Number Theory

Discover the Math Running Digital Security: Once considered the most abstract and least practical area of mathematics, number theory is now essential to our everyday digital world: every second, millions of secure internet transmissions rely on number theory for encryption. In this course, you’ll explore the world of mathematical reasoning and proof, learning the tools needed to understand the RSA algorithm—the backbone of global internet security. You’ll also invent your own encryption schemes and encounter games that use number theory. Alongside practical applications, you’ll get a taste of the rich history of this subject, from legendary mathematicians to the proof of Fermat’s Last Theorem (a famous problem solved just 20 years ago after 350 years of effort).

Why Take This Course? You’ll gain a solid foundation for upper-level university mathematics or theoretical computer science while understanding how number theory is applied in real-world encryption. This course makes mathematical reasoning and proof accessible and engaging, blending elegant concepts with practical uses. Ideal for students fascinated by math, cryptography, or computer science, you’ll discover how timeless mathematical ideas power our modern, connected world.

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. Some courses require additional materials which can be found here.

NCAA-approved course

UC-approved course

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