Join today, and become a member of a fun club united by a love of math. Whether listening to a presentation about the next big thing in math, participating in club math competitions, or enjoying pizza with your fellow math enthusiasts, meetings are a fun time with little extra commitment onto already busy schedules.
Next Meeting
Our next meeting will be after the break on December 2nd at room 114 in the McAllister building. A lecture will be given by Dr. Michael Steward. Details are below.
Speaker: Dr. Micheal Steward
Title: The Chicken McNugget Problem and Numerical Semigroups
Abstract: When Chicken McNuggets were first introduced, they were sold in packs of 6, 9, and 20 pieces. You could buy exactly 35 pieces by ordering one pack of each size, but you could not buy exactly 10 pieces by ordering full packs. What is the largest number of McNuggets that cannot be purchased?
The Chicken McNugget problem and the related Frobenius coin problem can be framed precisely by considering numerical semigroups. A numerical semigroup is an additive submonoid of the non-negative integers with finite complement. That is, it is a set of non-negative integers, containing zero, which is closed under addition and missing only finitely many of the non-negative integers. In this talk, we will discuss the solution to the Chicken McNugget problem and consider several further topics in numerical semigroup theory.
Problems of the Week
Easy Problems
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The product of three consecutive positive integers is 120. What are the three integers?
- Find a three-digit number such that its digits add up to 15, and it is divisible by both 5 and 9.
- Find all solutions to x^2 + y^2 = 2023.
Hard Problem
- In the triangle ABC, AB = 13, BC = 14, and CA = 15. Let O be the center of the circle inscribed in ABC. The incircle is tangent to AB at point D, to BC at point E, and to CA at point F. Find:
- the radius of the circle, r;
- the area of the triangle;
- the lengths of AD, BE, and CF.
- Prove that there are infinitely many primes of the form 4n + 3.