Applications Open! Enroll for Summer 2027 at 2026 Tuition Pricing Until Sept 30
Model a real-world problem in this 3-week discrete mathematics program for middle school students on UCLA’s campus.
Course Description
How can mathematics help divide something fairly, explain an election result, or find the best route through a network? Students investigate these questions through discrete mathematics, a field built around countable structures, logical relationships, and problems with clear constraints.
The course moves through game theory, fair division, election theory, arithmetic and geometric sequences, and several branches of graph theory. Students draw trees, test planar graphs, color maps, trace Euler paths and circuits, and explore matching in bipartite graphs. Later work introduces generating functions and number theory. Exercises, group discussion, and short checks ask students to show how they reached an answer, not simply report one.
A capstone gives the sequence a practical purpose. Students select a real-world scenario, model the problem, propose possible solutions, identify factors that could affect the result, and present how discrete mathematics might support future solutions. Three checkpoints support research, application, revision, and reflection.
This three-week course is part of Summer Discovery’s Institute for the Gifted program on UCLA’s campus. The course is available to residential and commuter students. Beyond class, students connect active academic exploration with campus life, growing independence, new friendships, and a clearer sense of what students may want to explore next.
What Will You Do?
• Test strategies through game-theory problems and examples
• Compare methods for fair division and election decisions
• Analyze arithmetic and geometric sequences
• Draw trees, planar graphs, and bipartite graphs
• Solve map-coloring, Euler-path, and matching problems
• Model a real-world scenario and present a capstone solution
Learning Outcomes
By the end of the course, students will be able to:
• Apply discrete-mathematics methods to constrained problems and real-world scenarios
• Analyze graphs, sequences, voting methods, and strategic choices
• Model a problem, compare possible solutions, and present a reasoned recommendation
Students will leave with a completed capstone analysis, broader exposure to advanced mathematics, and a clearer sense of which mathematical questions they may want to explore next.
Why Discrete Mathematics Skills Matter
Discrete mathematics helps students reason about choices, patterns, networks, and systems that do not always fit a continuous formula. Game theory asks them to consider how one decision affects another. Graph theory turns connections into structures that can be drawn, tested, and improved.
That work strengthens logical explanation and persistence. Students must define the problem, select a method, show each step, and decide whether a solution makes sense. These habits support mathematics and computer science, while also helping with puzzles, strategic decisions, research projects, and any task that requires organizing complex relationships.
Who Should Attend?
This gifted course is for middle school students who have completed 6th, 7th, or 8th grade and enjoy mathematical puzzles, patterns, strategy, or explaining why a solution works. It fits students who want to move beyond routine calculation and explore how mathematics can model decisions, networks, maps, and real-world systems.
Participants should be ready to work through multi-step problems, compare approaches, discuss ideas with classmates, and revise a capstone across several checkpoints. Curiosity and persistence matter because some questions may allow more than one useful method.
Gifted course. See Admissions Criteria for eligibility requirements.
Why UCLA?
UCLA gives middle-school students an energetic place to learn, have fun, and experience campus life in Los Angeles. The setting brings together science, technology, creativity, entertainment, and culture, helping new subjects feel connected to a wider world of ideas.
The program combines hands-on academics with friendships, campus activities, clear routines, and support as students become comfortable in a large university environment. Students can try new challenges, share interests with peers, and build confidence through participation without needing to decide where those interests will lead. For families, UCLA offers a structured middle-school experience that balances substantive learning with fun, community, and age-appropriate independence. Students leave with new memories and a clearer sense of what they may want to explore next.
Summer Discovery Certificate of Completion
After successfully finishing this course, you will be awarded a certification completion for your accomplishment.
*This is a preview, not what you will receive
UCLA
UCLA
UCLA
UCLA