Part IX: The graduate core
Specifications, semantics, algorithms with certificates, measurement, architecture, and machine learning you can derive and defend.
- GDGraduate-readiness diagnostic and repair map12 exercisesDo not treat advanced placement as a judgment about all your abilities. Attempt short unaided solutions; mark a topic not yet studied instead of guessing. This diagnostic locates a prerequisite, not a numerical “mastery…
- G01Specifications, invariants, and finite-state checking6 exercisesWrite a contract, prove a loop’s partial correctness and termination separately, and explain exactly what an exhaustive finite model establishes.
- G02Language semantics, scope, and type safety6 exercisesDefine the evaluation and typing rules of a small language, trace lexical scope, and explain progress/preservation without mistaking type safety for all-purpose correctness.
- G03Algorithm design, certificates, and honest complexity6 exercisesDerive a dynamic program, justify a residual-flow algorithm with a cut certificate, and separate mathematical operation counts from implementation costs.
- G04Probability, information, and credible measurement6 exercisesCondition on the correct event, distinguish uncertainty sources, compute a proportion interval, and design a paired experiment whose sampling unit matches its claim.
- G05Numerical linear algebra and optimization6 exercisesSolve a least-squares problem with an orthogonal transformation, distinguish conditioning from stability, and choose a justified step size for a quadratic objective.
- G06Scalable architecture and measured performance6 exercisesBuild a cost model, improve memory reuse without changing the specification, and defend a measured result with workload and correctness evidence.
- G07Network design, routing, and queueing6 exercisesTrace an address through a route table, budget transmission and queueing delay, and distinguish an offline model from a deployed secure network.
- G08Cloud systems, partial failure, and consistency6 exercisesSpecify a failure model, reason about incomplete requests and quorum intersections, and explain why availability mechanisms do not automatically provide linearizability.
- G09Systems analysis, contracts, and architecture decisions6 exercisesTurn a vague request into observable requirements, isolate invariants at interfaces, and defend an architecture with failure cases and alternatives.
- G10Project reasoning, dependency graphs, and risk6 exercisesCompute a critical path under explicit assumptions, distinguish uncertainty from a precise schedule, and plan reviewable milestones with acceptance evidence.
- G11Ethics, security boundaries, and accountable decisions6 exercisesMap a technical decision to affected people, calculate error rates with correct denominators, and propose safeguards whose effectiveness can be tested without claiming a metric certifies fairness.
- G12Machine learning objectives, generalization, and decisions6 exercisesDerive logistic loss and its gradient, separate fitting from evaluation, and implement a stable learner whose success is measured on an appropriate held-out unit.
- G13Neural computation and backpropagation you can derive6 exercisesTrace a network forward and backward, implement analytic gradients, challenge them with finite differences, and distinguish optimization failure from evaluation failure.
- G14Attention, embeddings, and transformer reasoning6 exercisesCompute and differentiate a small attention operation, enforce causal masking, account for memory costs, and distinguish a forward attention lab from a trained language model.
- G15Data engineering, clustering, and defensible inference6 exercisesSpecify data grain and availability, prevent group and preprocessing leakage, derive a clustering update, and distinguish association from causal evidence.
- G16Research literacy, reproducibility, and independent engineering evidence6 exercisesTurn a technical claim into a testable question, design a reproducible comparison, evaluate the limits of evidence, and communicate your own contribution honestly.
- GP1A typed compiler with a bytecode verifier1 exerciseBuild an end-to-end language tool that you can explain without relying on a large compiler framework. Prerequisites are G01–G03, the foundation’s C15–C16, and independent comfort with recursive tree traversal. The work…
- GP2A reproducible model with retry-safe local delivery1 exerciseIntegrate data contracts, ML evaluation, immutable artifacts, and failure handling. Prerequisites are G04–G05, G08–G09, G11–G12, and G15. This is not an online game service, a production message broker, a financial transaction…
- GACumulative reasoning and systems assessment6 exercisesPrerequisites: G01–G10. Reserve these questions until you can work without opening the earlier solutions. Use roughly 60–90 minutes or split into two sessions. Do not use timing as a gate when a documented accessibility or…
- GBCumulative learning, data, and research assessment6 exercisesPrerequisites: G11–G16 and the relevant project chapters. These are fresh synthesis tasks, not another count of earlier questions. A passing response should include assumptions and verification, not just arithmetic. Optional…
- W08Defending an independent engineering result5 exercisesCombine specification, mathematical reasoning, implementation, tests, and measurement in one defensible report; diagnose changed assumptions instead of relying on familiar patterns.
- From study outcomes to engineering evidenceThis book is a learning system, not an employment credential or a guarantee of mastery. A reviewer can evaluate a reproducible project, a correct proof, a clear design tradeoff, or a well-diagnosed failure. They cannot infer…
- chapter
- workshop: connects two subjects
- checkpoint, review or assessment