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: IRA
Introduction to Real Analysis gives advanced students the theoretical foundations underlying the topics taught in a typical Calculus AB and BC course. Introduction to Real Analysis will cover algebraic and order properties of the real numbers, the least upper bound axiom, limits, continuity, differentiation, the Riemann integral, sequences, and series. Definitions and proofs will be stressed throughout the course. Online course materials supplement the required textbook.
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.
See the List of Topics tab for the complete listing of topics covered.
A textbook purchase is required for this course:
An Introduction to Analysis, 2nd Ed, by Bilodeau, Thie, Keough
Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:
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.