Thinking and Problem Solving: A New Look at Mathematics

I. June 27–July 15, 2022
II. July 19–August 5, 2022
Day & Time:
Monday–Friday, 9:10–11:00 a.m. and 1:10–3:00 p.m.
Joe Quinn
One year of algebra as well as a familiarity with how to perform mathematical proofs. Participants should be comfortable with math and logical reasoning.

“I have gained a greater understanding of mathematics and was exposed to challenging and interesting problems.”   — From a program course evaluation 

Course Description

In this curricular option, which is intended for students who enjoy math and logical reasoning, participants develop a deeper appreciation for the richness of mathematics while further developing their thinking and problem-solving skills. The combination of subjects and methods enables participants to experience math in a way high schools are often unable to present it, approaching problems as open-ended opportunities for creativity, independent thinking, and intellectual excitement.

The course is divided into three units:

  • Logic: An exploration of logic builds the groundwork for further mathematical reasoning. What is mathematical logic? How does one structure a proof? How can this framework be applied to philosophical thought? One topic covered is game theory (how mathematicians study decision-making), which has applications in fields such as economics, biology, and psychology.
  • Counting and Probability: Abstract counting, in the form of combinatorics, serves as an introduction to set theory, which in turn sets the stage for probability theory. As an application, the class delves into cryptography, looking at how math can be used to create and read secret messages.
  • Advanced Topics: In the final week, building on what we have done already and depending one students’ interests, we look at a few advanced topics. Potential topics include planetary orbits, symmetry, topology, common statistical fallacies, and Markov chains.

After exploring these various applications of mathematics, participants select and complete a group project based upon their own interests within the field. The course concludes with group presentations on those projects. As collaboration and communication are essential in modern science, the presentations offer a valuable opportunity to practice and receive feedback.

Registration Guidance & Call Number(s)

Please note, this course may have multiple classes being offered in a particular session. Students should only register for one class and with one call number.

To view detailed information on a particular offering, click on the call number to be directed to the Directory of Classes catalogue.

Session 1 Classes

INMM0260 | Call Number: 10749

Session 2 Classes

INMM0260 | Call Number: 10750

Further guidance on the registration process can be found here.


Joe Quinn

Joe Quinn holds a PhD in mathematics from The Graduate Center, CUNY, and publishes in the field of geometric topology. He has taught and designed math curricula for Hunter College, Johns Hopkins Center for Talented Youth, Bronx Community College, Matemorfosis CIMAT (Guanajuato), MoMath, and Bridge to Enter Advanced Mathematics. He is the director of Hypothesis, a New York City based company that creates games and events based on conceptual math and art. Joe is passionate about transmitting knowledge between the math research community and the rest of the world, for the benefit of both parties.

Back to the Course Guide

Specific course detail such as hours and instructors are subject to change at the discretion of the University. Not all instructors listed for a course teach all sections of that course.