UMass Boston

Math Club

This Spring 2023, the Math Club will meet on Wednesdays from 1-2pm in the Conference room of the Math Department (W-03-154-28). Activities will include problem-solving sessions (with problems in math, probability, statistics and programming), presentations by students on math-related topics, interviews of faculty members about their research, Q&A with professionals from actuarial science, data science, finance, and more. Come join the fun and grab a slice of pizza!

Please contact Prof. David Degras for more information.

Recent Math Club Activities and Resources

Here are math challenges for this week - courtesy of the Riddler at fivethirtyeight.com:

  1. The Fibonacci sequence begins with the numbers 1 and 1,2 with each new term in the sequence equal to the sum of the preceding two. The first few numbers of the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. One can also make variations of the Fibonacci sequence by starting with a different pair of numbers. For example, the sequence that starts with 1 and 3 is 1, 3, 4, 7, 11, 18, 29, 47, 76 and so on. Generalizing further, a “tribonacci” sequence starts with three whole numbers, with each new term equal to the sum of the preceding three. Many tribonacci sequences include the number 2023. For example, if you start with 23, 1000 and 1000, then the very next term will be 2023. Your challenge is to find starting whole numbers a, b and c so that 2023 is somewhere in their tribonacci sequence, a ≤ b ≤ c, and the sum a + b + c is as small as possible.
     
  2. Every Christmas, Gary’s family has a gift exchange. There are 20 people in the gift exchange. In the first round, everyone writes down the name of a random person (other than themselves) and the names go in a hat. Then if two people randomly pick each other’s names out of that hat, they will exchange gifts, and they no longer participate in the drawing. The remaining family members go on to round two. Again, they write down the name of anyone left, and again, any two people who pick each other exchange gifts. This continues until everyone is paired up. And yes, if exactly two people remain, they still go through the process of selecting each other, even though they know who their partner will be. On average, what is the expected number of rounds until everyone is paired up?

Tools & Resources