About the Course

Introduction to Real Analysis

Begin exploring the theoretical foundations underlying the concepts taught in a typical single-variable Calculus course: 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 an integral part of this course as we use interactive online resources, graded homework, and cumulative exams to reinforce learning material. You’ll be assigned a CTY instructor to guide you through the course and provide one-on-one review sessions ahead of tests.

Recommended length of enrollment: 6 months

Time Commitment: 5-7 hours of independent work per week.

Course Overview

Apply any time and get started in 2 weeks

Classes

Students enroll in a course by selecting an open class below. Students progress at their own pace following course guidelines, with guidance from instructors who strive to meet individual needs. While the course provides students with independence and flexibility, students must manage their time to complete the course before the end date.

Note: You need an active CTY Account to complete registration through MyCTY.

Up to 9 months of access
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$1399 - $1455
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Testing and Prerequisites

  Math Verbal
Required Level CTY-Level Not required
Check your eligibility using existing test scores If you do not have existing test scores:

Students must achieve qualifying scores on an advanced assessment to be eligible for CTY programs. If you don’t have qualifying scores, you have several different testing options. We’ll help you find the right option for your situation.

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Course Prerequisites

Introduction to Real Analysis requires:

1 prerequisite

Successful completion of Introduction to Abstract Math or equivalent

Cost and Financial Aid

  • Tuition
    • Varies
  • Application fee
    • Nonrefundable Application Fee - $15 (Waived for financial aid applicants)
    • Nonrefundable International Fee - $20 (outside US only)
Financial Aid

CTY Financial Aid Availability for Online Programs:

Academic Year 2023-24 (Course start dates July 1, 2023- June 30, 2024): We have concluded our financial aid application review process for Academic Year 2023-2024 Online Programs.

Academic Year 2024-25 (Course start dates July 1, 2024- June 30, 2025): Financial Aid funding is currently available for all eligible students while funding lasts. If interested in applying for financial aid, please select a course with start date of July 1, 2024 or later.

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Course Materials

Please acquire all course materials by the course start date, unless noted as perishable. Items marked as “perishable” should not be acquired until the student needs them in the course. If you have questions about these materials or difficulty locating them, please contact [email protected].
 

Book Title: An Introduction to Analysis, 2nd edition
Author: Bilodeau, Thie, Keough
ISBN: 978-0-7637-7492-9

  • A proctor

Earning School Credit

Recommended school credit: One academic year

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Technical Requirements

This course requires a computer with high-speed Internet access and an up-to-date web browser such as Chrome or Firefox. You must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

This course uses a virtual classroom for instructor-student communication. The classroom works on standard computers with the Zoom desktop client, and on tablets or handhelds that support the Zoom Mobile app. Recorded meetings can only be viewed on a computer with the Zoom desktop client installed. The Zoom desktop client and Zoom Mobile App are both free to download.

Terms & Conditions

Students may interact in online classrooms and meetings that include peers, instructors, and occasional special guests.

About Mathematics at CTY

Our online Mathematics courses—spanning elementary through college-level curricula—cover a wide range of topics, from algebra and geometry to chess, cryptology, and AP Calculus and are guided by expert instructors. You’ll join group sessions with classmates to ensure you stay on track with challenging course content. Whether you’re looking for pure math fun and enrichment, to move up the math ladder and advance your honors and AP (and beyond) academic standing, or to train for mathematics competitions, there’s a CTY course that’s right for you.

New math enrichment courses available!

Explore our new math enrichment courses, including Excursions in Pre-algebra and Introduction to Logic and Proofs.

Join the exciting world of competitive math

Participate in the High School Math Club or enroll in 6 IP courses: Middle School Competitive Math I, Middle School Competitive Math II, Middle School Competitive Math III, Competitive Mathematics Prep, Competitive Mathematics I, Competitive Mathematics II.

Meet our Mathematics Instructors