Mathematical Foundations of Computing

Course Description

What are the theoretical limits of computing power? What problems can be solved with computers? Which ones cannot? And how can we reason about the answers to these questions with mathematical certainty? This course explores the answers to these questions and serves as an introduction to discrete mathematics, computability theory, and complexity theory. At the completion of the course, students will feel comfortable writing mathematical proofs, reasoning about discrete structures, reading and writing statements in first-order logic, and working with mathematical models of computing devices. Throughout the course, students will gain exposure to some of the most exciting mathematical and philosophical ideas of the late nineteenth and twentieth centuries. Specific topics covered include formal mathematical proofwriting, propositional and first-order logic, set theory, binary relations, functions (injections, surjections, and bijections), cardinality, basic graph theory, the pigeonhole principle, mathematical induction, finite automata, regular expressions, the Myhill-Nerode theorem, context-free grammars, Turing machines, decidable and recognizable languages, self-reference and undecidability, verifiers, and the P versus NP question. Students with significant proofwriting experience are encouraged to instead take CS154. Students interested in extra practice and support with the course are encouraged to concurrently enroll in CS103A.

Course Details

  • Intensive Study: Computer Science
  • Enrollment requirements: This is a 5 unit course. Only matriculated Stanford graduate students are allowed to enroll in it for 3, 4 or 5 units but must still do the standard 5 units of coursework. Visiting students must enroll in 5 units. 
  • Online Format: Both Synchronous & Asynchronous - This course is taught through a combination of synchronous and asynchronous opportunities. Students should check the Stanford Explore Courses website for information on the scheduling options.


CS 106B or equivalent. CS 106B may be taken concurrently with CS 103.

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