Expert-level database systems theory covering relational model, query processing and optimization, transaction management, concurrency control, recovery, and NoSQL systems.
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Relations: tables with rows and columns, schema defines types. Keys: superkey, candidate key, primary key, foreign key. Relational algebra: select, project, join, union, difference, rename. Normalization: 1NF, 2NF, 3NF, BCNF — eliminate redundancy and anomalies. Functional dependencies: X -> Y means X determines Y.
Query parsing: SQL to parse tree to logical plan. Query optimization: logical to physical plan, cost-based optimizer. Join algorithms: nested loop, hash join, sort-merge join. Index types: B-tree (range queries), hash index (equality), bitmap (low cardinality). Query plan: EXPLAIN output, seek vs scan, index usage.
ACID: atomicity, consistency, isolation, durability. Isolation levels: read uncommitted, read committed, repeatable read, serializable. Anomalies: dirty read, non-repeatable read, phantom read. MVCC: multi-version concurrency control — readers do not block writers.
Two-phase locking: growing phase acquires locks, shrinking releases. Deadlock: detection via waits-for graph, prevention via ordering. Optimistic concurrency: read, validate, write — no locks during read. Timestamp ordering: each transaction gets timestamp, conflicts resolved by order.
Write-ahead logging: log record before data page — guarantee durability. ARIES algorithm: analysis, redo, undo phases after crash. Checkpoints: reduce recovery time by limiting log replay. Shadow paging: copy-on-write alternative to logging.
| Pitfall | Fix |
|---|---|
| N+1 query problem | Use joins or eager loading |
| Missing index on join column | Always index foreign keys |
| Using serializable isolation unnecessarily | Profile and choose appropriate level |
| Not handling transaction rollback | Always handle errors and rollback explicitly |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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