The Frontier of Knowledge: An Intro to Mathematical Research and Discovery

Course Description

This course is an overview of the process of mathematical research, from forming the hypothesis to computational tools and types of proofs. We will begin by giving some examples that allow you to think like a mathematician, and provide you with an introduction to the programming environments used frequently by scientists and mathematicians. Then we will use computational techniques, hands-on experiments, and intuition to answer questions in various fields of mathematics as one would do in an actual research environment.

This course includes an academic project that you will work on over the two weeks and present on the final day to your peers. You will work together to apply these skills to a research project related to current mathematical inquiry, giving you insight into the difficulties and rewards of conducting research. By providing this unique short-term collaborative research process for you to experience, we will give you a head start on understanding what is involved in good mathematical research and determining whether it is something you want to pursue further in your studies.

At the end of the course, you will be able to:
• Understand and describe current open problems in mathematics using appropriate scientific language
• Write, read, and edit basic code
• Write a paper in mathematics and create a scientific presentation
• Understand the opportunities and challenges of a career in research mathematics

The skills you acquire in this course will be useful not only in enriching your high school studies but in giving you a head start on figuring out if a career in research is right for you. Armed with a well-rounded idea of what mathematical research is like, you will be more prepared to assess research projects that interest you in the future.


There are no specific classwork prerequisites for this course, but an interest in logic puzzles, mathematical puzzles, or problem solving is a good place to start.


One Section Available to Choose From:

Online sections of Pre-College courses are offered in one of the following modalities: Asynchronous, Mostly asynchronous, or Blended. Please review full information regarding the experience here.

Dates: July 18, 2022 - July 29, 2022
Duration: 2 Weeks
Meeting Times: M-F 8:30A-11:20A and 2 afternoon class sessions per week
Status: Closed
Format: On-Campus
Instructor(s): Erik Bergland
Teressa Chambers
Course Number: 10350