Introduction to Complex Analysis
- Grade 10+
This course will introduce you to the theory of functions of a complex variable—a core area of mathematics. We will also cover complex numbers and their properties, analytic functions and the Cauchy-Riemann equations, the logarithm and other elementary functions of a complex variable, integration of complex functions, the Cauchy integral theorem, the residue theorem, and applications to definite integrals. Definitions and proofs are used throughout the course to establish fundamental results in complex analysis. A CTY instructor will be available for learning support and one-on-one review sessions ahead of your graded assessments and exams.
Recommended length of enrollment: 6 months
Time Commitment: 5-7 hours of independent work per week.
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.
Testing and Prerequisites
|Required Level||CTY-Level||Not required|
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.Sign up for Testing Learn More
Course PrerequisitesIntroduction to Complex Analysis requires:
Cost and Financial Aid
- Nonrefundable Application Fee - $15 (Waived for financial aid applicants)
- Nonrefundable International Fee - $20 (outside US only)
We have concluded our financial aid application review process for Academic Year 2023-2024 Online Programs (Courses with start dates July 1, 2023-June 30, 2024). Our application for Academic Year 2024-2025 Online Programs is expected to open in January. We encourage those who may need assistance in the future to apply for aid as early as possible.
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: Complex Analysis: A First Course with Applications, 3rd edition
Author: Dennis G. Zill and Patrick D. Shanahan
You will need a parent or other adult to proctor exams.
Earning School Credit
Recommended school credit: One academic yearLearn More
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.
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.
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.