College of Liberal Arts & Sciences

# Graduate & Undergraduate Student Seminar (GAUSS)

**Abstract: **In math, people study equations as relations between independent and dependent variables. It is an interesting and often difficult problem to interchange the roles of these variables. In this talk, we will introduce the Mobius Inversion, a way of inverting formulas using Partial Ordered Sets. Our goal will be to apply this method to give a combinatorial proof of a formula in number theory relating the Euler number and the Mobius Function (two important functions in this field). The talk is self-contained and aimed towards undergraduate students seeking a good math time. There will be graphs, cool number theory results, some abstract algebra arguments (maybe), and fun discussion about the importance of this technique in "modern math".