regression/"
    },
    {
      "id": "original-ml-logistic",
      "title": "Logistic probability and cross-entropy",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "classification",
      "topic_title": "Classification",
      "skills": [
        "logistic-regression",
        "cross-entropy",
        "decision-boundary"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 6,
      "prerequisites": [
        "logarithms"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-logistic/",
      "url": "https://mlprep.iwase.dev/item/original-ml-logistic/"
    },
    {
      "id": "original-ml-metrics",
      "title": "Classification metrics from counts",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "classification",
      "topic_title": "Classification",
      "skills": [
        "confusion-matrix",
        "precision-recall"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 6,
      "prerequisites": [
        "fractions"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-metrics/",
      "url": "https://mlprep.iwase.dev/item/original-ml-metrics/"
    },
    {
      "id": "original-ml-gd",
      "title": "Gradient descent on a quadratic",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "gradient-descent",
      "topic_title": "Gradient Descent",
      "skills": [
        "gradient-update",
        "learning-rate",
        "convergence"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 7,
      "prerequisites": [
        "derivatives"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-gd/",
      "url": "https://mlprep.iwase.dev/item/original-ml-gd/"
    },
    {
      "id": "original-ml-sgd",
      "title": "Full gradient versus stochastic gradient",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "gradient-descent",
      "topic_title": "Gradient Descent",
      "skills": [
        "gradient-update",
        "sgd",
        "convergence"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 7,
      "prerequisites": [
        "expectation"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-sgd/",
      "url": "https://mlprep.iwase.dev/item/original-ml-sgd/"
    },
    {
      "id": "original-ml-pca",
      "title": "PCA direction and explained variance",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "dimensionality-reduction",
      "topic_title": "Dimensionality Reduction",
      "skills": [
        "pca-objective",
        "centering",
        "covariance-eigendecomposition",
        "explained-variance"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 7,
      "prerequisites": [
        "eigenvalues"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-pca/",
      "url": "https://mlprep.iwase.dev/item/original-ml-pca/"
    },
    {
      "id": "original-ml-kmeans",
      "title": "One k-means assignment and update",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "unsupervised-learning",
      "topic_title": "Unsupervised Learning",
      "skills": [
        "k-means",
        "clustering-objective"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 7,
      "prerequisites": [
        "squared-distance"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-kmeans/",
      "url": "https://mlprep.iwase.dev/item/original-ml-kmeans/"
    },
    {
      "id": "original-ml-gmm",
      "title": "Mixture responsibilities and EM",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "unsupervised-learning",
      "topic_title": "Unsupervised Learning",
      "skills": [
        "gaussian-mixtures",
        "expectation-maximization",
        "clustering-objective"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 7,
      "prerequisites": [
        "bayes-rule"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-gmm/",
      "url": "https://mlprep.iwase.dev/item/original-ml-gmm/"
    },
    {
      "id": "original-ml-forward-backprop",
      "title": "Forward pass and backpropagation",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "neural-networks",
      "topic_title": "Neural Networks",
      "skills": [
        "forward-pass",
        "activations",
        "chain-rule",
        "backpropagation"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 8,
      "prerequisites": [
        "chain-rule"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-forward-backprop/",
      "url": "https://mlprep.iwase.dev/item/original-ml-forward-backprop/"
    },
    {
      "id": "original-ml-network-params",
      "title": "Dense-network parameter count",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "neural-networks",
      "topic_title": "Neural Networks",
      "skills": [
        "parameter-count"
      ],
      "priority": "foundation",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 4,
      "prerequisites": [
        "matrix-shapes"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-network-params/",
      "url": "https://mlprep.iwase.dev/item/original-ml-network-params/"
    },
    {
      "id": "original-ml-convolution",
      "title": "Convolution output shape and parameters",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "convolution",
      "topic_title": "Convolution",
      "skills": [
        "output-shape",
        "padding-stride",
        "parameter-count"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 6,
      "prerequisites": [
        "integer-arithmetic"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-convolution/",
      "url": "https://mlprep.iwase.dev/item/original-ml-convolution/"
    },
    {
      "id": "original-ml-regularization",
      "title": "L1 versus L2 regularization",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "optimization",
      "topic_title": "Optimization",
      "skills": [
        "regularization",
        "objective-functions",
        "model-complexity",
        "generalization"
      ],
      "priority": "core",
      "difficulty": "easy",
      "origin": "original",
      "estimated_minutes": 6,
      "prerequisites": [
        "norms"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-regularization/",
      "url": "https://mlprep.iwase.dev/item/original-ml-regularization/"
    },
    {
      "id": "original-ml-finite-class-bound",
      "title": "Read a finite-class generalization bound",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "theory",
      "topic_title": "Theory",
      "skills": [
        "generalization",
        "model-complexity"
      ],
      "priority": "stretch",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 7,
      "prerequisites": [
        "logarithms",
        "probability"
      ],
      "summary": "Original practice item.",
      "path": "item/original-ml-finite-class-bound/",
      "url": "https://mlprep.iwase.dev/item/original-ml-finite-class-bound/"
    },
    {
      "id": "original-py-alias-copy",
      "title": "Aliasing and shallow copy",
      "area": "programming",
      "area_title": "Programming",
      "topic": "python",
      "topic_title": "Python",
      "skills": [
        "lists-tuples",
        "mutability",
        "aliasing",
        "shallow-copy"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "original",
      "estimated_minutes": 7,
      "prerequisites": [
        "lists"
      ],
      "summary": "Original practice item.",
      "path": "item/original-py-alias-copy/",
      "url": "https://mlprep.iwase.dev/item/original-py-alias-copy/"
    },
    {
      "id": "pml-book1-ex5.1",
      "title": "Reject option in classifiers",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "classification",
      "topic_title": "Classification",
      "skills": [
        "decision-boundary"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 12,
      "prerequisites": [
        "conditional-probability",
        "expected-loss"
      ],
      "summary": "Derives a confidence-dependent classification and rejection rule from explicit costs and posterior class probabilities.",
      "path": "item/pml-book1-ex5.1/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex5.1/"
    },
    {
      "id": "pml-book1-ex11.2",
      "title": "Centering and ridge regression",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "regression",
      "topic_title": "Regression",
      "skills": [
        "linear-regression",
        "normal-equations",
        "regularization"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 15,
      "prerequisites": [
        "matrix-multiplication",
        "centering"
      ],
      "summary": "Connects centering, the ridge objective, the intercept, and normal equations in one derivation.",
      "path": "item/pml-book1-ex11.2/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex11.2/"
    },
    {
      "id": "pml-book1-ex4.5",
      "title": "BIC for a two-dimensional discrete distribution",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "theory",
      "topic_title": "Theory",
      "skills": [
        "generalization",
        "overfitting",
        "model-complexity"
      ],
      "priority": "core",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 20,
      "prerequisites": [
        "maximum-likelihood",
        "logarithms",
        "cross-validation"
      ],
      "summary": "Compares nested models using fit, leave-one-out behavior, parameter count, and a complexity penalty.",
      "path": "item/pml-book1-ex4.5/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex4.5/"
    },
    {
      "id": "pml-book1-ex20.3",
      "title": "Deriving the second principal component",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "dimensionality-reduction",
      "topic_title": "Dimensionality Reduction",
      "skills": [
        "pca-objective",
        "covariance-eigendecomposition"
      ],
      "priority": "core",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 18,
      "prerequisites": [
        "eigenvectors",
        "lagrange-multipliers",
        "matrix-calculus"
      ],
      "summary": "Connects the constrained PCA reconstruction objective to the covariance eigenvector with the second-largest eigenvalue.",
      "path": "item/pml-book1-ex20.3/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex20.3/"
    },
    {
      "id": "pml-book1-ex10.1",
      "title": "Gradient and Hessian of multinomial logistic regression",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "classification",
      "topic_title": "Classification",
      "skills": [
        "logistic-regression",
        "cross-entropy"
      ],
      "priority": "supplementary",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 20,
      "prerequisites": [
        "softmax",
        "chain-rule",
        "matrix-calculus"
      ],
      "summary": "Derives the first- and second-order structure of multiclass logistic loss.",
      "path": "item/pml-book1-ex10.1/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex10.1/"
    },
    {
      "id": "pml-book1-ex13.1",
      "title": "Backpropagation for a multilayer perceptron",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "neural-networks",
      "topic_title": "Neural Networks",
      "skills": [
        "forward-pass",
        "activations",
        "chain-rule",
        "backpropagation"
      ],
      "priority": "core",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 20,
      "prerequisites": [
        "softmax",
        "cross-entropy",
        "matrix-calculus",
        "relu"
      ],
      "summary": "Derives layer errors, parameter gradients, and the input gradient for a one-hidden-layer classifier.",
      "path": "item/pml-book1-ex13.1/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex13.1/"
    },
    {
      "id": "pml-book1-ex11.4",
      "title": "Reducing elastic net to lasso",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "optimization",
      "topic_title": "Optimization",
      "skills": [
        "objective-functions",
        "regularization"
      ],
      "priority": "supplementary",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 15,
      "prerequisites": [
        "l1-norm",
        "l2-norm",
        "linear-regression"
      ],
      "summary": "Transforms a mixed regularization objective into a standard lasso problem on augmented data.",
      "path": "item/pml-book1-ex11.4/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex11.4/"
    },
    {
      "id": "pml-book1-ex20.1",
      "title": "Expectation-maximization for factor analysis",
      "area": "machine-learning",
      "area_title": "Machine Learning",
      "topic": "unsupervised-learning",
      "topic_title": "Unsupervised Learning",
      "skills": [
        "expectation-maximization"
      ],
      "priority": "supplementary",
      "difficulty": "hard",
      "origin": "external",
      "estimated_minutes": 30,
      "prerequisites": [
        "multivariate-gaussian",
        "matrix-calculus",
        "latent-variables"
      ],
      "summary": "Derives E- and M-step updates for a latent Gaussian factor model.",
      "path": "item/pml-book1-ex20.1/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex20.1/"
    },
    {
      "id": "harvard-stat110-f2011-sp5-continuous-q1",
      "title": "Lognormal transformation by the CDF method",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "continuous-random-variables",
        "transformations"
      ],
      "priority": "supplementary",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 12,
      "prerequisites": [
        "normal-distribution",
        "chain-rule"
      ],
      "summary": "A compact test of transforming a continuous random variable using a CDF before differentiating for the density.",
      "path": "item/harvard-stat110-f2011-sp5-continuous-q1/",
      "url": "https://mlprep.iwase.dev/item/harvard-stat110-f2011-sp5-continuous-q1/"
    },
    {
      "id": "pml-book1-ex2.9",
      "title": "Bayes rule and diagnostic evidence",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "probability",
      "topic_title": "Probability",
      "skills": [
        "total-probability",
        "bayes-rule",
        "conditional-probability"
      ],
      "priority": "supplementary",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 12,
      "prerequisites": [
        "conditional-probability"
      ],
      "summary": "Connects Bayes rule to evidence interpretation and exposes the common confusion between a likelihood and a posterior.",
      "path": "item/pml-book1-ex2.9/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex2.9/"
    },
    {
      "id": "pml-book1-ex3.4",
      "title": "Linear transformations and quadratic expectations",
      "area": "mathematics",
      "area_title": "Mathematics",
      "topic": "statistics",
      "topic_title": "Statistics",
      "skills": [
        "covariance-correlation"
      ],
      "priority": "supplementary",
      "difficulty": "medium",
      "origin": "external",
      "estimated_minutes": 15,
      "prerequisites": [
        "expectation",
        "covariance",
        "matrix-multiplication"
      ],
      "summary": "Exercises the matrix identities behind transformed covariance and expected quadratic forms used throughout machine learning.",
      "path": "item/pml-book1-ex3.4/",
      "url": "https://mlprep.iwase.dev/item/pml-book1-ex3.4/"
    }
  ]
}