Extensions

MoMath's online math program for grades 6–12

featuring Chaim Goodman-Strauss

Prerequisites | Registration and Policies

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Spring 2025

An Introduction to the Theory of Computation

May 18 through June 29
Sundays, 1:00 pm to 2:30 pm ET

(online)

Register

 

Spring minicourse: An Introduction to the Theory of Computation

Incredibly, mathematics can actually establish limits on mathematical knowledge. In this course, we’ll explore a few problems that we can prove are “undecidable” (i.e., problems for which there can be no general method to solve them)!

Even in recreational mathematics, such problems can appear.  We can ask whether or not a given polygon can be used to tessellate the plane, and, in many cases, we can determine the answer.  We can tell that a square does tessellate and that a pentagonal star does not.  The famous Hat tile can tessellate, but only aperiodically.  It remains open, though, whether there is a single general procedure to answer this question for all possible polygons in finite time.  It may be that this is impossible: It is known that there can never be any general procedure to determine whether or not a set of five or more shapes tessellates.

We will see how undecidability connects to the foundations of mathematical logic through the Theory of Computation, which addresses the nature of computation itself and what it can — and cannot — accomplish.

While this is much more a logic course than a computer course, in order to carry out some experiments, we will be playing with small Python scripts.  No previous coding knowledge required.

Online sessions will be held on Sundays, from 1:00 pm to 2:30 pm ET, on the following dates:

  • May 18
  • June 1
  • June 15
  • June 29

Materials needed:  Pencil, paper, access to online-python.com (or any Python coding environment), printed copy of course packet (to be sent in separate email).

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Prerequisites

Students who have participated in an accelerated or gifted program or have demonstrated strong math skills and knowledge are best suited for success in this program.  There is no admissions process for this program; students may register for the course if they would enjoy a math program that challenges mathematically-precocious students who seek a deeper study of mathematics that what is typically offered in the standard school curriculum.

Registration and Policies

Space is limited, and enrollment is on a first-come, first-served basis.  There are no refunds or credits for missed classes or withdrawals, or for any other reason.  The pace of the instruction is designed for an accelerated audience; please note that recordings of the program will not be available for review or purchase.  By registering, parents and students attest that the student meets the prerequisites for this series.

MoMath will make every effort to run classes as scheduled, however, occasionally severe inclement weather or other unusual circumstances beyond MoMath’s control may require that a class be cancelled.  If such a cancellation occurs, MoMath may, at its sole discretion, offer make-up sessions.

Note that the series will run only if a minimum number of participants register before the start date of the first session of the series.  In the rare event that the series is cancelled, registrants will be notified and provided with a full refund.

MoMath does not provide make-up classes for absences.  Each Extensions course accepts a limited enrollment in order to provide individualized attention to each student.  While many reasons may cause a student to miss a class, a registered student holds a reserved seat while others may be turned away due to limited capacity.  Additionally, the Museum provides staffing and other resources based on registration.  For these reasons, the Museum has a strict no-refund and no make-up policy.

All Extensions participants are expected to exhibit good behavior to ensure a positive experience for everyone.  At its sole discretion, MoMath may remove a student from the session or from the entire series for behavioral reasons.  If a student is removed for behavioral reasons, for either the day or the remainder of the program, no refund will be issued.