Eligibility: CTY-level or Advanced CTY-level math score required
Prerequisites: Successful completion of Linear Algebra and Introduction to Abstract Math or the equivalent
Course Format: Individually Paced
Course Length: Typically 6 months
Recommended School Credit: One full year of high school credit or one semester of college credit equal to or greater than an AP class
Course Code: ENT
Elementary Number Theory gives advanced students an introduction to the deep theory of the integers, with focus on the properties of prime numbers, and integer or rational solutions to equations. This course covers topics similar to the third year undergraduate, in-person Elementary Number Theory course at Johns Hopkins University. This course focuses on detailed exploration of topics as well as proof techniques. Historical background for various problems will be provided throughout the course. Prime numbers and elliptic curves are studied with applications to cryptography.
Each student is assigned to a CTY instructor to help them during their course. Students can contact their instructor via email with any questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well to prepare for the graded assessments, which include homework, chapter exams, and a cumulative midterm and final. Instructors use virtual classroom software allowing video, voice, text, screen sharing and whiteboard interaction.
For a detailed list of topics, click the List of Topics tab.
For enrollment starting on or after January 1, 2019, a proctor is required for this course if the student’s goal is to obtain a grade. Please review Proctor Requirements for more details.
A textbook purchase is required for this course:
A Friendly Introduction to Number Theory, 4th ed., by Joseph H. Silverman
This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.
This course uses an online classroom for individual or group discussions with the instructor. The classroom works on standard computers with the Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile app.