About the Course

Introduction to Complex Analysis

  • All Grades
  • CTY-Level
  • Individually Paced

Begin your introduction to the theory of functions of a complex variable—a fundamental area of mathematics. You’ll 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 will be essential throughout the course as applications to physics and engineering and interactive online resources guide you through the material.

A CTY instructor will be on-hand for learning support and one-on-one review sessions ahead of your graded assessments and exams.

The recommended length of enrollment for this course is 6 months.

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

Students may enroll in this course at any time during the year.


Enrollment and tuition are time-based—students may enroll in a course by selecting an open class below. Students will progress at their own pace, with guidance from instructors who strive to meet individual needs. Note: You will need to have an active CTY Account to complete registration through MyCTY.
Synchronous class meetings typically last about an hour.

3 Months

3 months
Choose your start date

6 Months

6 months
Choose your start date

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 Complex Analysis requires:

1 prerequisite

Successful completion of Multivariable Calculus and Introduction to Abstract Math or the 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 is available

We are committed to serving all talented youth regardless of financial circumstances. Financial assistance is available based on need.

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Course Materials

Please acquire all course materials by the course start date. If you have questions about these materials or difficulty locating them, please contact ctyinfo@jhu.edu.

Book Title: Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3rd edition
Author: Edward B. Saff and A.D. Snider
ISBN-13: 978-0139078743
ISBN-10: 0139078746

  • A proctor

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, Mathematical Modeling, and Introduction to Logic and Proofs.

Meet our Mathematics Instructors