Pre-College Instructor, Mathematics (On-Campus), Summer 2025

Company Description

Columbia University's Pre-College Programs offer high-achieving high school students the opportunity to engage in exploratory coursework at the college level, studying alongside peers from around the world. This highly selective program is open to students entering grades 9 and through the summer after their senior year.

Job Description

Columbia University’s Pre-College Programs for High School Students is seeking qualified candidates to develop and teach on-campus courses during Summer ’25. 

Reporting to the Senior Director of Instruction and Curriculum for Pre-College Programs, Pre-College Instructors develop and deliver immersive non-credit courses for high-achieving high school students. They guide and supervise students when classes are in session, and write a holistic evaluation of each course participant after classes conclude. For more information on the program–including course sessions and times–please see here.

Course Descriptions

A Bridge to Higher Mathematics
This course focuses on theoretical mathematics that is not typically part of a traditional high school curriculum. The course covers a variety of topics including: logic, set theory, number theory and combinatorics. An emphasis is placed on proof throughout the course and different techniques of proof, including mathematical induction, direct proof and proof by contradiction will be discussed. While some applications will be considered, this course will primarily focus on theoretical concepts.

This course is titled A Bridge to Higher Mathematics because it helps teach students the reasoning and proof-writing skills needed for higher-level university mathematics, and more generally, STEM courses. It gives students a path for learning the skills needed to succeed in higher-level mathematics.

Thinking and Problem Solving: Math in the Real World
In this course intended for students who enjoy mathematics and logical reasoning, participants explore innovative ways in which math is used in the real world, in fields such as economics, computer science, media, and the physical sciences. By engaging with challenging practical problems, students hone their independent thinking and problem-solving skills.

Areas covered include the following:

• Graph theory, a topic heavily developed by both mathematicians and computer scientists. We explore algorithmic ways to compute, for example, the optimal path between two points on a map (minimizing cost, time, or another parameter). Another application is minimizing the cost of an electrical network which has to provide power to all residents in a new neighborhood.
• Probability and its numerous applications. We look at how probabilities are applied in economics and in popular media, and examine how they can sometimes be counter-intuitive or even deceptive.
• Various counting methods, combinatorics, and examples of Nash equilibria. We study applications of these techniques in economics (the prisoner's dilemma), computer science (assessing the complexity of an algorithm), finance (loans and investments), and biology (population growth).

Students work individually and in groups to find creative solutions to given problems. Each student also works on a project of his or her own choosing, on a topic about which he or she is passionate.

Course Schedules
A Bridge to Higher Mathematics
Summer A: June 30th to July 18th - 11:10am-1:00pm & 3:10pm- 5:00pm EST (no class July 4th)
                              -OR-
Summer B: July 22nd to August 8th - 11:10am-1:00pm & 3:10pm- 5:00pm EST

Thinking and Problem Solving: Math in the Real World 
Summer A: June 30th to July 18th - 9:10am - 11:00am & 1:10 - 3:00pm (no class July 4th)
                               -OR-
Summer B: July 22nd to August 8th - 9:10am - 11:00am & 1:10 - 3:00pm

Please Note: Course(s) and course availability is subject to change. Dates and class times are tentative and subject to change.

Responsibilities

• Develop course content, syllabus, lesson plans, and assigned work, in accordance with Pre-College templates and regulations
• Lead and attend all class sessions, including escorting students to and from campus for field trips 
• Establish and maintain a dynamic in-class environment tailored for our high school population
• Evaluate student work and write a holistic evaluation of each participant after the course ends
• Monitor and address student concerns and inquiries (you will have aroun