The University of Chicago Summer
Proof-based Discrete Mathematics

Proof-based Discrete Mathematics


Course Status: Pre-College Application: Jan 2026

Applications for Pre-College courses will open in early January. We encourage you to review the courses offered below. Remember: you can select up to 3 in your application. We look forward to seeing you!

Course Description

This course will introduce you to higher-level mathematical argumentation and proof, an understanding of which is crucial to making the transition from high school to undergraduate math coursework.

What we take as given early on in the study of mathematics actually has reasoning behind it, and this course will show you how to begin to uncover and articulate that reasoning for yourself.

To do so, we will focus on the seemingly simple question, “How do we count?” Answering this question will require thinking in terms of sets rather than numbers, so we will begin with naïve (as opposed to axiomatic) set theory and basic set operations, then see how these operations correspond to counting problems including infinite sets. We will also consider topics such as paradoxes of infinity, countability and uncountability, and advanced theories about counting.

On a daily basis, you will attend lectures, work in small groups, and present your mathematical arguments and findings in a mutually supportive, inclusive, and welcoming space.

Course Criteria

Prerequisites: Algebra 1, Algebra 2 and Geometry.

Math Intensive
Students should expect daily class and homework activities to involve coding.

Academic Interest

Computer Science, Data Science, Math, and Statistics, Physical Sciences (e.g., astronomy, physics)

Application Materials

A complete application includes a transcript, two short essays, a letter of recommendation, writing sample, application fee, and a submitted parent confirmation. If you are seeking need-based financial aid, you must indicate that in your application before it is submitted. Please refer to the Application Instructions for complete details.

Instructor(s)

Matthew Gelvin

Cost

$9,300

Need-based financial aid is available. Students should refer the Costs & Aid page and apply for aid when they submit their application to Summer Session.

Course Duration

3 Week Immersion

Session

Session 1

Arrival & Departure Dates

June 13th - July 3rd

Course Dates

June 15th - July 2nd

Class Days

Mon, Tue, Wed, Thu, Fri

Class Time

9:00 am - 3:00 pm

Eligibility

9th Grade, 10th Grade, 11th Grade

Course Code

MATH 10301 30

Modality

Residential

Syllabus

Preview Sample Syllabus

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