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Description: The binomial transform is a transformation that takes a sequence as an input and gives another sequence as an output according to a certain rule. As an example, we have that the binomial transform of the famous Fibonacci sequence (0,1,1,2,3,5,8,...) is the negated Fibonacci sequence (0,-1,-1,-2,-3,-5,-8,...). We will explore binomial transforms of various sequences. We will make use of the On-Line Encyclopedia of Integer Sequences, which you can see at . In this specific project, we will continue the explorations we started in Fall 2020. However, participation in the Fall 2020 project or any previous knowledge of the binomial transform is NOT required or needed. We will start from the very beginning, define what the binomial transform is, and jump into investigating binomial transforms of various sequences we find interesting!

Team: (Participation restricted to Smith Hall FYAE students.) We are looking for a team of 4-6 students to meet on Zoom for 1 hour each week and the expectation is that the participants will have to devote another 2 hours of work weekly outside the Zoom meeting.

Qualifications: We are looking for motivated students who love doing Math and are ready to explore and research new topics!

Application: Write a one-paragraph statement as to why you would like to participate in the project. Mention any knowledge you may have of the binomial transform (but don't worry if you are unfamiliar with it - we will introduce it during our first meeting). Also write a paragraph about yourself such as your year at ¶¶ÒõÂÃÐÐÉä (freshman, sophomore, etc), planned major, previous math and programming classes you may have taken, and any other interesting piece of information about you! Please include the times during the week (Monday through Friday 8am-5pm) that you CANNOT meet for our hourly weekly meetings on Zoom. Send your application to ilia.mishev@colorado.edu with the subject title BINOMIAL_TRANSFORM_APPLICATION.

Deadline to submit application: January 22, 2021.

Course credit: You will receive 2 math course credits (independent study in MATH) for your successful participation during the semester.

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