Analysis of algorithms and the major paradigms of algorithm design: recursion, divide-and-conquer, dynamic programming, greedy, and graph algorithms. Covers formal models of computation (finite automata, Turing machines) and the limits of computation — reductions, undecidability, and NP-completeness.

The logical organization of databases: entity-relationship modeling and the relational model. Functional dependencies and normalization, query-language design and optimization, security and integrity, concurrency control, and distributed databases.

Core data structures — lists, stacks, queues, and trees — implemented in an object-oriented language. Solving computational problems with searches over graphs and trees, plus elementary analysis of algorithms.

Fundamentals of computer architecture from the logic-gate level up: digital logic design, machine-level programming, performance models of modern architectures, and hardware primitives for parallelism and security.

Discrete mathematical structures used throughout computer science: sets, propositions, Boolean algebra, induction, recursion, relations, functions, and graphs.

Mathematical statistics built on probability: the calculus of probability, random variables, expectation, distribution functions, the central limit theorem, point estimation, confidence intervals, and hypothesis testing.

Linear algebra with hands-on computation and data-science applications: linear systems, matrix operations, vector spaces, linear transformations, eigenvalues and eigenvectors, orthogonality, linear regression, linear dynamical systems, and the singular value decomposition.

How humans built technologies to augment language — from writing and printing into the digital age. Explores automatic speech recognition, speech synthesis, and machine translation, the machine-learning theory behind them, and how they shape human-machine interaction.