Course Information

Random and Prime (COMP 4111 R)

Term: 2023-24 Academic Year Spring


Michael Siff
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Mon-Wed, 9:30 AM - 10:55 AM (1/24/2024 - 5/7/2024) Location: SLC SC 301


This course is a journey analogous to space exploration. Our infinite cosmos will be the set of natural numbers. Our exploratory rocket ships will be computer programs of our own design. The planets possibly bearing alien life forms are different classes of prime numbers. More literally, this course is a research-driven introduction to elementary number theory, its essential application to computer-network security, and its purported implications for the future of money (think of the buzzwords “crypto,” “blockchain,” and “bitcoin”). We will write a series of computer programs of increasing sophistication, whose aim will be to identify patterns among prime numbers. We will pose philosophical questions regarding the nature of modern mathematics and computer science; for instance, to what extent can a computer be used to prove theorems? We will investigate what it means to be random: Can true randomness be generated by an algorithmic process? We will see examples of how some problems that