Eligibility: CTY-level or Advanced CTY-level math score required
Prerequisites: Successful completion of 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 equal to or greater than an AP class or one semester of college credit
Course Code: IRA
Introduction to Real Analysis provides advanced students with the theoretical foundations underlying the topics taught in a typical single variable Calculus 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 virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile app. Students who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.