Collatz Conjecture Plot

Supervisor: Mike Noyes


Description:  Take any positive integer.  If it is even, divide it by 2.  If it is odd, multiply it by 3 and add 1.  This produces a new positive integer.  Repeat this process, producing a sequence of positive integers.  Does this sequence eventually reach the number 1?  The Collatz Conjecture, which is also known as the 3n+1 Problem, states that the sequence produced by every positive integer eventually reaches the number 1.  This has been an open question since at least 1937, when it was first formally stated.  We will look at the numerical evidence supporting the conjecture and investigate some of the fascinating properties connected to it.  We will use a variety of technological tools to help our exploration, including Microsoft Excel and other software packages/programming languages, and the Online Encyclopedia of Integer Sequences ( website.

Students: A team of (around) 4 students.

Timeline:  We will meet for 1 hour each week during the Spring 2021 semester.  Students will also be expected to work an addition 3 hours a week outside of class.


Prerequisites:  Successful completion of MATH 2001 is required.  Experience with programming is encouraged, though not required.


Application Details:  The deadline for this application is Monday January 11th for Spring 2021.  To apply, send an email to Mike Noyes at  Please include the phrase "EML Application" in the subject line of the email.  In the email itself, make sure to include the following:


  • All Math/Stats/CS classes that you have taken at CU and the grade received (if it's easier to attach your transcript, that's fine).

  • Any programming or computer skills that you have (this is not required but is helpful to know).

  • Your scheduling availability for the Spring 2021 semester (please include your course schedule and also any other major time commitments that you will have, such as on-campus jobs, off-campus jobs, etc).

  • A brief statement about why you are interested in working on this project.

  • Any other relevant information that you'd like to share with me.


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