ML Prep

Mathematics Screening

Answer each question independently. Difficulty varies, and you can complete the list over several sittings.

Review results

Linear Algebra

Move between algebraic, geometric, and spectral views of matrices.

  1. Matrix arithmetic and invariantsEasy · 4 min · 5 skills
  2. One reduction, four structural conclusionsEasy · 5 min · 5 skills
  3. Detect dependence and use a basisEasy · 3 min · 3 skills
  4. Projection and orthogonal residualMedium · 3 min · 2 skills
  5. Thin QR and a least-squares fitMedium · 5 min · 2 skills
  6. Diagonalize a symmetric matrixMedium · 5 min · 4 skills
  7. Certify a quadratic formHard · 5 min · 2 skills
  8. SVD, best rank one, and PCA energyHard · 5 min · 3 skills

Calculus

Differentiate, approximate, and optimize scalar and vector-valued functions.

  1. Limit, continuity, derivative, and integralEasy · 3 min · 4 skills
  2. Gradient and a normalized directionEasy · 3 min · 3 skills
  3. Vector chain ruleMedium · 4 min · 2 skills
  4. A two-variable quadratic approximationMedium · 5 min · 2 skills
  5. Classify all stationary pointsHard · 6 min · 3 skills
  6. Minimum under an equality constraintMedium · 4 min · 1 skills
  7. Implicit tangent slopeMedium · 3 min · 1 skills
  8. Matrix derivative with a numeric checkHard · 5 min · 1 skills

Probability

Reason from events and conditioning through multivariate random variables and limit theorems.

  1. Count a union of selection eventsEasy · 3 min · 3 skills
  2. Bayes rule with a base rateMedium · 4 min · 4 skills
  3. A small discrete distributionEasy · 3 min · 5 skills
  4. Transform an exponential variableMedium · 4 min · 5 skills
  5. Read dependence from a joint tableHard · 6 min · 5 skills
  6. Condition first, then remove conditioningMedium · 4 min · 3 skills
  7. Approximate a binomial central rangeMedium · 4 min · 2 skills
  8. State the LLN operationallyEasy · 2 min · 1 skills
  9. Linear image of a multivariate GaussianHard · 5 min · 3 skills

Statistics

Derive estimators and interpret uncertainty, tests, and simple models.

  1. Sampling distribution and standard errorEasy · 3 min · 4 skills
  2. Bias, variance, MSE, and consistencyMedium · 6 min · 4 skills
  3. Build and maximize a likelihoodMedium · 4 min · 2 skills
  4. Conjugate update and MAPMedium · 4 min · 2 skills
  5. Method of moments for an endpointEasy · 2 min · 1 skills
  6. Confidence interval with known varianceMedium · 3 min · 1 skills
  7. Hypotheses, critical region, and p-valueMedium · 4 min · 3 skills
  8. Type II error and power at an alternativeHard · 5 min · 3 skills
  9. Chi-square goodness of fitHard · 5 min · 2 skills
  10. Fit a simple regression lineMedium · 5 min · 1 skills