Databases

The mathematical contract behind relational databases: relations as sets of typed tuples, integrity constraints as invariants, and a closed algebra that turns queries into expressions the optimizer can safely transform.

A derivation-first guide to functional and multivalued dependencies, attribute closure, candidate keys, minimal covers, 3NF/BCNF/4NF, and decompositions that are lossless and—when possible—dependency-preserving.

How PostgreSQL transaction boundaries, constraints, WAL, atomic DML, retries, idempotency, outbox delivery, and two-phase commit combine—and where ACID stops.

PostgreSQL tuple-version visibility, statement and transaction snapshots, concurrency anomalies, Read Committed, Repeatable Read, Serializable Snapshot Isolation, and whole-transaction retries.

PostgreSQL table, row, predicate, and advisory locks; precise SELECT FOR UPDATE semantics; NOWAIT and SKIP LOCKED; deadlock prevention, retries, timeouts, and production diagnosis.

How Bigtable-style systems combine sparse sorted rows, column families, timestamped versions, range tablets, logs, memtables, SSTables, compaction, garbage collection, and replication—and why row-key design is the query plan.