Combinatorics and Graph Theory
- Grades 7-11
- Advanced CTY-Level
If you’ve ever wanted to know how to turn tedious counting problems into simple solutions—like how to figure out the total number of games played in the March Madness tournament without needing to count every matchup on your bracket, one by one—this course is for you. It explores enumerative combinatorics and the different techniques for working through mathematical proofs using binomial coefficients, permutations, and partitions. You’ll investigate graph theory and its applications in fields like navigation, computer science, and counterterrorism. One famous graph-theory question posed in the early 1800s—Can you color any map using just four colors so that no two adjacent areas share the same color?—took more than 100 years for mathematicians to answer. You’ll analyze problems like these while learning concepts like cycles, planarity, algorithms, and graph colorings that are used to solve them. Along the way, you’ll encounter fun and challenging problems that can be solved with creativity and determination—even without a background in college-level math.
Note: Students who have taken CTY's Discrete Math course should not take this course.
Typical Class Size: 16
Testing and Prerequisites
|Required Level||Advanced 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 PrerequisitesCombinatorics and Graph Theory requires:
Cost and Financial Aid
- Nonrefundable Application Fee - $50 (Waived for financial aid applicants)
- Nonrefundable International Fee - $250 (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.
About Mathematics at CTY
Explore the study of shapes
Geometry courses allow students to describe the world around them in basic and profound ways. Our younger students learn about shape, scale, and proportion in Geometry and Spatial Sense. Middle School students explore beautiful applications of lines, angles, non-Euclidean geometry, and more in Geometry through Art. And advanced students explore the underlying mathematics and fundamental characteristics of shapes, distance, and continuous deformations in our proof-based Topology course.
Dive deep into logic and reasoning
Our courses in formal logic give you the tools to question the world around you. Younger students are introduced to different types of reasoning, as well as the strengths and weaknesses inherent in various forms of critical analysis in Inductive and Deductive Reasoning. Older students explore how logical reasoning can explain (or fail to explain) counter-intuitive results in Paradoxes and Infinities, or take a more rigorous approach to formal logic in Mathematical Logic.