Course Catalog

Number Theory

  • Semester 1 2024-2025

    Aug 28, 2024-Dec 13, 2024 For Members Register

Course Overview

Once thought of as the purest but least applicable part of mathematics, number theory is now by far the most commonly applied: every one of the millions of secure internet transmissions occurring each second is encrypted using ideas from number theory.

This course covers the fundamentals of this classical, elegant, yet supremely relevant subject. It provides a foundation for further study of number theory, but even more, it develops the skills of mathematical reasoning and proof in a concrete and intuitive way and is necessary preparation for any future course in upper-level college mathematics or theoretical computer science.

Students progressively develop the tools needed to understand the RSA algorithm, the most common encryption scheme used worldwide. Along the way, they invent some encryption schemes of their own and discover how to play games using number theory. Students also get a taste of the history of the subject, which involves the most famous mathematicians from antiquity to the present day, and see parts of the story of Fermat’s Last Theorem, a 350-year-old statement that was fully proven only 20 years ago.

While most calculations are simple enough to do by hand, students sometimes use the computer to see how the fundamental ideas can be applied to the huge numbers needed for modern applications.

Prerequisite: A strong background in Precalculus and above as well as a desire to do rigorous mathematics and proofs

Students in GOA courses will need reliable access to a computer with webcam/microphone connections, an email address (preferably school-based), a Web-conferencing app (GOA courses use Zoom), and a Word processing app (GOA courses use Google’s G Suite). When necessary, alternative arrangements may be made.

NCAA-approved course

UC-approved course

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